PATENT ABSTRACT
There is disclosed a method and system of physically solving the charge, mass, and current density functions of amino acids and peptide bonds with charged functional groups for proteins of any size and complexity by addition of the units, bases, 2-deoxyribose, ribose, phosphate backbone with charged functional groups for DNA of any size and complexity by addition of the units, organic ions, halobenzenes, phosphines, phosphates, phosphine oxides, phosphates, organogermanium and digermanium, organolead, organoarsenic, organoantimony, organobismuth, or any portion of these species using Maxwell&#39;s equations and computing and rendering the physical nature of the chemical bond using the solutions. The results can be displayed on visual or graphical media. The display can be static or dynamic such that electron motion and specie&#39;s vibrational, rotational, and translational motion can be displayed in an embodiment. The displayed information is useful to anticipate reactivity and physical properties. The insight into the nature of the chemical bond of at least one species can permit the solution and display of those of other species to provide utility to anticipate their reactivity and physical properties.

PATENT DESCRIPTION
[0001]    This application claims priority to U.S. Application Nos.: 61/018,595, filed 2 Jan. 2008; 61/027,977, filed 12 Feb. 2008; 61/029,712 filed 19 Feb. 2008; and 61/082,701 filed 22 Jul. 2008, the complete disclosures of which are incorporated herein by reference. 
     
    
       [0002]    This invention relates to a system and method of physically solving the charge, mass, and current density functions of polyatomic molecules, polyatomic molecular ions, diatomic molecules, molecular radicals, molecular ions, or any portion of these species in solution and undergoing reaction, and computing and rendering the nature of these species using the solutions. The results can be displayed on visual or graphical media. The displayed information provides insight into the nature of these species and is useful to anticipate their reactivity, physical properties, and spectral absorption and emission, and permits the solution and display of other compositions of matter. 
         [0003]    Rather than using postulated unverifiable theories that treat atomic particles as if they were not real, physical laws are now applied to atoms and ions. In an attempt to provide some physical insight into atomic problems and starting with the same essential physics as Bohr of the e −  moving in the Coulombic field of the proton, a classical solution to the bound electron is derived which yields a model that is remarkably accurate and provides insight into physics on the atomic level. The proverbial view deeply seated in the wave-particle duality notion that there is no large-scale physical counterpart to the nature of the electron is shown not to be correct. Physical laws and intuition may be restored when dealing with the wave equation and quantum atomic problems. 
         [0004]    Specifically, a theory of classical physics (CP) was derived from first principles as reported previously [reference Nos. 1-13] that successfully applies physical laws to the solution of atomic problems that has its basis in a breakthrough in the understanding of the stability of the bound electron to radiation. Rather than using the postulated Schrödinger boundary condition: “ψ→0 as r→∞, which leads to a purely mathematical model of the electron, the constraint is based on experimental observation. Using Maxwell&#39;s equations, the structure of the electron is derived as a boundary-value problem wherein the electron comprises the source current of time-varying electromagnetic fields during transitions with the constraint that the bound n=1 state electron cannot radiate energy. Although it is well known that an accelerated point particle radiates, an extended distribution modeled as a superposition of accelerating charges does not have to radiate. A simple invariant physical model arises naturally wherein the predicted results are extremely straightforward and internally consistent requiring minimal math, as in the case of the most famous equations of Newton and Maxwell on which the model is based. No new physics is needed; only the known physical laws based on direct observation are used. 
         [0005]    Applicant&#39;s previously filed WO2005/067678 discloses a method and system of physically solving the charge, mass, and current density functions of atoms and atomic ions and computing and rendering the nature of these species using the solutions. The complete disclosure of this published PCT application is incorporated herein by reference. 
         [0006]    Applicant&#39;s previously filed WO2005/116630 discloses a method and system of physically solving the charge, mass, and current density functions of excited states of atoms and atomic ions and computing and rendering the nature of these species using the solutions. The complete disclosure of this published PCT application is incorporated herein by reference. 
         [0007]    Applicant&#39;s previously filed applications (see, e.g., WO/2008/085804—solving and rendering the function of various groups), and U.S. Published Patent Application No. 20050209788A1 (method and system of physically solving the charge, mass, and current density functions of hydrogen-type molecules and molecular ions and computing and rendering the nature of the chemical bond using the solutions) are incorporated herein by reference. 
         [0008]    Applicant&#39;s previously filed WO2007/051078 discloses a method and system of physically solving the charge, mass, and current density functions of polyatomic molecules and polyatomic molecular ions and computing and rendering the nature of these species using the solutions. The complete disclosure of this published PCT application is incorporated herein by reference. This incorporated application discloses complete flow charts and written description of a computer program and systems that can be modified using the novel equations and description below to physically solve the charge, mass, and current density functions of the specific groups of molecules and molecular ions disclosed herein and computing and rendering the nature of the specific groups of molecules and molecular ions disclosed herein. 
         [0009]    The old view that the electron is a zero or one-dimensional point in an all-space probability wave function ψ(x) is not taken for granted. Rather, atomic and molecular physics theory, derived from first principles, must successfully and consistently apply physical laws on all scales [1-13]. Stability to radiation was ignored by all past atomic models, but in this case, it is the basis of the solutions wherein the structure of the electron is first solved and the result determines the nature of the atomic and molecular electrons involved in chemical bonds. 
         [0010]    Historically, the point at which quantum mechanics broke with classical laws can be traced to the issue of nonradiation of the one electron atom. Bohr just postulated orbits stable to radiation with the further postulate that the bound electron of the hydrogen atom does not obey Maxwell&#39;s equations—rather it obeys different physics [1-13]. Later physics was replaced by “pure mathematics” based on the notion of the inexplicable wave-particle duality nature of electrons which lead to the Schrödinger equation wherein the consequences of radiation predicted by Maxwell&#39;s equations were ignored. Ironically, Bohr, Schrödinger, and Dirac used the Coulomb potential, and Dirac used the vector potential of Maxwell&#39;s equations. But, all ignored electrodynamics and the corresponding radiative consequences. Dirac originally attempted to solve the bound electron physically with stability with respect to radiation according to Maxwell&#39;s equations with the further constraints that it was relativistically invariant and gave rise to electron spin [14]. He and many founders of QM such as Sommerfeld, Bohm, and Weinstein wrongly pursued a planetary model, were unsuccessful, and resorted to the current mathematical-probability-wave model that has many problems [1-18]. Consequently, Feynman for example, attempted to use first principles including Maxwell&#39;s equations to discover new physics to replace quantum mechanics [19]. 
         [0011]    Starting with the same essential physics as Bohr, Schrödinger, and Dirac of e −  moving in the Coulombic field of the proton and an electromagnetic wave equation and matching electron source current rather than an energy diffusion equation originally sought by Schrödinger, advancements in the understanding of the stability of the bound electron to radiation are applied to solve for the exact nature of the electron. Rather than using the postulated Schrödinger boundary condition: “ψ=0 as r→∞”, which leads to a purely mathematical model of the electron, the constraint is based on experimental observation. Using Maxwell&#39;s equations, the structure of the electron is derived as a boundary-value problem wherein the electron comprises the source current of time-varying electromagnetic fields during transitions with the constraint that the bound n=1 state electron cannot radiate energy. Although it is well known that an accelerated point particle radiates, an extended distribution modeled as a superposition of accelerating charges does not have to radiate. The physical boundary condition of nonradiation of that was imposed on the bound electron follows from a derivation by Haus [20]. The function that describes the motion of the electron must not possess spacetime Fourier components that are synchronous with waves traveling at the speed of light. Similarly, nonradiation is demonstrated based on the electron&#39;s electromagnetic fields and the Poynting power vector. A simple invariant physical model arises naturally wherein the results are extremely straightforward, internally consistent, and predictive of conjugate parameters for the first time, requiring minimal math as in the case of the most famous exact equations (no uncertainty) of Newton and Maxwell on which the model is based. No new physics is needed; only the known physical laws based on direct observation are used. 
         [0012]    The structure of the bound atomic electron was solved by first considering one-electron atoms [1-13]. Since the hydrogen atom is stable and nonradiative, the electron has constant energy. Furthermore, it is time dynamic with a corresponding current that serves as a source of electromagnetic radiation during transitions. The wave equation solutions of the radiation fields permit the source currents to be determined as a boundary-value problem. These source currents match the field solutions of the wave equation for two dimensions plus time when the nonradiation condition is applied. Then, the mechanics of the electron can be solved from the two-dimensional wave equation plus time in the form of an energy equation wherein it provides for conservation of energy and angular momentum as given in the Electron Mechanics and the Corresponding Classical Wave Equation for the Derivation of the Rotational Parameters of the Electron section of Ref. [1]. Once the nature of the electron is solved, all problems involving electrons can be solved in principle. Thus, in the case of one-electron atoms, the electron radius, binding energy, and other parameters are solved after solving for the nature of the bound electron. 
         [0013]    For time-varying spherical electromagnetic fields, Jackson [21] gives a generalized expansion in vector spherical waves that are convenient for electromagnetic boundary-value problems possessing spherical symmetry properties and for analyzing multipole radiation from a localized source distribution. The Green function G (x′, x) which is appropriate to the equation 
         [0000]      (∇ 2   +k   2 ) G ( x′,x )=−δ( x′−x ) 
         [0000]    in the infinite domain with the spherical wave expansion for the outgoing wave Green function is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           G 
                            
                           
                             ( 
                             
                               
                                 x 
                                 ′ 
                               
                               , 
                               x 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                              
                             
                               
                                 - 
                                  
                               
                                
                               
                                   
                               
                                
                               k 
                                
                               
                                  
                                 
                                   x 
                                   - 
                                   
                                     x 
                                     ′ 
                                   
                                 
                                  
                               
                             
                           
                           
                              
                             
                               x 
                               - 
                               
                                 x 
                                 ′ 
                               
                             
                              
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           ik 
                            
                           
                             
                               ∑ 
                               
                                 l 
                                 = 
                                 0 
                               
                               ∞ 
                             
                              
                             
                               
                                 
                                   j 
                                   l 
                                 
                                  
                                 
                                   ( 
                                   
                                     kr 
                                     &lt; 
                                   
                                   ) 
                                 
                               
                                
                               
                                 
                                   h 
                                   l 
                                   
                                     ( 
                                     1 
                                     ) 
                                   
                                 
                                  
                                 
                                   ( 
                                   
                                     kr 
                                     &gt; 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             ∑ 
                             
                               m 
                               = 
                               
                                 - 
                                 l 
                               
                             
                             l 
                           
                            
                           
                             
                               
                                 Y 
                                 
                                   l 
                                   , 
                                   m 
                                 
                                 * 
                               
                                
                               
                                 ( 
                                 
                                   
                                     θ 
                                     ′ 
                                   
                                   , 
                                   
                                     φ 
                                     ′ 
                                   
                                 
                                 ) 
                               
                             
                              
                             
                               
                                 Y 
                                 
                                   l 
                                   , 
                                   m 
                                 
                               
                                
                               
                                 ( 
                                 
                                   θ 
                                   , 
                                   φ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Jackson [21] further gives the general multipole field solution to Maxwell&#39;s equations in a source-free region of empty space with the assumption of a time dependence e iω   t : 
         [0000]    
       
         
           
             
               
                 
                   
                     B 
                     = 
                     
                       
                         ∑ 
                         
                           l 
                           , 
                           m 
                         
                       
                        
                       
                         [ 
                         
                           
                             
                               
                                 
                                   
                                     
                                       a 
                                       E 
                                     
                                      
                                     
                                       ( 
                                       
                                         l 
                                         , 
                                         m 
                                       
                                       ) 
                                     
                                   
                                    
                                   
                                     
                                       f 
                                       l 
                                     
                                      
                                     
                                       ( 
                                       kr 
                                       ) 
                                     
                                   
                                    
                                   
                                     X 
                                     
                                       l 
                                       , 
                                       m 
                                     
                                   
                                 
                                 - 
                               
                             
                           
                           
                             
                               
                                 
                                   i 
                                   k 
                                 
                                  
                                 
                                   
                                     a 
                                     M 
                                   
                                    
                                   
                                     ( 
                                     
                                       l 
                                       , 
                                       m 
                                     
                                     ) 
                                   
                                 
                                  
                                 
                                   ∇ 
                                   
                                     × 
                                     
                                       
                                         g 
                                         l 
                                       
                                        
                                       
                                         ( 
                                         kr 
                                         ) 
                                       
                                     
                                      
                                     
                                       X 
                                       
                                         l 
                                         , 
                                         m 
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     E 
                     = 
                     
                       
                         ∑ 
                         
                           l 
                           , 
                           m 
                         
                       
                        
                       
                         [ 
                         
                           
                             
                               
                                 
                                   
                                     i 
                                     k 
                                   
                                    
                                   
                                     
                                       a 
                                       E 
                                     
                                      
                                     
                                       ( 
                                       
                                         l 
                                         , 
                                         m 
                                       
                                       ) 
                                     
                                   
                                    
                                   
                                     ∇ 
                                     
                                       × 
                                       
                                         
                                           f 
                                           l 
                                         
                                          
                                         
                                           ( 
                                           kr 
                                           ) 
                                         
                                       
                                        
                                       
                                         X 
                                         
                                           l 
                                           , 
                                           m 
                                         
                                       
                                     
                                   
                                 
                                 + 
                               
                             
                           
                           
                             
                               
                                 
                                   
                                     a 
                                     M 
                                   
                                    
                                   
                                     ( 
                                     
                                       l 
                                       , 
                                       m 
                                     
                                     ) 
                                   
                                 
                                  
                                 
                                   
                                     g 
                                     l 
                                   
                                    
                                   
                                     ( 
                                     kr 
                                     ) 
                                   
                                 
                                  
                                 
                                   X 
                                   
                                     l 
                                     , 
                                     m 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where the cgs units used by Jackson are retained in this section. The radial functions ƒ l (kr) and g l (kr) are of the form: 
         [0000]        g   l ( kr )= A   l   (1)   h   l   (1)   +A   l   (2)   h   l   (2)    (4) 
         [0000]    X l,m  is the vector spherical harmonic defined by 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         X 
                         
                           l 
                           , 
                           m 
                         
                       
                        
                       
                         ( 
                         
                           θ 
                           , 
                           φ 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         1 
                         
                           
                             l 
                              
                             
                               ( 
                               
                                 l 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                        
                       
                         
                           LY 
                           
                             l 
                             , 
                             m 
                           
                         
                          
                         
                           ( 
                           
                             θ 
                             , 
                             φ 
                           
                           ) 
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   where 
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
             
               
                 
                   L 
                   = 
                   
                     
                       1 
                       i 
                     
                      
                     
                       ( 
                       
                         r 
                         × 
                         ∇ 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0014]    The coefficients a E (l, m) and a m (l, m) of Eq. (3) specify the amounts of electric (l, m) multipole and magnetic (l, m) multipole fields, and are determined by sources and boundary conditions as are the relative proportions in Eq. (4). Jackson gives the result of the electric and magnetic coefficients from the sources as 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         a 
                         E 
                       
                        
                       
                         ( 
                         
                           l 
                           , 
                           m 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         
                           4 
                            
                           π 
                            
                           
                               
                           
                            
                           
                             k 
                             2 
                           
                         
                         
                           i 
                            
                           
                             
                               l 
                                
                               
                                 ( 
                                 
                                   l 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                        
                       
                         ∫ 
                         
                           
                             Y 
                             l 
                             
                               m 
                               * 
                             
                           
                            
                           
                             { 
                             
                               
                                 
                                   
                                     
                                       ρ 
                                        
                                       
                                         
                                           ∂ 
                                           
                                             ∂ 
                                             r 
                                           
                                         
                                          
                                         
                                           [ 
                                           
                                             r 
                                              
                                             
                                                 
                                             
                                              
                                             
                                               
                                                 j 
                                                 l 
                                               
                                                
                                               
                                                 ( 
                                                 kr 
                                                 ) 
                                               
                                             
                                           
                                           ] 
                                         
                                       
                                     
                                     + 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       
                                         ik 
                                         c 
                                       
                                        
                                       
                                         ( 
                                         
                                           r 
                                           · 
                                           J 
                                         
                                         ) 
                                       
                                        
                                       
                                         
                                           j 
                                           l 
                                         
                                          
                                         
                                           ( 
                                           kr 
                                           ) 
                                         
                                       
                                     
                                     - 
                                   
                                 
                               
                               
                                 
                                   
                                     ik 
                                      
                                     
                                         
                                     
                                      
                                     
                                       ∇ 
                                       
                                         · 
                                         
                                           ( 
                                           
                                             r 
                                             × 
                                             M 
                                           
                                           ) 
                                         
                                       
                                     
                                      
                                     
                                       
                                         j 
                                         l 
                                       
                                        
                                       
                                         ( 
                                         kr 
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                             } 
                           
                            
                           
                             
                                
                               3 
                             
                              
                             x 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   and 
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       a 
                       M 
                     
                      
                     
                       ( 
                       
                         l 
                         , 
                         m 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           - 
                           4 
                         
                          
                         π 
                          
                         
                             
                         
                          
                         
                           k 
                           2 
                         
                       
                       
                         
                           l 
                            
                           
                             ( 
                             
                               l 
                               + 
                               1 
                             
                             ) 
                           
                         
                       
                     
                      
                     
                       ∫ 
                       
                         
                           
                             j 
                             l 
                           
                            
                           
                             ( 
                             kr 
                             ) 
                           
                         
                          
                         
                           Y 
                           l 
                           
                             m 
                             * 
                           
                         
                          
                         
                           L 
                           · 
                           
                             ( 
                             
                               
                                 J 
                                 c 
                               
                               + 
                               
                                 ∇ 
                                 
                                   × 
                                   M 
                                 
                               
                             
                             ) 
                           
                         
                          
                         
                           
                              
                             3 
                           
                            
                           x 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0000]    respectively, where the distribution of charge ρ(x,t), current J(x,t), and intrinsic magnetization M(x,t) are harmonically varying sources: ρ(x)e −ω     n     t , J(x)e −ω     n     t , and M(x)e −ω     n     t . 
         [0015]    The electron current-density function can be solved as a boundary value problem regarding the time varying corresponding source current J(x)e −ω     n     t  that gives rise to the time-varying spherical electromagnetic fields during transitions between states with the further constraint that the electron is nonradiative in a state defined as the n=1 state. The potential energy, V(r), is an inverse-radius-squared relationship given by given by Gauss&#39; law which for a point charge or a two-dimensional spherical shell at a distance r from the nucleus the potential is 
         [0000]    
       
         
           
             
               
                 
                   
                     V 
                      
                     
                       ( 
                       r 
                       ) 
                     
                   
                   = 
                   
                     - 
                     
                       
                          
                         2 
                       
                       
                         4 
                          
                         
                           πɛ 
                           0 
                         
                          
                         r 
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0016]    Thus, consideration of conservation of energy would require that the electron radius must be fixed. Addition constraints requiring a two-dimensional source current of fixed radius are matching the delta function of Eq. (1) with no singularity, no time dependence and consequently no radiation, absence of self-interaction (See Appendix III of Ref. [1]), and exact electroneutrality of the hydrogen atom wherein the electric field is given by 
         [0000]    
       
         
           
             
               
                 
                   
                     n 
                     · 
                     
                       ( 
                       
                         
                           E 
                           1 
                         
                         - 
                         
                           E 
                           2 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       σ 
                       s 
                     
                     
                       ɛ 
                       0 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where n is the normal unit vector, E 1  and E 2  are the electric field vectors that are discontinuous at the opposite surfaces, σ s  is the discontinuous two-dimensional surface charge density, and E 2 =0. Then, the solution for the radial electron function, which satisfies the boundary conditions is a delta function in spherical coordinates—a spherical shell [22] 
         [0000]    
       
         
           
             
               
                 
                   
                     f 
                      
                     
                       ( 
                       r 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       
                         r 
                         2 
                       
                     
                      
                     
                       δ 
                        
                       
                         ( 
                         
                           r 
                           - 
                           
                             r 
                             n 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where r n  is an allowed radius. This function defines the charge density on a spherical shell of a fixed radius (See  FIG. 1 ), not yet determined, with the charge motion confined to the two-dimensional spherical surface. The integer subscript n is determined during photon absorption as given in the Excited States of the One-Electron Atom (Quantization) section of Ref. [1]. It is shown in this section that the force balance between the electric fields of the electron and proton plus any resonantly absorbed photons gives the result that r n =nr 1  wherein n is an integer in an excited state. 
         [0017]      FIG. 1 . A bound electron is a constant two-dimensional spherical surface of charge (zero thickness, total charge=θ=π, and total mass=m e ), called an electron orbitsphere. The corresponding uniform current-density function having angular momentum components of 
         [0000]    
       
         
           
             
               L 
               xy 
             
             = 
             
               
                 
                   ℏ 
                   4 
                 
                  
                 
                     
                 
                  
                 and 
                  
                 
                     
                 
                  
                 
                   L 
                   z 
                 
               
               = 
               
                 ℏ 
                 2 
               
             
           
         
       
     
         [0000]    give rise to the phenomenon of electron spin. 
         [0018]    Given time harmonic motion and a radial delta function, the relationship between an allowed radius and the electron wavelength is given by 
         [0000]      2πr n =λ n    (12) 
         [0019]    Based on conservation of the electron&#39;s angular momentum of , the magnitude of the velocity and the angular frequency for every point on the surface of the bound electron are 
         [0000]    
       
         
           
             
               
                 
                   
                     v 
                     n 
                   
                   = 
                   
                     
                       h 
                       
                         
                           m 
                           e 
                         
                          
                         
                           λ 
                           n 
                         
                       
                     
                     = 
                     
                       
                         h 
                         
                           
                             m 
                             e 
                           
                            
                           2 
                            
                           π 
                            
                           
                               
                           
                            
                           
                             r 
                             n 
                           
                         
                       
                       = 
                       
                         ℏ 
                         
                           
                             m 
                             e 
                           
                            
                           
                             r 
                             n 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
             
               
                 
                   
                     ω 
                     n 
                   
                   = 
                   
                     ℏ 
                     
                       
                         m 
                         e 
                       
                        
                       
                         r 
                         n 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
         [0020]    To further match the required multipole electromagnetic fields between transitions of states, the trial nonradiative source current functions are time and spherical harmonics, each having an exact radius and an exact energy. Then, each allowed electron charge-density (mass-density) function is the product of a radial delta function 
         [0000]    
       
         
           
             
               ( 
               
                 
                   f 
                    
                   
                     ( 
                     r 
                     ) 
                   
                 
                 = 
                 
                   
                     1 
                     
                       r 
                       2 
                     
                   
                    
                   
                     δ 
                      
                     
                       ( 
                       
                         r 
                         - 
                         
                           r 
                           n 
                         
                       
                       ) 
                     
                   
                 
               
               ) 
             
             , 
           
         
       
     
         [0000]    two angular functions (spherical harmonic functions Y l   m (θ,φ)=P l   m (cos θ)e imφ ), and a time-harmonic function e iω     n     t . The spherical harmonic Y 0   0 (θ,φ)=1 is also an allowed solution that is in fact required in order for the electron charge and mass densities to be positive definite and to give rise to the phenomena of electron spin. The real parts of the spherical harmonics vary between −1 and 1. But the mass of the electron cannot be negative; and the charge cannot be positive. Thus, to insure that the function is positive definite, the form of the angular solution must be a superposition: 
         [0000]      Y 0   0 (θ,φ)+Y l   m (θ,φ)   (15) 
         [0021]    The current is constant at every point on the surface for the s orbital corresponding to Y 0   0 (θ,φ). The quantum numbers of the spherical harmonic currents can be related to the observed electron orbital angular momentum states. The currents corresponding to s, p, d, f, etc. orbitals are 
         [0000]    
       
         
           
             
               
                 
                   
                     l 
                     = 
                     0 
                   
                    
                   
                     
 
                   
                    
                   
                     
                       ρ 
                        
                       
                         ( 
                         
                           r 
                           , 
                           θ 
                           , 
                           φ 
                           , 
                           t 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         
                           e 
                           
                             8 
                              
                             π 
                              
                             
                                 
                             
                              
                             
                               r 
                               2 
                             
                           
                         
                          
                         
                           [ 
                           
                             δ 
                              
                             
                               ( 
                               
                                 r 
                                 - 
                                 
                                   r 
                                   n 
                                 
                               
                               ) 
                             
                           
                           ] 
                         
                       
                        
                       
                         [ 
                         
                           
                             
                               Y 
                               0 
                               0 
                             
                              
                             
                               ( 
                               
                                 θ 
                                 , 
                                 φ 
                               
                               ) 
                             
                           
                           + 
                           
                             
                               Y 
                               l 
                               m 
                             
                              
                             
                               ( 
                               
                                 θ 
                                 , 
                                 φ 
                               
                               ) 
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
             
               
                 
                   
                     l 
                     ≠ 
                     0 
                   
                    
                   
                     
 
                   
                    
                   
                     
                       ρ 
                        
                       
                         ( 
                         
                           r 
                           , 
                           θ 
                           , 
                           φ 
                           , 
                           t 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         
                           e 
                           
                             4 
                              
                             
                                 
                             
                              
                             π 
                              
                             
                                 
                             
                              
                             
                               r 
                               2 
                             
                           
                         
                          
                         
                           [ 
                           
                             δ 
                              
                             
                               ( 
                               
                                 r 
                                 - 
                                 
                                   r 
                                   n 
                                 
                               
                               ) 
                             
                           
                           ] 
                         
                       
                        
                       
                         [ 
                         
                           
                             
                               Y 
                               0 
                               0 
                             
                              
                             
                               ( 
                               
                                 θ 
                                 , 
                                 φ 
                               
                               ) 
                             
                           
                           + 
                           
                             Re 
                              
                             
                               { 
                               
                                 
                                   
                                     Y 
                                     l 
                                     m 
                                   
                                    
                                   
                                     ( 
                                     
                                       θ 
                                       , 
                                       φ 
                                     
                                     ) 
                                   
                                 
                                  
                                 
                                    
                                   
                                     
                                       ω 
                                       n 
                                     
                                      
                                     t 
                                   
                                 
                               
                               } 
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where Y l   m (θ,φ) are the spherical harmonic functions that spin about the z-axis with angular frequency ω n  with Y 0   0  (θ,φ) the constant function.
   Re{Y l   m (θ,φ)e iω     n     t }=P l   m (cos θ)cos(mφ+ω n t) and to keep the form of the spherical harmonic as a traveling wave about the z-axis, ω n =mω n .   
 
         [0023]    The Fourier transform of the electron charge-density function is a solution of the four-dimensional wave equation in frequency space (k, ω-space). Then the corresponding Fourier transform of the current-density function K (s, Θ, Φ, ω) is given by multiplying by the constant angular frequency. 
         [0000]    
       
         
           
             
               
                 
                   
                     K 
                      
                     
                       ( 
                       
                         s 
                         , 
                         Θ 
                         , 
                         Φ 
                         , 
                         ω 
                       
                       ) 
                     
                   
                   = 
                   
                     4 
                      
                     π 
                      
                     
                         
                     
                      
                     
                       ω 
                       n 
                     
                      
                     
                       
                         
                           sin 
                            
                           
                             ( 
                             
                               2 
                                
                               
                                 s 
                                 n 
                               
                                
                               
                                 r 
                                 n 
                               
                             
                             ) 
                           
                         
                         
                           2 
                            
                           
                             s 
                             n 
                           
                            
                           
                             r 
                             n 
                           
                         
                       
                       ⊗ 
                       2 
                     
                      
                     π 
                      
                     
                       
                         ∑ 
                         
                           υ 
                           = 
                           1 
                         
                         ∞ 
                       
                        
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   - 
                                   1 
                                 
                                 ) 
                               
                               
                                 υ 
                                 - 
                                 1 
                               
                             
                              
                             
                               
                                 ( 
                                 
                                   π 
                                    
                                   
                                       
                                   
                                    
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   Θ 
                                 
                                 ) 
                               
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     υ 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 ( 
                                 
                                   υ 
                                   - 
                                   1 
                                 
                                 ) 
                               
                               ! 
                             
                              
                             
                               
                                 ( 
                                 
                                   υ 
                                   - 
                                   1 
                                 
                                 ) 
                               
                               ! 
                             
                           
                         
                          
                         
                           
                             
                               Γ 
                                
                               
                                 ( 
                                 
                                   1 
                                   2 
                                 
                                 ) 
                               
                             
                              
                             
                               Γ 
                                
                               
                                 ( 
                                 
                                   υ 
                                   + 
                                   
                                     1 
                                     2 
                                   
                                 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 ( 
                                 
                                   π 
                                    
                                   
                                       
                                   
                                    
                                   cos 
                                    
                                   
                                       
                                   
                                    
                                   Θ 
                                 
                                 ) 
                               
                               
                                 
                                   2 
                                    
                                   υ 
                                 
                                 + 
                                 1 
                               
                             
                              
                             
                               2 
                               
                                 υ 
                                 + 
                                 1 
                               
                             
                           
                         
                          
                         
                           
                             2 
                              
                             
                               υ 
                               ! 
                             
                           
                           
                             
                               ( 
                               
                                 υ 
                                 - 
                                 1 
                               
                               ) 
                             
                             ! 
                           
                         
                          
                         
                           
                             s 
                             
                               
                                 - 
                                 2 
                               
                                
                               υ 
                             
                           
                           ⊗ 
                           2 
                         
                          
                         π 
                          
                         
                           
                             ∑ 
                             
                               υ 
                               = 
                               1 
                             
                             ∞ 
                           
                            
                           
                             
                               
                                 
                                   
                                     ( 
                                     
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                   
                                     υ 
                                     - 
                                     1 
                                   
                                 
                                  
                                 
                                   
                                     ( 
                                     
                                       πsin 
                                        
                                       
                                           
                                       
                                        
                                       Φ 
                                     
                                     ) 
                                   
                                   
                                     2 
                                      
                                     
                                       ( 
                                       
                                         υ 
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     ( 
                                     
                                       υ 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                   ! 
                                 
                                  
                                 
                                   
                                     ( 
                                     
                                       υ 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                   ! 
                                 
                               
                             
                              
                             
                               
                                 
                                   Γ 
                                    
                                   
                                     ( 
                                     
                                       1 
                                       2 
                                     
                                     ) 
                                   
                                 
                                  
                                 
                                   Γ 
                                    
                                   
                                     ( 
                                     
                                       υ 
                                       + 
                                       
                                         1 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               
                                 
                                   
                                     ( 
                                     
                                       π 
                                        
                                       
                                           
                                       
                                        
                                       cos 
                                        
                                       
                                           
                                       
                                        
                                       Φ 
                                     
                                     ) 
                                   
                                   
                                     
                                       2 
                                        
                                       υ 
                                     
                                     + 
                                     1 
                                   
                                 
                                  
                                 
                                   2 
                                   
                                     υ 
                                     + 
                                     1 
                                   
                                 
                               
                             
                              
                             
                               
                                 2 
                                  
                                 
                                   υ 
                                   ! 
                                 
                               
                               
                                 
                                   ( 
                                   
                                     υ 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                                 ! 
                               
                             
                              
                             
                               s 
                               
                                 
                                   - 
                                   2 
                                 
                                  
                                 υ 
                               
                             
                              
                             
                               
                                 1 
                                 
                                   4 
                                    
                                   π 
                                 
                               
                                
                               
                                 [ 
                                 
                                   
                                     δ 
                                      
                                     
                                       ( 
                                       
                                         ω 
                                         - 
                                         
                                           ω 
                                           n 
                                         
                                       
                                       ) 
                                     
                                   
                                   + 
                                   
                                     δ 
                                      
                                     
                                       ( 
                                       
                                         ω 
                                         + 
                                         
                                           ω 
                                           n 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 ] 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
         [0024]    The motion on the orbitsphere is angular; however, a radial correction exists due to special relativistic effects. Consider the radial wave vector of the sinc function. When the radial projection of the velocity is c 
         [0000]        s   n   ·v   n   =s   n   ·c=ω   n    (19) 
         [0000]    the relativistically corrected wavelength is (Eq. (1.247) of Ref. [1]) 
         [0000]      r n =λ n    (20) 
         [0025]    Substitution of Eq. (20) into the sinc function results in the vanishing of the entire Fourier transform of the current-density function. Thus, spacetime harmonics of 
         [0000]    
       
         
           
             
               
                 ω 
                 n 
               
               c 
             
             = 
             k 
           
         
       
     
         [0000]    or 
         [0000]    
       
         
           
             
               
                 
                   ω 
                   n 
                 
                 c 
               
                
               
                 
                   ɛ 
                   
                     ɛ 
                     o 
                   
                 
               
             
             = 
             k 
           
         
       
     
         [0000]    for which the Fourier transform of the current-density function is nonzero do not exist. Radiation due to charge motion does not occur in any medium when this boundary condition is met. There is acceleration without radiation. (Also see Abbott and Griffiths and Goedecke [23-24]). Nonradiation is also shown directly using Maxwell&#39;s equations directly in Appendix I of Ref. [1]. However, in the case that such a state arises as an excited state by photon absorption, it is radiative due to a radial dipole term in its current-density function since it possesses spacetime Fourier transform components synchronous with waves traveling at the speed of light as shown in the Instability of Excited States section of Ref. [1]. The radiation emitted or absorbed during electron transitions is the multipole radiation given by Eq. (2) as given in the Excited States of the One-Electron Atom (Quantization) section and the Equation of the Photon section of Ref. [1] wherein Eqs. (4.18-4.23) give a macro-spherical wave in the far-field. 
         [0026]    The corresponding uniform current density function Y 0   0 (θ,φ) corresponding to Eqs. (16-17) that gives rise to the spin of the electron is generated from a basis set current-vector field defined as the orbitsphere current-vector field (“orbitsphere-cvf”). The orbitsphere-cvf comprises a continuum of correlated orthogonal great circle current-density elements (one dimensional “current loops”). The current pattern comprising two components is generated over the surface by two sets (Steps One and Two) of rotations of two orthogonal great circle current loops that serve as basis elements about each of the (i x , i y ,0i z ) and 
         [0000]    
       
         
           
             
               
                 ( 
                 
                   
                     
                       - 
                       
                         1 
                         
                           2 
                         
                       
                     
                      
                     
                       i 
                       x 
                     
                   
                   , 
                   
                     
                       1 
                       
                         2 
                       
                     
                      
                     
                       i 
                       y 
                     
                   
                   , 
                   
                     i 
                     z 
                   
                 
                 ) 
               
               - 
               axes 
             
             , 
           
         
       
     
         [0000]    respectively, by π radians. In Appendix II of Ref. [1], the continuous uniform electron current density function Y 0   0 (θ,φ) having the angular momentum components of 
         [0000]    
       
         
           
             
               L 
               xy 
             
             = 
             
               
                 
                   ℏ 
                   4 
                 
                  
                 
                     
                 
                  
                 and 
                  
                 
                     
                 
                  
                 
                   L 
                   z 
                 
               
               = 
               
                 ℏ 
                 2 
               
             
           
         
       
     
         [0000]    is then exactly generated from this orbitsphere-cvf as a basis element by a convolution operator comprising an autocorrelation-type function. The positive Cartesian quadrant view of a representation of the total current pattern of the uniform current pattern of the Y 0   0 (θ,φ) orbitsphere comprising the superposition of 144 current elements each of STEP ONE and STEP TWO is shown in  FIG. 2A , and this representation with 144 vectors overlaid for each of STEP ONE and STEP TWO giving the direction of the current of each great circle element is shown in  FIG. 2B . As the number of great circles goes to infinity the current distribution becomes exactly continuous and uniform. A representation of the positive Cartesian quadrant view of the total uniform current-density pattern of STEP ONE and STEP TWO of the Y 0   0 (θ,φ) orbitsphere with 144 vectors per STEP overlaid on the continuous bound-electron current density giving the direction of the current of each great circle element is shown in  FIG. 2C . This superconducting current pattern is confined to two spatial dimensions. 
         [0027]      FIGS. 2A-C . The bound electron exists as a spherical two-dimensional supercurrent (electron orbitsphere), an extended distribution of charge and current completely surrounding the nucleus. Unlike a spinning sphere, there is a complex pattern of motion on its surface (indicated by vectors) that give rise to two orthogonal components of angular momentum ( FIG. 1 ) that give rise to the phenomenon of electron spin. (A) A great-circle representation of the positive Cartesian quadrant view of the total uniform current-density pattern of the Y 0   0 (θ,φ) orbitsphere comprising the superposition of the representations of STEP ONE and STEP TWO, each with 144 great circle current elements. (B) A great-circle representation of the positive Cartesian quadrant view of the total uniform current-density pattern of the Y 0   0 (θ,φ) orbitsphere comprising the superposition of representations of STEP ONE and STEP TWO, each with 144 vectors overlaid giving the direction of the current of each great circle element. (C) A representation of the positive Cartesian quadrant view of the total uniform current-density pattern of STEP ONE and STEP TWO of the Y 0   0 (θ,φ) orbitsphere with 144 vectors per STEP overlaid on the continuous bound-electron current density giving the direction of the current of each great circle element (nucleus not to scale). 
         [0028]    Thus, a bound electron is a constant two-dimensional spherical surface of charge (zero thickness and total charge=−e), called an electron orbitsphere that can exist in a bound state at only specified distances from the nucleus determined by an energy minimum for the n=1 state and integer multiples of this radius due to the action of resonant photons as shown in the Determination of Orbitsphere Radii section and Excited States of the One-Electron Atom (Quantization) section of Ref. [1], respectively. The bound electron is not a point, but it is point-like (behaves like a point at the origin). The free electron is continuous with the bound electron as it is ionized and is also point-like as shown in the Electron in Free Space section of Ref. [1]. The total function that describes the spinning motion of each electron orbitsphere is composed of two functions. One function, the spin function (see  FIG. 1  for the charge function and  FIG. 2  for the current function), is spatially uniform over the orbitsphere, where each point moves on the surface with the same quantized angular and linear velocity, and gives rise to spin angular momentum. It corresponds to the nonradiative n=1, l=0 state of atomic hydrogen which is well known as an s state or orbital. The other function, the modulation function, can be spatially uniform—in which case there is no orbital angular momentum and the magnetic moment of the electron orbitsphere is one Bohr magneton—or not spatially uniform—in which case there is orbital angular momentum. The modulation function rotates with a quantized angular velocity about a specific (by convention) z-axis. The constant spin function that is modulated by a time and spherical harmonic function as given by Eq. (17) is shown in  FIG. 3  for several l values. The modulation or traveling charge-density wave that corresponds to an orbital angular momentum in addition to a spin angular momentum are typically referred to as p, d, f, etc. orbitals and correspond to an l quantum number not equal to zero. 
         [0029]      FIG. 3 . The orbital function modulates the constant (spin) function, (shown for t=0; three-dimensional view). 
         [0030]    It was shown previously [1-13] that classical physics gives closed form solutions for the atom including the stability of the n=1 state and the instability of the excited states, the equation of the photon and electron in excited states, the equation of the free electron, and photon which predict the wave particle duality behavior of particles and light. The current and charge density functions of the electron may be directly physically interpreted. For example, spin angular momentum results from the motion of negatively charged mass moving systematically, and the equation for angular momentum, r×p, can be applied directly to the wavefunction (a current density function) that describes the electron. The magnetic moment of a Bohr magneton, Stern Gerlach experiment, g factor, Lamb shift, resonant line width and shape, selection rules, correspondence principle, wave-particle duality, excited states, reduced mass, rotational energies, and momenta, orbital and spin splitting, spin-orbital coupling, Knight shift, and spin-nuclear coupling, and elastic electron scattering from helium atoms, are derived in closed form equations based on Maxwell&#39;s equations. The agreement between observations and predictions based on closed-form equations with fundamental constants only matches to the limit permitted by the error in the measured fundamental constants. 
         [0031]    In contrast to the failure of the Bohr theory and the nonphysical, unpredictive, adjustable-parameter approach of quantum mechanics, multielectron atoms [1, 5] and the nature of the chemical bond [1, 6] are given by exact closed-form solutions containing fundamental constants only. Using the nonradiative electron current-density functions, the radii are determined from the force balance of the electric, magnetic, and centrifugal forces that correspond to the minimum of energy of the atomic or ionic system. The ionization energies are then given by the electric and magnetic energies at these radii. The spreadsheets to calculate the energies from exact solutions of one through twenty-electron atoms are available from the internet [25]. For 400 atoms and ions the agreement between the predicted and experimental results are remarkable [5]. Here I extend these results to the nature of the chemical bond. In this regard, quantum mechanics has historically sought the lowest energy of the molecular system, but this is trivially the case of the electrons inside the nuclei. Obviously, the electrons must obey additional physical laws since matter does not exist in a state with the electrons collapsed into the nuclei. Specifically, molecular bonding is due to the physics of Newton&#39;s and Maxwell&#39;s laws together with achieving an energy minimum. 
         [0032]    The structure of the bound molecular electron was solved by first considering the one-electron molecule H 2   +  and then the simplest molecule H 2 [1, 6]. The nature of the chemical bond was solved in the same fashion as that of the bound atomic electron. First principles including stability to radiation requires that the electron charge of the molecular orbital is a prolate spheroid, a solution of the Laplacian as an equipotential minimum energy surface in the natural ellipsoidal coordinates compared to spheroidal in the atomic case, and the current is time harmonic and obeys Newton&#39;s laws of mechanics in the central field of the nuclei at the foci of the spheroid. There is no a priori reason why the electron position must be a solution of the three-dimensional wave equation plus time and cannot comprise source currents of electromagnetic waves that are solutions of the three-dimensional wave equation plus time. Then, the special case of nonradiation determines that the current functions are confined to two-spatial dimensions plus time and match the electromagnetic wave-equation solutions for these dimensions. 
         [0033]    In addition to the important result of stability to radiation, several more very important physical results are subsequently realized: (i) The charge is distributed on a two-dimension surface; thus, there are no infinities in the corresponding fields (Eq. (10)). Infinite fields are simply renormalized in the case of the point-particles of quantum mechanics, but it is physically gratifying that none arise in this case since infinite fields have never been measured or realized in the laboratory. (ii) The hydrogen molecular ion or molecule has finite dimensions rather than extending over all space. From measurements of the resistivity of hydrogen as a function of pressure, the finite dimensions of the hydrogen molecule are evident in the plateau of the resistivity versus pressure curve of metallic hydrogen [26]. This is in contradiction to the predictions of quantum probability functions such as an exponential radial distribution in space. Furthermore, despite the predictions of quantum mechanics that preclude the imaging of a molecule orbital, the full three-dimensional structure of the outer molecular orbital of N 2  has been recently tomographically reconstructed [27]. The charge-density surface observed is similar to that shown in  FIG. 4  for H 2  which is direct evidence that MO&#39;s electrons are not point-particle probability waves that have no form until they are “collapsed to a point” by measurement. Rather they are physical, two-dimensional equipotential charge density functions as derived herein. (iii) Consistent with experiments, neutral scattering is predicted without violation of special relativity and causality wherein a point must be everywhere at once as required in the QM case. (iv) There is no electron self-interaction. The continuous charge-density function is a two-dimensional equipotential energy surface with an electric field that is strictly normal for the elliptic parameter ξ&gt;0 according to Gauss&#39; law and Faraday&#39;s law. The relationship between the electric field equation and the electron source charge-density function is given by Maxwell&#39;s equation in two dimensions [28,29] (Eq. (10)). This relation shows that only a two-dimensional geometry meets the criterion for a fundamental particle. This is the nonsingularity geometry that is no longer divisible. It is the dimension from which it is not possible to lower dimensionality. In this case, there is no electrostatic self-interaction since the corresponding potential is continuous across the surface according to Faraday&#39;s law in the electrostatic limit, and the field is discontinuous, normal to the charge according to Gauss&#39; law [28-30]. (v) The instability of electron-electron repulsion of molecular hydrogen is eliminated since the central field of the hydrogen molecular ion relative to a second electron at ξ&gt;0 which binds to form the hydrogen molecule is that of a single charge at the foci. (vi) The ellipsoidal MOs allow exact spin pairing over all time that is consistent with experimental observation. This aspect is not possible in the QM model. 
         [0034]      FIGS. 4A-B . Prolate spheroidal H 2  MO, an equipotential minimum energy two-dimensional surface of charge and current that is stable to radiation. (A) External surface showing the charge density that is proportional to the distance from the origin to the tangent to the surface with the maximum density of the MO closest to the nuclei, an energy minimum. (B) Prolate spheroid parameters of molecules and molecular ions where a is the semimajor axis, 2a is the total length of the molecule or molecular ion along the principal axis, b=c is the semiminor axis, 2b=2c is the total width of the molecule or molecular ion along the minor axis, c′ is the distance from the origin to a focus (nucleus), 2c′ is the internuclear distance, and the protons are at the foci. 
         [0035]    Current algorithms to solve molecules are based on nonphysical models based on the concept that the electron is a zero or one-dimensional point in an all-space probability wave function ψ(x) that permits the electron to be over all space simultaneously and give output based on trial and error or direct empirical adjustment of parameters. These models ultimately cannot be the actual description of a physical electron in that they inherently violate physical laws. They suffer from the same shortcomings that plague atomic quantum theory, infinities, instability with respect to radiation according to Maxwell&#39;s equations, violation of conservation of linear and angular momentum, lack of physical relativistic invariance, and the electron is unbounded such that the edge of molecules does not exist. There is no uniqueness, as exemplified by the average of 150 internally inconsistent programs per molecule for each of the 788 molecules posted on the NIST website [31]. 
         [0036]    Furthermore, from a physical perspective, the implication for the basis of the chemical bond according to quantum mechanics being the exchange integral and the requirement of zero-point vibration, “strictly quantum mechanical phenomena,” is that the theory cannot be a correct description of reality as described for even the simple bond of molecular hydrogen as reported previous [1, 6]. Even the premise that “electron overlap” is responsible for bonding is opposite to the physical reality that negative charges repel each other with an inverse-distance-squared force dependence that becomes infinite. A proposed solution based on physical laws and fully compliant with Maxwell&#39;s equations solves the parameters of molecules even to infinite length and complexity in closed form equations with fundamental constants only. 
         [0037]    For the first time in history, the key building blocks of organic chemistry have been solved from two basic equations. Now, the true physical structure and parameters of an infinite number of organic molecules up to infinite length and complexity can be obtained to permit the engineering of new pharmaceuticals and materials at the molecular level. The solutions of the basic functional groups of organic chemistry were obtained by using generalized forms of a geometrical and an energy equation for the nature of the H—H bond. The geometrical parameters and total bond energies of about 800 exemplary organic molecules were calculated using the functional group composition. The results obtained essentially instantaneously match the experimental values typically to the limit of measurement [1]. The solved function groups are given in Table 1. 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 Partial List of Organic Functional Groups Solved by Classical Physics. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Continuous-Chain Alkanes 
                 N-alkyl Amides 
                 Phenol 
               
               
                 Branched Alkanes 
                 N,N-dialkyl Amides 
                 Aniline 
               
               
                 Alkenes 
                 Urea 
                 Aryl Nitro Compounds 
               
               
                 Branched Alkenes 
                 Carboxylic Acid Halides 
                 Benzoic Acid Compounds 
               
               
                 Alkynes 
                 Carboxylic Acid Anhydrides 
                 Anisole 
               
               
                 Alkyl Fluorides 
                 Nitriles 
                 Pyrrole 
               
               
                 Alkyl Chlorides 
                 Thiols 
                 Furan 
               
               
                 Alkyl Bromides 
                 Sulfides 
                 Thiophene 
               
               
                 Alkyl Iodides 
                 Disulfides 
                 Imidizole 
               
               
                 Alkenyl Halides 
                 Sulfoxides 
                 Pyridine 
               
               
                 Aryl Halides 
                 Sulfones 
                 Pyrimidine 
               
               
                 Alcohols 
                 Sulfites 
                 Pyrazine 
               
               
                 Ethers 
                 Sulfates 
                 Quinoline 
               
               
                 Primary Amines 
                 Nitroalkanes 
                 Isoquinoline 
               
               
                 Secondary Amines 
                 Alkyl Nitrates 
                 Indole 
               
               
                 Tertiary Amines 
                 Alkyl Nitrites 
                 Adenine 
               
               
                 Aldehydes 
                 Conjugated Alkenes 
                 Fullerene (C 60 ) 
               
               
                 Ketones 
                 Conjugated Polyenes 
                 Graphite 
               
               
                 Carboxylic Acids 
                 Aromatics 
                 Phosphines 
               
               
                 Carboxylic Acid Esters 
                 Napthalene 
                 Phosphine Oxides 
               
               
                 Amides 
                 Toluene 
                 Phosphites 
               
               
                   
                 Chlorobenzene 
                 Phosphates 
               
               
                   
               
             
          
         
       
     
         [0038]    The two basic equations that solves organic molecules, one for geometrical parameters and the other for energy parameters, were applied to bulk forms of matter containing trillions of trillions of electrons. For example, using the same alkane- and alkene-bond solutions as elements in an infinite network, the nature of the solid molecular bond for all known allotropes of carbon (graphite, diamond, C 60 , and their combinations) were solved. By further extension of this modular approach, the solid molecular bond of silicon and the nature of semiconductor bond were solved. The nature of other fundamental forms of matter such as the nature of the ionic bond, the metallic bond, and additional major fields of chemistry such as that of silicon, organometallics, and boron were solved exactly such that the position and energy of each and every electron is precisely specified. The implication of these results is that it is possible using physical laws to solve the structure of all types of matter. Some of the solved forms of matter of infinite extent as well as additional major fields of chemistry are given in Table 2. In all cases, the agreement with experiment is remarkable [1]. 
         [0000]    
       
         
               
             
               
               
             
           
               
                 TABLE 2  
               
               
                   
               
               
                 Partial List of Additional Molecules and Compositions of Matter Solved 
               
               
                 by Classical Physics. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Solid Molecular Bond of the Three Allotropes 
               
               
                   
                 of Carbon 
               
               
                   
                   Diamond 
               
               
                   
                   Graphite 
               
               
                   
                   Fullerene (C 60 ) 
               
               
                   
                 Solid Ionic Bond of Alkali-Hydrides 
               
               
                   
                   Alkali-Hydride Crystal Structures 
               
               
                   
                     Lithium Hydride 
               
               
                   
                     Sodium Hydride 
               
               
                   
                     Potassium Hydride 
               
               
                   
                     Rubidium &amp; Cesium Hydride 
               
               
                   
                     Potassium Hydrino Hydride 
               
               
                   
                 Solid Metallic Bond of Alkali Metals 
               
               
                   
                   Alkali Metal Crystal Structures 
               
               
                   
                     Lithium Metal 
               
               
                   
                     Sodium Metal 
               
               
                   
                     Potassium Metal 
               
               
                   
                     Rubidium &amp; Cesium Metals 
               
               
                   
                 Alkyl Aluminum Hydrides 
               
               
                   
                 Silicon Groups and Molecules 
               
               
                   
                   Silanes 
               
               
                   
                   Alkyl Silanes and Disilanes 
               
               
                   
                 Solid Semiconductor Bond of Silicon 
               
               
                   
                   Insulator-Type Semiconductor Bond 
               
               
                   
                   Conductor-Type Semiconductor Bond 
               
               
                   
                 Boron Molecules 
               
               
                   
                   Boranes 
               
               
                   
                     Bridging Bonds of Boranes 
               
               
                   
                   Alkoxy Boranes 
               
               
                   
                   Alkyl Boranes 
               
               
                   
                   Alkyl Borinic Acids 
               
               
                   
                   Tertiary Aminoboranes 
               
               
                   
                   Quaternary Aminoboranes 
               
               
                   
                   Borane Amines 
               
               
                   
                 Halido Boranes Organometallic Molecular 
               
               
                   
                 Functional Groups and Molecules 
               
               
                   
                   Alkyl Aluminum Hydrides 
               
               
                   
                     Bridging Bonds of 
               
               
                   
                     Organoaluminum Hydrides 
               
               
                   
                   Organogermanium and Digermanium 
               
               
                   
                   Organolead 
               
               
                   
                   Organoarsenic 
               
               
                   
                   Organoantimony 
               
               
                   
                   Organobismuth 
               
               
                   
                 Organic Ions 
               
               
                   
                   1° Amino 
               
               
                   
                   2° Amino 
               
               
                   
                   Carboxylate 
               
               
                   
                   Phosphate 
               
               
                   
                   Nitrate 
               
               
                   
                   Sulfate 
               
               
                   
                   Silicate 
               
               
                   
                 Proteins 
               
               
                   
                   Amino Acids 
               
               
                   
                   Peptide Bonds 
               
               
                   
                 DNA 
               
               
                   
                   Bases 
               
               
                   
                   2-deoxyribose 
               
               
                   
                   Ribose 
               
               
                   
                   Phosphate Backbone 
               
               
                   
                   
               
             
          
         
       
     
         [0039]    The background theory of classical physics (CP) for the physical solutions of atoms and atomic ions is disclosed in Mills journal publications [1-13], R. Mills,  The Grand Unified Theory of Classical Quantum Mechanics,  January 2000 Edition, BlackLight Power, Inc., Cranbury, N.J., (“&#39;00 Mills GUT”), provided by BlackLight Power, Inc., 493 Old Trenton Road, Cranbury, N.J., 08512; R. Mills,  The Grand Unified Theory of Classical Quantum Mechanics,  September 2001 Edition, BlackLight Power, Inc., Cranbury, N.J., Distributed by Amazon.com (“&#39;01 Mills GUT”), provided by BlackLight Power, Inc., 493 Old Trenton Road, Cranbury, N.J., 08512; R. Mills,  The Grand Unified Theory of Classical Quantum Mechanics,  July 2004 Edition, BlackLight Power, Inc., Cranbury, N.J., (“&#39;04 Mills GUT”), provided by BlackLight Power, Inc., 493 Old Trenton Road, Cranbury, N.J., 08512; R. Mills,  The Grand Unified Theory of Classical Quantum Mechanics,  January 2005 Edition, BlackLight Power, Inc., Cranbury, N.J., (“&#39;05 Mills GUT”), provided by BlackLight Power, Inc., 493 Old Trenton Road, Cranbury, N.J., 08512; R. L. Mills, “The Grand Unified Theory of Classical Quantum Mechanics”, June 2006 Edition, Cadmus Professional Communications-Science Press Division, Ephrata, Pa., ISBN 0963517171, Library of Congress Control Number 2005936834, (“&#39;06 Mills GUT”), provided by BlackLight Power, Inc., 493 Old Trenton Road, Cranbury, N.J., 08512; ; R. Mills,  The Grand Unified Theory of Classical Quantum Mechanics,  October 2007 Edition, BlackLight Power, Inc., Cranbury, N.J., (“&#39;07 Mills GUT”), provided by BlackLight Power, Inc., 493 Old Trenton Road, Cranbury, N.J., 08512; R. Mills,  The Grand Unified Theory of Classical Physics,  June 2008 Edition, BlackLight Power, Inc., Cranbury, N.J., (“&#39;08 Mills GUT-CP”); in prior published PCT applications WO05/067678; WO2005/116630; WO2007/051078; WO2007/053486; and WO2008/085,804, and U.S. Pat. No. 7,188,033; U.S. Application Nos.: 60/878,055, filed 3 Jan. 2007; 60/880,061, filed 12 Jan. 2007; 60/898,415, filed 31 Jan. 2007; 60/904,164, filed 1 Mar. 2007; 60/907,433, filed 2 Apr. 2007; 60/907,722, filed 13 Apr. 2007; 60/913,556, filed 24 Apr. 2007; 60/986,675, filed 9 Nov. 2007; 60/988,537, filed 16 Nov. 2007; 61/018,595, filed 2 Jan. 2008; 61/027,977, filed 12 Feb. 2008; 61/029,712, filed 19 Feb. 2008; and 61/082,701, filed 22 Jul. 22 2008, the entire disclosures of which are all incorporated herein by reference (hereinafter “Mills Prior Publications”). 
         [0040]    The present disclosure, an exemplary embodiment of which is also referred to as Millsian software and systems, stems from a new fundamental insight into the nature of the atom. Applicant&#39;s theory of Classical Physics (CP) reveals the nature of atoms and molecules using classical physical laws for the first time. As discussed above, traditional quantum mechanics can solve neither multi-electron atoms nor molecules exactly. By contrast, CP produces exact, closed-form solutions containing physical constants only for even the most complex atoms and molecules. 
         [0041]    The present invention is the first and only molecular modeling program ever built on the CP framework. All the major functional groups that make up most organic molecules and the most common classes of molecules have been solved exactly in closed-form solutions with CP. By using these functional groups as building blocks, or independent units, a potentially infinite number of organic molecules can be solved. As a result, the present invention can be used to visualize the exact 3D structure and calculate the heats of formation of an infinite number of molecules, and these solutions can be used in modeling applications. 
         [0042]    For the first time, the significant building-block molecules of chemistry have been successfully solved using classical physical laws in exact closed-form equations having fundamental constants only. The major functional groups have been solved from which molecules of infinite length can be solved almost instantly with a computer program. The predictions are accurate within experimental error for over 800 exemplary molecules, typically a factor of 1000 times more accuracy then those given by the current Hartree-Fock algorithm based on QM [2]. 
         [0043]    The present invention&#39;s advantages over other models includes: Rendering true molecular structures; Providing precisely all characteristics, spatial and temporal charge distributions and energies of every electron in every bond, and of every bonding atom; Facilitating the identification of biologically active sites in drugs; and facilitating drug design. 
         [0044]    An objective of the present invention is to solve the charge (mass) and current-density functions of specific groups of molecules and molecular ions disclosed herein or any portion of these species from first principles. In an embodiment, the solution for the molecules and molecular ions, or any portion of these species is derived from Maxwell&#39;s equations invoking the constraint that the bound electron before excitation does not radiate even though it undergoes acceleration. 
         [0045]    Another objective of the present invention is to generate a readout, display, or image of the solutions so that the nature of the molecules and molecular ions, or any portion of these species be better understood and potentially applied to predict reactivity and physical and optical properties. 
         [0046]    Another objective of the present invention is to apply the methods and systems of solving the nature of the atoms, molecules, and molecular ions, or any portion of these species and their rendering to numerical or graphical form to apply to further functional groups such as amino acids and peptide bonds with charged functional groups for proteins of any size and complexity by addition of the units, bases, 2-deoxyribose, ribose, phosphate backbone with charged functional groups for DNA of any size and complexity by addition of the units, organic ions, halobenzenes, phosphines, phosphates, phosphine oxides, phosphates, organogermanium and digermanium, organolead, organoarsenic, organoantimony, organobismuth, or any portion of these species. 
         [0047]    These objectives and other objectives are obtained by a system of computing and rendering the nature of at least one specie selected from the groups of molecules and polyatomic molecules disclosed herein, comprising physical, Maxwellian solutions of charge, mass, and current density functions of said specie, said system comprising processing means for processing physical, Maxwellian equations representing charge, mass, and current density functions of said specie; and an output device in communication with the processing means for displaying said physical, Maxwellian solutions of charge, mass, and current density functions of said specie. 
         [0048]    Also provided is a composition of matter comprising a plurality of atoms having a novel property or use discovered by calculation of at least one of (i) a bond distance between two of the atoms, (ii) a bond angle between three of the atoms, (iii) a bond energy between two of the atoms, (iv) orbital intercept distances and angles, (v) charge-density functions of atomic, hybridized, and molecular orbitals, (vi) orientations distances, and energies of species in different physical states such as solid, liquid, and gas, and (vii) reaction parameters with other species. 
         [0049]    The parameters such as bond distance, bond angle, bond energy, species orientations and reactions being calculated from physical solutions of the charge, mass, and current density functions of atoms and atomic ions, which solutions are derived from Maxwell&#39;s equations using a constraint that a bound electron(s) does not radiate under acceleration. 
         [0050]    The presented exact physical solutions for known species of the groups of molecules and molecular ions disclosed herein can be applied to other unknown species. These solutions can be used to predict the properties of presently unknown species and engineer compositions of matter in a manner that is not possible using past quantum mechanical techniques. The molecular solutions can be used to design synthetic pathways and predict product yields based on equilibrium constants calculated from the heats of formation. Not only can new stable compositions of matter be predicted, but now the structures of combinatorial chemistry reactions can be predicted. 
         [0051]    Pharmaceutical applications include the ability to graphically or computationally render the structures of drugs in solution that permit the identification of the biologically active parts of the specie to be identified from the common spatial charge-density functions of a series of active species. Novel drugs can now be designed according to geometrical parameters and bonding interactions with the data of the structure of the active site of the drug. 
         [0052]    The system can be used to calculate conformations, folding, and physical properties, and the exact solutions of the charge distributions in any given specie are used to calculate the fields. From the fields, the interactions between groups of the same specie or between groups on different species are calculated wherein the interactions are distance and relative orientation dependent. The fields and interactions can be determined using a finite-element-analysis approach of Maxwell&#39;s equations. The approach can be applied to solid, liquid, and gases phases of a species or a species present in a mixture or solution. 
         [0053]    Embodiments of the system for performing computing and rendering of the nature of the groups of molecules and molecular ions, or any portion of these species using the physical solutions and their phases or structures in different media may comprise a general purpose computer. Such a general purpose computer may have any number of basic configurations. For example, such a general purpose computer may comprise a central processing unit (CPU), one or more specialized processors, system memory, a mass storage device such as a magnetic disk, an optical disk, or other storage device, an input means, such as a keyboard or mouse, a display device, and a printer or other output device. A system implementing the present invention can also comprise a special purpose computer or other hardware system and all should be included within its scope. A complete description of how a computer can be used is disclosed in Applicant&#39;s prior incorporated WO2007/051078 application. 
         [0054]    Although not preferred, any of the calculated and measured values and constants recited in the equations herein can be adjusted, for example, up to ±10%, if desired. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0055]      FIG. 1 . Is a drawing of a bound electron with a constant two-dimensional spherical surface of charge (zero thickness, total charge=θ=π, and total mass=m e ), called an electron orbitsphere. 
           [0056]      FIGS. 2A-C . An electron orbitsphere of a great-circle representation of the positive Cartesian quadrant view of the total uniform current-density pattern of the Y 0   0 (θ,φ) orbitsphere, wherein (A) is shown with 144 great circle current elements; (B) is shown with 144 vectors overlaid giving the direction of the current of each great circle element; and (C) is shown with 144 vectors per step overlaid on the continuous bound-electron current density giving the direction of the current of each great circle element (nucleus not to scale). 
           [0057]      FIG. 3 . The orbital function modulates the constant (spin) function, (shown for t=0; three-dimensional view). 
           [0058]      FIGS. 4A-B . Prolate spheroidal H 2  MO, with (A) External surface showing the charge density that is proportional to the distance from the origin to the tangent to the surface; and (B) Prolate spheroid parameters of molecules and molecular ions where a is the semimajor axis, 2a is the total length of the molecule or molecular ion along the principal axis, b=c is the semiminor axis, 2b=2c is the total width of the molecule or molecular ion along the minor axis, c′ is the distance from the origin to a focus (nucleus), 2c′ is the internuclear distance, and the protons are at the foci. 
           [0059]      FIG. 5 . Color scale, translucent view of the charge-density of chlorobenzene showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei (red, not to scale). 
           [0060]      FIG. 6 . Adenine. 
           [0061]      FIG. 7 . Color scale, charge-density of adenine showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0062]      FIG. 8 . Thymine. 
           [0063]      FIG. 9 . Color scale, charge-density of thymine showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0064]      FIG. 10 . Guanine. 
           [0065]      FIG. 11 . Color scale, charge-density of guanine showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0066]      FIG. 12 . Cytosine. 
           [0067]      FIG. 13 . Color scale, charge-density of cytosine showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0068]      FIG. 14 . Color scale, charge-density of triphenylphosphine showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0069]      FIG. 15 . Color scale, charge-density of tri-isopropyl phosphite showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0070]      FIG. 16 . Color scale, charge-density of trimethylphosphine oxide showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0071]      FIG. 17 . Color scale, charge-density of tri-isopropyl phosphate showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0072]      FIG. 18 . Color scale, charge-density of protonated lysine ion showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0073]      FIG. 19 . Color scale, charge-density of 2-deoxy-D-ribose showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0074]      FIG. 20 . Color scale, charge-density of D-ribose showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0075]      FIG. 21 . Color scale, charge-density of alpha-2-deoxy-D-ribose showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0076]      FIG. 22 . Color scale, charge-density of alpha-D-ribose showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0077]      FIG. 23 . Designation of the atoms of the nucleotide bond. Oligonucleotide disclosed as SEQ ID NO: 1. 
           [0078]      FIG. 24 . The color scale rendering of the charge-density of the exemplary tetra-nucleotide, (deoxy)adenosine monophosphate—(deoxy)thymidine monophosphate—(deoxy)guanosine monophosphate—(deoxy)cytidine monophosphate (ATGC) showing the orbitals of the atoms at their radii and the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond. 
           [0079]      FIG. 25 . Color scale rendering of the charge-density of the DNA fragment 
           [0000]                                ACTGACTGACTG   (SEQ ID NO: 1)                       TGACTGACTGAC            
showing the orbitals of the atoms at their radii and the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond.
 
           [0080]      FIG. 26 . Aspartic acid. 
           [0081]      FIG. 27 . Color scale, charge-density of aspartic acid showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0082]      FIG. 28 . Glutamic acid. 
           [0083]      FIG. 29 . Color scale, charge-density of glutamic acid showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0084]      FIG. 30 . Cysteine. 
           [0085]      FIG. 31 . Color scale, charge-density of cysteine showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0086]      FIG. 32 . Lysine. 
           [0087]      FIG. 33 . Color scale, charge-density of lysine showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0088]      FIG. 34 . Arginine. 
           [0089]      FIG. 35 . Color scale, charge-density of arginine showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0090]      FIG. 36 . Histidine. 
           [0091]      FIG. 37 . Color scale, charge-density of histidine showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0092]      FIG. 38 . Asparagine. 
           [0093]      FIG. 39 . Color scale, charge-density of asparagine showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0094]      FIG. 40 . Glutamine. 
           [0095]      FIG. 41 . Color scale, charge-density of glutamine showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0096]      FIG. 42 . Threonine. 
           [0097]      FIG. 43 . Color scale, charge-density of threonine showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0098]      FIG. 44 . Tyrosine. 
           [0099]      FIG. 45 . Color scale, charge-density of tyrosine showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0100]      FIG. 46 . Serine. 
           [0101]      FIG. 47 . Color scale, charge-density of serine showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0102]      FIG. 48 . Tryptophan. 
           [0103]      FIG. 49 . Color scale, charge-density of tryptophan showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0104]      FIG. 50 . Phenylalanine. 
           [0105]      FIG. 51 . Color scale, charge-density of phenylalanine showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0106]      FIG. 52 . Proline. 
           [0107]      FIG. 53 . Color scale, charge-density of proline showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0108]      FIG. 54 . Methionine. 
           [0109]      FIG. 55 . Color scale, charge-density of methionine showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0110]      FIG. 56 . Leucine. 
           [0111]      FIG. 57 . Color scale, charge-density of leucine showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0112]      FIG. 58 . Isoleucine. 
           [0113]      FIG. 59 . Color scale, charge-density of isoleucine showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0114]      FIG. 60 . Valine. 
           [0115]      FIG. 61 . Color scale, charge-density of valine showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0116]      FIG. 62 . Alanine. 
           [0117]      FIG. 63 . Color scale, charge-density of alanine showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0118]      FIG. 64 . Glycine. 
           [0119]      FIG. 65 . Color scale, charge-density of glycine showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0120]      FIG. 66 . Color scale, charge-density of the polypeptide phenylalanine-leucine-glutamine-aspartic acid (phe-leu-gln-asp) (SEQ ID NO: 2) showing the orbitals of the atoms at their radii and the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond. 
           [0121]      FIG. 67 . Color scale, charge-density of Ge(CH 2 CH 3 ) 4  showing the orbitals of the Ge and C atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atoms participating in each bond, and the hydrogen nuclei. 
           [0122]      FIG. 68 . Color scale, charge-density of (C 2 H 5 ) 3  GeGe(C 2 H 5 ) 3  showing the orbitals of the Ge and C atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atoms participating in each bond, and the hydrogen nuclei. 
           [0123]      FIG. 69 . Tin Tetrachloride. Color scale, translucent view of the charge-density of SnCl 4  showing the orbitals of the Sn and Cl atoms at their radii, the ellipsoidal surface of each H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atoms participating in each bond, and the nuclei (red, not to scale). 
           [0124]      FIGS. 70A  and B. Hexaphenyldistannane. Color scale, opaque view of the charge-density of (C 6 H 5 ) 3 SnSn(C 6 H 5 ) 3  showing the orbitals of the Sn and C atoms at their radii and the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atoms participating in each bond. 
           [0125]      FIG. 71 . Color scale, charge-density of Pb(CH 2 CH 3 ) 4  showing the orbitals of the Pb and C atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atoms participating in each bond, and the hydrogen nuclei. 
           [0126]      FIG. 72 . Color scale, charge-density of triphenylarsine showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0127]      FIG. 73 . Color scale, charge-density of triphenylstibine showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
           [0128]      FIG. 74 . Color scale, charge-density of triphenylbismuth showing the orbitals of the atoms at their radii, the ellipsoidal surface of each H or H 2 -type ellipsoidal MO that transitions to the corresponding outer shell of the atom(s) participating in each bond, and the hydrogen nuclei. 
       
    
    
     DESCRIPTION OF THE INVENTION 
       [0129]    The present disclosure comprises molecular modeling methods and systems for solving atomic and molecular structures based on applying the classical laws of physics, (Newton&#39;s and Maxwell&#39;s Laws) to the atomic scale. The functional groups such as amino acids and peptide bonds with charged functional groups, bases, 2-deoxyribose, ribose, phosphate backbone with charged functional groups, organic ions, halobenzenes, phosphines, phosphates, phosphine oxides, phosphates, organogermanium and digermanium, organolead, organoarsenic, organoantimony, and organobismuth have been solved in analytical equations. By using these functional groups as building blocks, or independent units, a potentially infinite number of molecules can be solved. As a result, the method and systems of the present Invention can visualize the exact three-dimensional structure and calculate physical characteristics of many molecules, up to arbitrary length and complexity. Even complex proteins and DNA (the molecules that encode genetic information) may be solved in real-time interactively on a personal computer. By contrast, previous software based on traditional quantum methods must resort to approximations and run on powerful computers for even the simplest systems. 
       II. Methodological Outline  
     A. The Nature of the Chemical Bond of Hydrogen 
       [0130]    The nature of the chemical bond of functional groups is solved by first solving the simplest molecule, molecular hydrogen as given in the Nature of the Chemical Bond of Hydrogen-Type Molecules section of Ref. [1]. The hydrogen molecule charge and current density functions, bond distance, and energies are solved from the Laplacian in ellipsoidal coordinates with the constraint of nonradiation [1, 6]. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         ( 
                         
                           η 
                           - 
                           ζ 
                         
                         ) 
                       
                        
                       
                         R 
                         ξ 
                       
                        
                       
                         ∂ 
                         
                           ∂ 
                           ξ 
                         
                       
                        
                       
                         ( 
                         
                           
                             R 
                             ξ 
                           
                            
                           
                             
                               ∂ 
                               φ 
                             
                             
                               ∂ 
                               ξ 
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       
                         ( 
                         
                           ζ 
                           - 
                           ξ 
                         
                         ) 
                       
                        
                       
                         R 
                         η 
                       
                        
                       
                         ∂ 
                         
                           ∂ 
                           η 
                         
                       
                        
                       
                         ( 
                         
                           
                             R 
                             η 
                           
                            
                           
                             
                               ∂ 
                               φ 
                             
                             
                               ∂ 
                               η 
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       
                         ( 
                         
                           ξ 
                           - 
                           η 
                         
                         ) 
                       
                        
                       
                         R 
                         ζ 
                       
                        
                       
                         ∂ 
                         
                           ∂ 
                           ζ 
                         
                       
                        
                       
                         ( 
                         
                           
                             R 
                             ζ 
                           
                            
                           
                             
                               ∂ 
                               φ 
                             
                             
                               ∂ 
                               ζ 
                             
                           
                         
                         ) 
                       
                     
                   
                   = 
                   0 
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
         [0000]    a. The Geometrical Parameters of the Hydrogen Molecule 
         [0131]    As shown in  FIG. 4 , the nuclei are at the foci of the electrons comprising a two-dimensional, equipotential-energy, charge- and current-density surface that obeys Maxwell&#39;s equations including stability to radiation and Newton&#39;s laws of motion. The force balance equation for the hydrogen molecule is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         ℏ 
                         2 
                       
                       
                         
                           m 
                           e 
                         
                          
                         
                           a 
                           2 
                         
                          
                         
                           b 
                           2 
                         
                       
                     
                      
                     D 
                   
                   = 
                   
                     
                       
                         
                            
                           2 
                         
                         
                           8 
                            
                           π 
                            
                           
                               
                           
                            
                           
                             ɛ 
                             o 
                           
                            
                           
                             ab 
                             2 
                           
                         
                       
                        
                       D 
                     
                     + 
                     
                       
                         
                           ℏ 
                           2 
                         
                         
                           2 
                            
                           
                             m 
                             e 
                           
                            
                           
                             a 
                             2 
                           
                            
                           
                             b 
                             2 
                           
                         
                       
                        
                       D 
                     
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where 
         [0000]        D=r ( t )· i   ξ   (23) 
         [0000]    is the time dependent distance from the origin to the tangent plane at a point on the ellipsoidal MO. Eq. (22) has the parametric solution 
         [0000]        r ( t )= ia  cos ω t+jb  sin ω t    (24) 
         [0000]    when the semimajor axis, a, is 
         [0000]      a=a 0    (25) 
         [0000]    The internuclear distance, 2c′, which is the distance between the foci is 
         [0000]      2c′=√{square root over (2)}a 0    (26) 
         [0000]    The experimental internuclear distance is √{square root over (2)}a 0 . The semiminor axis is 
         [0000]    
       
         
           
             
               
                 
                   b 
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                      
                     
                       a 
                       o 
                     
                   
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The eccentricity, e, is 
         [0000]    
       
         
           
             
               
                 
                   e 
                   = 
                   
                     1 
                     
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   28 
                   ) 
                 
               
             
           
         
       
     
         [0000]    b. The Energies of the Hydrogen Molecule 
         [0132]    The potential energy of the two electrons in the central field of the protons at the foci is 
         [0000]    
       
         
           
             
               
                 
                   
                     V 
                     e 
                   
                   = 
                   
                     
                       
                         
                           
                             - 
                             2 
                           
                            
                           
                              
                             2 
                           
                         
                         
                           8 
                            
                           
                             πɛ 
                             o 
                           
                            
                           
                             
                               
                                 a 
                                 2 
                               
                               - 
                               
                                 b 
                                 2 
                               
                             
                           
                         
                       
                        
                       ln 
                        
                       
                           
                       
                        
                       
                         
                           a 
                           + 
                           
                             
                               
                                 a 
                                 2 
                               
                               - 
                               
                                 b 
                                 2 
                               
                             
                           
                         
                         
                           a 
                           - 
                           
                             
                               
                                 a 
                                 2 
                               
                               - 
                               
                                 b 
                                 2 
                               
                             
                           
                         
                       
                     
                     = 
                     
                       
                         - 
                         67.836 
                       
                        
                       
                           
                       
                        
                       eV 
                     
                   
                 
               
               
                 
                   ( 
                   29 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The potential energy of the two protons is 
         [0000]    
       
         
           
             
               
                 
                   
                     V 
                     p 
                   
                   = 
                   
                     
                       
                          
                         2 
                       
                       
                         8 
                          
                         
                           πɛ 
                           o 
                         
                          
                         
                           
                             
                               a 
                               2 
                             
                             - 
                             
                               b 
                               2 
                             
                           
                         
                       
                     
                     = 
                     
                       19.242 
                        
                       
                           
                       
                        
                       eV 
                     
                   
                 
               
               
                 
                   ( 
                   30 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The kinetic energy of the electrons is 
         [0000]    
       
         
           
             
               
                 
                   T 
                   = 
                   
                     
                       
                         
                           ℏ 
                           2 
                         
                         
                           4 
                            
                           
                             m 
                             e 
                           
                            
                           a 
                            
                           
                             
                               
                                 a 
                                 2 
                               
                               - 
                               
                                 b 
                                 2 
                               
                             
                           
                         
                       
                        
                       ln 
                        
                       
                           
                       
                        
                       
                         
                           a 
                           + 
                           
                             
                               
                                 a 
                                 2 
                               
                               - 
                               
                                 b 
                                 2 
                               
                             
                           
                         
                         
                           a 
                           - 
                           
                             
                               
                                 a 
                                 2 
                               
                               - 
                               
                                 b 
                                 2 
                               
                             
                           
                         
                       
                     
                     = 
                     
                       
                         - 
                         33.918 
                       
                        
                       
                           
                       
                        
                       eV 
                     
                   
                 
               
               
                 
                   ( 
                   31 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The energy, V m , of the magnetic force between the electrons is 
         [0000]    
       
         
           
             
               
                 
                   
                     V 
                     m 
                   
                   = 
                   
                     
                       
                         
                           - 
                           
                             ℏ 
                             2 
                           
                         
                         
                           4 
                            
                           
                             m 
                             e 
                           
                            
                           a 
                            
                           
                             
                               
                                 a 
                                 2 
                               
                               - 
                               
                                 b 
                                 
                                   2 
                                    
                                   
                                       
                                   
                                 
                               
                             
                           
                         
                       
                        
                       ln 
                        
                       
                           
                       
                        
                       
                         
                           a 
                           + 
                           
                             
                               
                                 a 
                                 2 
                               
                               - 
                               
                                 b 
                                 2 
                               
                             
                           
                         
                         
                           a 
                           - 
                           
                             
                               
                                 a 
                                 2 
                               
                               - 
                               
                                 b 
                                 2 
                               
                             
                           
                         
                       
                     
                     = 
                     
                       
                         - 
                         16.959 
                       
                        
                       
                           
                       
                        
                       eV 
                     
                   
                 
               
               
                 
                   ( 
                   32 
                   ) 
                 
               
             
           
         
       
     
         [0133]    During bond formation, the electrons undergo a reentrant oscillatory orbit with vibration of the protons. The corresponding energy {square root over (E)} osc  is the difference between the Doppler and average vibrational kinetic energies: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       E 
                       _ 
                     
                     osc 
                   
                   = 
                   
                     
                       
                         
                           E 
                           _ 
                         
                         D 
                       
                       + 
                       
                         
                           E 
                           _ 
                         
                         Kvib 
                       
                     
                     = 
                     
                       
                         
                           ( 
                           
                             
                               V 
                               
                                 e 
                                  
                                 
                                     
                                 
                               
                             
                             + 
                             T 
                             + 
                             
                               V 
                               m 
                             
                             + 
                             
                               V 
                               p 
                             
                           
                           ) 
                         
                          
                         
                           
                             
                               2 
                                
                               
                                 
                                   E 
                                   _ 
                                 
                                 K 
                               
                             
                             
                               M 
                                
                               
                                   
                               
                                
                               
                                 c 
                                 2 
                               
                             
                           
                         
                       
                       + 
                       
                         
                           1 
                           2 
                         
                          
                         ℏ 
                          
                         
                           
                             k 
                             μ 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   33 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The total energy is 
         [0000]    
       
         
           
             
               
                 
                   
                     E 
                     T 
                   
                   = 
                   
                     
                       V 
                       e 
                     
                     + 
                     T 
                     + 
                     
                       V 
                       m 
                     
                     + 
                     
                       V 
                       p 
                     
                     + 
                     
                       
                         E 
                         _ 
                       
                       osc 
                     
                   
                 
               
               
                 
                   ( 
                   34 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           E 
                           T 
                         
                         = 
                           
                          
                         
                           - 
                           
                             
                               
                                  
                                 2 
                               
                               
                                 8 
                                  
                                 π 
                                  
                                 
                                     
                                 
                                  
                                 
                                   ɛ 
                                   o 
                                 
                                  
                                 
                                   a 
                                   0 
                                 
                               
                             
                              
                             
                               [ 
                               
                                 
                                   
                                     
                                       ( 
                                       
                                         
                                           2 
                                            
                                           
                                             2 
                                           
                                         
                                         - 
                                         
                                           2 
                                         
                                         + 
                                         
                                           
                                             2 
                                           
                                           2 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 
                                   
                                     
                                       
                                         ln 
                                          
                                         
                                             
                                         
                                          
                                         
                                           
                                             
                                               2 
                                             
                                             + 
                                             1 
                                           
                                           
                                             
                                               2 
                                             
                                             - 
                                             1 
                                           
                                         
                                       
                                       - 
                                       
                                         2 
                                       
                                     
                                   
                                 
                               
                               ] 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             [ 
                             
                               1 
                               + 
                               
                                 
                                   
                                     2 
                                      
                                     ℏ 
                                      
                                     
                                       
                                         
                                            
                                           2 
                                         
                                         
                                           4 
                                            
                                           
                                             πɛ 
                                             o 
                                           
                                            
                                           
                                             a 
                                             0 
                                             3 
                                           
                                         
                                       
                                       
                                         m 
                                         e 
                                       
                                     
                                   
                                   
                                     
                                       m 
                                       e 
                                     
                                      
                                     
                                       c 
                                       2 
                                     
                                   
                                 
                               
                             
                             ] 
                           
                           - 
                           
                             
                               1 
                               2 
                             
                              
                             ℏ 
                              
                             
                               
                                 k 
                                 μ 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             31.689 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   35 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The energy of two hydrogen atoms is 
         [0000]        E (2 H[a   H ])=−27.21 eV   (36) 
         [0000]    The bond dissociation energy, E D , is the difference between the total energy of the corresponding hydrogen atoms (Eq. (36)) and E T  (Eq. (35)). 
         [0000]        E   D   =E (2 H[a   H ])− E   T =4.478 eV   (37) 
         [0000]    The experimental energy is E D =4.478 eV. The calculated and experimental parameters of H 2 , D 2 , H 2   + , and D 2   +  from Ref. [6] and Chp. 11 of Ref. [1] are given in Table 3. 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 The Maxwellian closed-form calculated and experimental 
               
               
                 parameters of H 2 , D 2 , H 2   +  and D 2   + . 
               
             
          
           
               
                 Parameter 
                 Calculated 
                 Experimental 
               
               
                   
               
               
                 H 2  Bond Energy 
                 4.478 eV 
                 4.478 eV 
               
               
                 D 2  Bond Energy 
                 4.556 eV 
                 4.556 eV 
               
               
                 H 2   +  Bond Energy 
                 2.654 eV 
                 2.651 eV 
               
               
                 D 2   +  Bond Energy 
                 2.696 eV 
                 2.691 eV 
               
               
                 H 2  Total Energy 
                 31.677 eV 
                 31.675 eV 
               
               
                 D 2  Total Energy 
                 31.760 eV 
                 31.760 eV 
               
               
                 H 2  Ionization Energy 
                 15.425 eV 
                 15.426 eV 
               
               
                 D 2  Ionization Energy 
                 15.463 eV 
                 15.466 eV 
               
               
                 H 2   +  Ionization Energy 
                 16.253 eV 
                 16.250 eV 
               
               
                 D 2   +  Ionization Energy 
                 16.299 eV 
                 16.294 eV 
               
               
                 H 2   +  Magnetic Moment 
                 9.274 × 10 −24  JT −1  (μ B ) 
                 9.274 × 10 −24   
               
               
                   
                   
                 JT −1  (μ B ) 
               
               
                 Absolute H 2  Gas-Phase 
                 −28.0 ppm 
                 −28.0 ppm 
               
               
                 NMR Shift 
               
               
                 H 2  Internuclear Distance a   
                 0.748 Å 
                 0.741 Å 
               
               
                   
                 {square root over (2)}a o   
               
               
                 D 2  Internuclear Distance a   
                 0.748 Å 
                 0.741 Å 
               
               
                   
                 {square root over (2)}a o   
               
               
                 H 2   +  Internuclear Distance 
                 1.058 Å 
                 1.06 Å 
               
               
                   
                 2a o   
               
               
                 D 2   +  Internuclear Distance a   
                 1.058 Å 
                 1.0559 Å 
               
               
                   
                 2a o   
               
               
                 H 2  Vibrational Energy 
                 0.517 eV 
                 0.516 eV 
               
               
                 D 2  Vibrational Energy 
                 0.371 eV 
                 0.371 eV 
               
               
                 H 2  ω e χ e   
                 120.4 cm −1   
                 121.33 cm −1   
               
               
                 D 2  ω e χ e   
                 60.93 cm −1   
                 61.82 cm −1   
               
               
                 H 2   +  Vibrational Energy 
                 0.270 eV 
                 0.271 eV 
               
               
                 D 2   +  Vibrational Energy 
                 0.193 eV 
                 0.196 eV 
               
               
                 H 2  J = 1 to J = 0 Rotational 
                 0.0148 eV 
                 0.01509 eV 
               
               
                 Energy a   
               
               
                 D 2  J = 1 to J = 0 Rotational 
                 0.00741 eV 
                 0.00755 eV 
               
               
                 Energy a   
               
               
                 H 2   +  J = 1 to J = 0 Rotational 
                 0.00740 eV 
                 0.00739 eV 
               
               
                 Energy 
               
               
                 D 2   +  J = 1 to J = 0 Rotational 
                 0.00370 eV 
                 0.003723 eV 
               
               
                 Energy a   
               
               
                   
               
               
                   a Not corrected for the slight reduction in internuclear distance due to Ē osc . 
               
             
          
         
       
     
       B. Derivation of the General Geometrical and Energy Equations of Organic Chemistry 
       [0134]    Organic molecules comprising an arbitrary number of atoms can be solved using similar principles and procedures as those used to solve alkanes of arbitrary length. Alkanes can be considered to be comprised of the functional groups of CH 3 , CH 2 , and C—C. These groups with the corresponding geometrical parameters and energies can be added as a linear sum to give the solution of any straight chain alkane as shown in the Continuous-Chain Alkanes section of Ref. [1]. Similarly, the geometrical parameters and energies of all functional groups such as those given in Table 1 can be solved. The functional-group solutions can be made into a linear superposition and sum, respectively, to give the solution of any organic molecule. The solutions of the functional groups can be conveniently obtained by using generalized forms of the geometrical and energy equations. The derivation of the dimensional parameters and energies of the function groups are given in the Nature of the Chemical Bond of Hydrogen-Type Molecules, Polyatomic Molecular Ions and Molecules, More Polyatomic Molecules and Hydrocarbons, and Organic Molecular Functional Groups and Molecules sections of Ref. [1]. (Reference to equations of the form Eq. (15.number), Eq. (11.number), Eq. (13.number), and Eq. (14.number) will refer to the corresponding equations of Ref [1].) Additional derivations for other non-organic function groups given in Table 2 are derived in the following sections of Ref. [1]: Applications: Pharmaceuticals, Specialty Molecular Functional Groups and Molecules, Dipoles and Interactions, Nature of the Solid Molecular Bond of the Three Allotropes of Carbon, Silicon Molecular Functional Groups and Molecules, Nature of the Solid Semiconductor Bond of Silicon, Boron Molecues, and Organometallic Molecular Functional Groups and Molecules sections. 
         [0135]    Consider the case wherein at least two atomic orbital hybridize as a linear combination of electrons at the same energy in order to achieve a bond at an energy minimum, and the sharing of electrons between two or more such orbitals to form a MO permits the participating hybridized orbitals to decrease in energy through a decrease in the radius of one or more of the participating orbitals. The force-generalized constant k′ of a H 2 -type ellipsoidal MO due to the equivalent of two point charges of at the foci is given by: 
         [0000]    
       
         
           
             
               
                 
                   
                     k 
                     ′ 
                   
                   = 
                   
                     
                       
                         C 
                         1 
                       
                        
                       
                         C 
                         2 
                       
                        
                       2 
                        
                       
                          
                         2 
                       
                     
                     
                       4 
                        
                       
                         πɛ 
                         0 
                       
                     
                   
                 
               
               
                 
                   ( 
                   38 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where C 1  is the fraction of the H 2 -type ellipsoidal MO basis function of a chemical bond of the molecule or molecular ion which is 0.75 (Eq. (13.59)) in the case of H bonding to a central atom and 0.5 (Eq. (14.152)) otherwise, and C 2  is the factor that results in an equipotential energy match of the participating at least two molecular or atomic orbitals of the chemical bond. From Eqs. (13.58-13.63), the distance from the origin of the MO to each focus c′ is given by: 
         [0000]    
       
         
           
             
               
                 
                   
                     c 
                     ′ 
                   
                   = 
                   
                     
                       a 
                        
                       
                         
                           
                             
                               ℏ 
                               2 
                             
                              
                             4 
                              
                             
                               πɛ 
                               0 
                             
                           
                           
                             
                               m 
                               e 
                             
                              
                             
                                
                               2 
                             
                              
                             2 
                              
                             
                               C 
                               1 
                             
                              
                             
                               C 
                               2 
                             
                              
                             a 
                           
                         
                       
                     
                     = 
                     
                       
                         
                           aa 
                           0 
                         
                         
                           2 
                            
                           
                             C 
                             1 
                           
                            
                           
                             C 
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   39 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The internuclear distance is 
         [0000]    
       
         
           
             
               
                 
                   
                     2 
                      
                     
                       c 
                       ′ 
                     
                   
                   = 
                   
                     2 
                      
                     
                       
                         
                           aa 
                           0 
                         
                         
                           2 
                            
                           
                             C 
                             1 
                           
                            
                           
                             C 
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   40 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The length of the semiminor axis of the prolate spheroidal MO b=c is given by 
         [0000]        b =√{square root over ( a   2   −c   ′2 )}  (41) 
         [0136]    And, the eccentricity, e, is 
         [0000]    
       
         
           
             
               
                 
                   e 
                   = 
                   
                     
                       c 
                       ′ 
                     
                     a 
                   
                 
               
               
                 
                   ( 
                   42 
                   ) 
                 
               
             
           
         
       
     
         [0000]    From Eqs. (11.207-11.212), the potential energy of the two electrons in the central field of the nuclei at the foci is 
         [0000]    
       
         
           
             
               
                 
                   
                     V 
                     e 
                   
                   = 
                   
                     
                       n 
                       1 
                     
                      
                     
                       c 
                       1 
                     
                      
                     
                       c 
                       2 
                     
                      
                     
                       
                         
                           - 
                           2 
                         
                          
                         
                            
                           2 
                         
                       
                       
                         8 
                          
                         
                           πɛ 
                           o 
                         
                          
                         
                           
                             
                               a 
                               2 
                             
                             - 
                             
                               b 
                               2 
                             
                           
                         
                       
                     
                      
                     ln 
                      
                     
                         
                     
                      
                     
                       
                         a 
                         + 
                         
                           
                             
                               a 
                               2 
                             
                             - 
                             
                               b 
                               2 
                             
                           
                         
                       
                       
                         a 
                         - 
                         
                           
                             
                               a 
                               2 
                             
                             - 
                             
                               b 
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   43 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The potential energy of the two nuclei is 
         [0000]    
       
         
           
             
               
                 
                   
                     V 
                     p 
                   
                   = 
                   
                     
                       n 
                       1 
                     
                      
                     
                       
                          
                         2 
                       
                       
                         8 
                          
                         
                           πɛ 
                           o 
                         
                          
                         
                           
                             
                               a 
                               2 
                             
                             - 
                             
                               b 
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   44 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The kinetic energy of the electrons is 
         [0000]    
       
         
           
             
               
                 
                   T 
                   = 
                   
                     
                       n 
                       1 
                     
                      
                     
                       c 
                       1 
                     
                      
                     
                       c 
                       2 
                     
                      
                     
                       
                         ℏ 
                         2 
                       
                       
                         2 
                          
                         
                           m 
                           e 
                         
                          
                         a 
                          
                         
                           
                             
                               a 
                               2 
                             
                             - 
                             
                               b 
                               2 
                             
                           
                         
                       
                     
                      
                     ln 
                      
                     
                         
                     
                      
                     
                       
                         a 
                         + 
                         
                           
                             
                               a 
                               2 
                             
                             - 
                             
                               b 
                               2 
                             
                           
                         
                       
                       
                         a 
                         - 
                         
                           
                             
                               a 
                               2 
                             
                             - 
                             
                               b 
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   45 
                   ) 
                 
               
             
           
         
       
     
         [0000]    And, the energy, V m , of the magnetic force between the electrons is 
         [0000]    
       
         
           
             
               
                 
                   
                     V 
                     m 
                   
                   = 
                   
                     
                       n 
                       1 
                     
                      
                     
                       c 
                       1 
                     
                      
                     
                       c 
                       2 
                     
                      
                     
                       
                         - 
                         
                           ℏ 
                           2 
                         
                       
                       
                         4 
                          
                         
                           m 
                           e 
                         
                          
                         a 
                          
                         
                           
                             
                               a 
                               2 
                             
                             - 
                             
                               b 
                               2 
                             
                           
                         
                       
                     
                      
                     ln 
                      
                     
                         
                     
                      
                     
                       
                         a 
                         + 
                         
                           
                             
                               a 
                               2 
                             
                             - 
                             
                               b 
                               2 
                             
                           
                         
                       
                       
                         a 
                         - 
                         
                           
                             
                               a 
                               2 
                             
                             - 
                             
                               b 
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   46 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The total energy of the H 2 -type prolate spheroidal MO, E T (H 2 MO), is given by the sum of the energy terms: 
         [0000]    
       
         
           
             
               
                 
                   
                     E 
                     
                       T 
                       
                         ( 
                         
                           
                             H 
                             2 
                           
                            
                           MO 
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       V 
                       e 
                     
                     + 
                     T 
                     + 
                     
                       V 
                       m 
                     
                     + 
                     
                       V 
                       p 
                     
                   
                 
               
               
                 
                   ( 
                   47 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           E 
                           
                             T 
                             
                               ( 
                               
                                 
                                   H 
                                   2 
                                 
                                  
                                 MO 
                               
                               ) 
                             
                           
                         
                         = 
                           
                          
                         
                           - 
                           
                             
                               
                                 
                                   n 
                                   1 
                                 
                                  
                                 
                                    
                                   2 
                                 
                               
                               
                                 8 
                                  
                                 π 
                                  
                                 
                                     
                                 
                                  
                                 
                                   ɛ 
                                   o 
                                 
                                  
                                 
                                   
                                     
                                       a 
                                       2 
                                     
                                     - 
                                     
                                       b 
                                       2 
                                     
                                   
                                 
                               
                             
                              
                             
                               [ 
                               
                                 
                                   
                                     
                                       
                                         c 
                                         1 
                                       
                                        
                                       
                                         
                                           c 
                                           2 
                                         
                                          
                                         
                                           ( 
                                           
                                             2 
                                             - 
                                             
                                               
                                                 a 
                                                 0 
                                               
                                               a 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       
                                         ln 
                                          
                                         
                                             
                                         
                                          
                                         
                                           
                                             a 
                                             + 
                                             
                                               
                                                 
                                                   a 
                                                   2 
                                                 
                                                 - 
                                                 
                                                   b 
                                                   2 
                                                 
                                               
                                             
                                           
                                           
                                             a 
                                             - 
                                             
                                               
                                                 
                                                   a 
                                                   2 
                                                 
                                                 - 
                                                 
                                                   b 
                                                   2 
                                                 
                                               
                                             
                                           
                                         
                                       
                                       - 
                                       1 
                                     
                                   
                                 
                               
                               ] 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           - 
                           
                             
                               
                                 
                                   n 
                                   1 
                                 
                                  
                                 
                                    
                                   2 
                                 
                               
                               
                                 8 
                                  
                                 
                                   πɛ 
                                   0 
                                 
                                  
                                 
                                   c 
                                   ′ 
                                 
                               
                             
                              
                             
                               [ 
                               
                                 
                                   
                                     c 
                                     1 
                                   
                                    
                                   
                                     
                                       c 
                                       2 
                                     
                                      
                                     
                                       ( 
                                       
                                         2 
                                         - 
                                         
                                           
                                             a 
                                             0 
                                           
                                           a 
                                         
                                       
                                       ) 
                                     
                                   
                                    
                                   ln 
                                    
                                   
                                       
                                   
                                    
                                   
                                     
                                       a 
                                       + 
                                       
                                         c 
                                         ′ 
                                       
                                     
                                     
                                       a 
                                       - 
                                       
                                         c 
                                         ′ 
                                       
                                     
                                   
                                 
                                 - 
                                 1 
                               
                               ] 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   48 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where n 1  is the number of equivalent bonds of the MO. c 1  is the fraction of the H 2 -type ellipsoidal MO basis function of an MO which is 0.75 (Eqs. (13.67-13.73)) in the case of H bonding to an unhybridized central atom and 1 otherwise, and c 2  is the factor that results in an equipotential energy match of the participating the MO and the at least two atomic orbitals of the chemical bond. Specifically, to meet the equipotential condition and energy matching conditions for the union of the H 2 -type-ellipsoidal-MO and the HOs or AOs of the bonding atoms, the factor c 2  of a H 2 -type ellipsoidal MO may given by (i) one, (ii) the ratio of the Coulombic or valence energy of the AO or HO of at least one atom of the bond and 13.605804 eV, the Coulombic energy between the electron and proton of H, (iii) the ratio of the valence energy of the AO or HO of one atom and the Coulombic energy of another, (iv) the ratio of the valence energies of the AOs or HOs of two atoms, (v) the ratio of two c 2  factors corresponding to any of cases (ii)-(iv), and (vi) the product of two different c 2  factors corresponding to any of the cases (i)-(v). Specific examples of the factor c 2  of a H 2 -type ellipsoidal MO given in previously [1 9  are
       0.936127, the ratio of the ionization energy of N 14.53414 eV and 13.605804 eV, the Coulombic energy between the electron and proton of H;   0.91771, the ratio of 14.82575 eV, −E Coulomb (C,2sp 3 ), and 13.605804 eV;   0.87495, the ratio of 15.55033 eV, −E Coulomb (C ethane ,2sp 3 ), and 13.605804 eV;   0.85252, the ratio of 15.95955 eV, −E Coulomb (C ethylene ,2sp 3 ), and 13.605804 eV;   0.85252, the ratio of 15.95955 eV, −E Coulomb (C benzene ,2sp 3 ), and 13.605804 eV, and   0.86359, the ratio of 15.55033 eV, −E Coulomb (C alkane ,2sp 3 ), and 11605804 eV.       
 
         [0143]    In the generalization of the hybridization of at least two atomic-orbital shells to form a shell of hybrid orbitals, the hybridized shell comprises a linear combination of the electrons of the atomic-orbital shells. The radius of the hybridized shell is calculated from the total Coulombic energy equation by considering that the central field decreases by an integer for each successive electron of the shell and that the total energy of the shell is equal to the total Coulombic energy of the initial AO electrons. The total energy E T (atom,msp 3 ) (m is the integer of the valence shell) of the AO electrons and the hybridized shell is given by the sum of energies of successive ions of the atom over the n electrons comprising total electrons of the at least one AO shell. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       E 
                       T 
                     
                      
                     
                       ( 
                       
                         atom 
                         , 
                         
                           msp 
                           3 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     - 
                     
                       
                         ∑ 
                         
                           m 
                           = 
                           1 
                         
                         n 
                       
                        
                       
                         IP 
                         m 
                       
                     
                   
                 
               
               
                 
                   ( 
                   49 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where IP m  is the m th ionization energy (positive) of the atom. The radius r msp     3    of the hybridized shell is given by: 
         [0000]    
       
         
           
             
               
                 
                   
                     r 
                     
                       msp 
                       3 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         
                           q 
                           = 
                           
                             Z 
                             - 
                             n 
                           
                         
                          
                         
                             
                         
                       
                       
                         Z 
                         - 
                         1 
                       
                     
                      
                     
                       
                         
                           - 
                           
                             ( 
                             
                               Z 
                               - 
                               q 
                             
                             ) 
                           
                         
                          
                         
                            
                           2 
                         
                       
                       
                         8 
                          
                         
                           πɛ 
                           0 
                         
                          
                         
                           
                             E 
                             T 
                           
                            
                           
                             ( 
                             
                               atom 
                               , 
                               
                                 msp 
                                 3 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   50 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Then, the Coulombic energy E Coulomb  (atom, msp 3 ) of the outer electron of the atom msp 3  shell is given by 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       E 
                       Coulomb 
                     
                      
                     
                       ( 
                       
                         atom 
                         , 
                         
                           msp 
                           3 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       - 
                       
                          
                         
                           2 
                            
                           
                               
                           
                         
                       
                     
                     
                       8 
                        
                       π 
                        
                       
                           
                       
                        
                       
                         ɛ 
                         0 
                       
                        
                       
                         r 
                         
                           msp 
                           3 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   51 
                   ) 
                 
               
             
           
         
       
     
         [0144]    In the case that during hybridization at least one of the spin-paired AO electrons is unpaired in the hybridized orbital (HO), the energy change for the promotion to the unpaired state is the magnetic energy E(magnetic) at the initial radius r of the AO electron: 
         [0000]    
       
         
           
             
               
                 
                   
                     E 
                      
                     
                       ( 
                       magnetic 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         2 
                          
                         
                           πμ 
                           0 
                         
                          
                         
                            
                           2 
                         
                          
                         
                           ℏ 
                           2 
                         
                       
                       
                         
                           m 
                           e 
                           2 
                         
                          
                         
                           r 
                           3 
                         
                       
                     
                      
                     
                         
                     
                     = 
                     
                       
                         8 
                          
                         
                           πμ 
                           o 
                         
                          
                         
                           μ 
                           B 
                           2 
                         
                       
                       
                         r 
                         3 
                       
                     
                   
                 
               
               
                 
                   ( 
                   52 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Then, the energy E(atom,msp 3 ) of the outer electron of the atom msp 3  shell is given by the sum of E Coulomb (atom, msp 3 ) and E(magnetic): 
         [0000]    
       
         
           
             
               
                 
                   
                     E 
                      
                     
                       ( 
                       
                         atom 
                         , 
                         
                           msp 
                           3 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         - 
                         
                            
                           2 
                         
                       
                       
                         8 
                          
                         
                           πɛ 
                           0 
                         
                          
                         
                           r 
                           
                             msp 
                             3 
                           
                         
                       
                     
                     + 
                     
                       
                         2 
                          
                         
                           πμ 
                           0 
                         
                          
                         
                            
                           2 
                         
                          
                         
                           ℏ 
                           2 
                         
                       
                       
                         
                           m 
                           e 
                           2 
                         
                          
                         
                           r 
                           3 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   53 
                   ) 
                 
               
             
           
         
       
     
         [0145]    Consider next that the at least two atomic orbitals hybridize as a linear combination of electrons at the same energy in order to achieve a bond at an energy minimum with another atomic orbital or hybridized orbital. As a further generalization of the basis of the stability of the MO, the sharing of electrons between two or more such hybridized orbitals to form a MO permits the participating hybridized orbitals to decrease in energy through a decrease in the radius of one or more of the participating orbitals. In this case, the total energy of the hybridized orbitals is given by the sum of E(atom,msp 3 ) and the next energies of successive ions of the atom over the n electrons comprising the total electrons of the at least two initial AO shells. Here, E(atom,msp 3 ) is the sum of the first ionization energy of the atom and the hybridization energy. An example of E(atom,msp 3 ) for E(C,2sp 3 ) is given in Eq. (14.503) where the sum of the negative of the first ionization energy of C, −11.27671 eV, plus the hybridization energy to form the C2sp 3  shell given by Eq. (14.146) is 
         [0000]        E ( C, 2 sp   3 )=−14.63489 eV. 
         [0146]    Thus, the sharing of electrons between two atom msp 3  HOs to form an atom-atom-bond MO permits each participating hybridized orbital to decrease in radius and energy. In order to further satisfy the potential, kinetic, and orbital energy relationships, each atom msp 3  HO donates an excess of 25% per bond of its electron density to the atom-atom-bond MO to form an energy minimum wherein the atom-atom bond comprises one of a single, double, or triple bond. In each case, the radius of the hybridized shell is calculated from the Coulombic energy equation by considering that the central field decreases by an integer for each successive electron of the shell and the total energy of the shell is equal to the total Coulombic energy of the initial AO electrons plus the hybridization energy. The total energy E T (mol.atom,msp 3 ) (m is the integer of the valence shell) of the HO electrons is given by the sum of energies of successive ions of the atom over the n electrons comprising total electrons of the at least one initial AO shell and the hybridization energy: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       E 
                       T 
                     
                      
                     
                       ( 
                       
                         
                           mol 
                           . 
                           atom 
                         
                         , 
                         
                           msp 
                           3 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       E 
                        
                       
                         ( 
                         
                           atom 
                           , 
                           
                             msp 
                             3 
                           
                         
                         ) 
                       
                     
                     - 
                     
                       
                         ∑ 
                         
                           m 
                           = 
                           2 
                         
                         n 
                       
                        
                       
                         IP 
                         m 
                       
                     
                   
                 
               
               
                 
                   ( 
                   54 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where IP m  is the m th ionization energy (positive) of the atom and the sum of −IP 1  plus the hybridization energy is E(atom,msp 3 ). Thus, the radius r msp     3    of the hybridized shell due to its donation of a total charge −Qe to the corresponding MO is given by is given by: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           
                             msp 
                             3 
                           
                         
                         = 
                           
                          
                         
                           
                             ( 
                             
                               
                                 
                                   ∑ 
                                   
                                     q 
                                     = 
                                     
                                       Z 
                                       - 
                                       n 
                                     
                                   
                                   
                                     Z 
                                     - 
                                     1 
                                   
                                 
                                  
                                 
                                   ( 
                                   
                                     Z 
                                     - 
                                     q 
                                   
                                   ) 
                                 
                               
                               - 
                               Q 
                             
                             ) 
                           
                            
                           
                             
                               - 
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 
                                   E 
                                   T 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       mol 
                                       . 
                                       atom 
                                     
                                     , 
                                     
                                       msp 
                                       3 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             ( 
                             
                               
                                 
                                   ∑ 
                                   
                                     q 
                                     = 
                                     
                                       Z 
                                       - 
                                       n 
                                     
                                   
                                   
                                     Z 
                                     - 
                                     1 
                                   
                                 
                                  
                                 
                                   ( 
                                   
                                     Z 
                                     - 
                                     q 
                                   
                                   ) 
                                 
                               
                               - 
                               
                                 s 
                                  
                                 
                                   ( 
                                   0.25 
                                   ) 
                                 
                               
                             
                             ) 
                           
                            
                           
                             
                               - 
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 
                                   E 
                                   T 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       mol 
                                       . 
                                       atom 
                                     
                                     , 
                                     
                                       msp 
                                       3 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   55 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where −e is the fundamental electron charge and s=1,2,3 for a single, double, and triple bond, respectively. The Coulombic energy E Coulomb (mol.atom,msp 3 ) of the outer electron of the atom msp 3  shell is given by 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       E 
                       Coulomb 
                     
                      
                     
                       ( 
                       
                         
                           mol 
                           . 
                           atom 
                         
                         , 
                         
                           msp 
                           3 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       - 
                       
                          
                         2 
                       
                     
                     
                       8 
                        
                       
                         πɛ 
                         0 
                       
                        
                       
                         r 
                         
                           msp 
                           3 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   56 
                   ) 
                 
               
             
           
         
       
     
         [0147]    In the case that during hybridization at least one of the spin-paired AO electrons is unpaired in the hybridized orbital (HO), the energy change for the promotion to the unpaired state is the magnetic energy E(magnetic) at the initial radius r of the AO electron given by Eq. (52). Then, the energy E (mol.atom,msp 3 ) of the outer electron of the atom msp 3  shell is given by the sum of E Coulomb  (mol.atom,msp 3 ) and E(magnetic): 
         [0000]    
       
         
           
             
               
                 
                   
                     E 
                      
                     
                       ( 
                       
                         
                           mol 
                           . 
                           atom 
                         
                         , 
                         
                           msp 
                           3 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         - 
                         
                            
                           2 
                         
                       
                       
                         8 
                          
                         
                           πɛ 
                           0 
                         
                          
                         
                           r 
                           
                             msp 
                             3 
                           
                         
                       
                     
                     + 
                     
                       
                         2 
                          
                         
                           πμ 
                           0 
                         
                          
                         
                            
                           2 
                         
                          
                         
                           ℏ 
                           2 
                         
                       
                       
                         
                           m 
                           e 
                           2 
                         
                          
                         
                           r 
                           3 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   57 
                   ) 
                 
               
             
           
         
       
     
         [0000]    E T  (atom-atom, msp 3 ), the energy change of each atom msp 3  shell with the formation of the atom-atom-bond MO is given by the difference between E(mol.atom,msp 3 ) and E (atom,msp 3 ): 
         [0000]        E   T (atom-atom, msp 3 )= E (mol.atom,msp 3 )− E (atom,msp 3 )   (58) 
         [0000]    In the case of the C2sp 3  HO, the initial parameters (Eqs. (14.142-14.146)) are 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           
                             2 
                              
                             
                               sp 
                               3 
                             
                           
                         
                         = 
                           
                          
                         
                           
                             ∑ 
                             
                               n 
                               = 
                               2 
                             
                             5 
                           
                            
                           
                             
                               
                                 ( 
                                 
                                   Z 
                                   - 
                                   n 
                                 
                                 ) 
                               
                                
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               
                                 
                                   πɛ 
                                   0 
                                 
                                  
                                 
                                   ( 
                                   
                                     e 
                                      
                                     
                                         
                                     
                                      
                                     148.25751 
                                      
                                     
                                         
                                     
                                      
                                     eV 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             10 
                              
                             
                                 
                             
                              
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 ( 
                                 
                                   e 
                                    
                                   
                                       
                                   
                                    
                                   148.25751 
                                    
                                   
                                       
                                   
                                    
                                   eV 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           0.91771 
                            
                           
                             a 
                             0 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   59 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             Coulomb 
                           
                            
                           
                             ( 
                             
                               C 
                               , 
                               
                                 2 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             
                               r 
                               
                                 2 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             0.91771 
                              
                             
                               a 
                               0 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             14.82575 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   60 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           E 
                            
                           
                             ( 
                             magnetic 
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             2 
                              
                             
                               πμ 
                               0 
                             
                              
                             
                                
                               2 
                             
                              
                             
                               ℏ 
                               2 
                             
                           
                           
                             
                               
                                 m 
                                 e 
                                 2 
                               
                                
                               
                                 ( 
                                 
                                   r 
                                   3 
                                 
                                 ) 
                               
                             
                             3 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             8 
                              
                             
                               πμ 
                               o 
                             
                              
                             
                               μ 
                               B 
                               2 
                             
                           
                           
                             
                               ( 
                               
                                 0.84317 
                                  
                                 
                                   a 
                                   0 
                                 
                               
                               ) 
                             
                             3 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           0.19086 
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   61 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           E 
                            
                           
                             ( 
                             
                               C 
                               , 
                               
                                 2 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               - 
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 r 
                                 
                                   2 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                             
                           
                           + 
                           
                             
                               2 
                                
                               
                                 πμ 
                                 0 
                               
                                
                               
                                  
                                 2 
                               
                                
                               
                                 ℏ 
                                 2 
                               
                             
                             
                               
                                 
                                   m 
                                   e 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     r 
                                     3 
                                   
                                   ) 
                                 
                               
                               3 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               14.82575 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             0.19086 
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             14.63489 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   62 
                   ) 
                 
               
             
             
               
                 
                   
                     In 
                      
                     
                         
                     
                      
                     
                       Eq 
                       . 
                       
                           
                       
                        
                       
                         ( 
                         55 
                         ) 
                       
                     
                   
                   , 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       ∑ 
                       
                         q 
                         = 
                         
                           Z 
                           - 
                           n 
                         
                       
                       
                         Z 
                         - 
                         1 
                       
                     
                      
                     
                       ( 
                       
                         Z 
                         - 
                         q 
                       
                       ) 
                     
                   
                   = 
                   10 
                 
               
               
                 
                   ( 
                   63 
                   ) 
                 
               
             
             
               
                 
                   
                     Eqs 
                     . 
                     
                         
                     
                      
                     
                       ( 
                       14.147 
                       ) 
                     
                   
                    
                   
                       
                   
                    
                   and 
                    
                   
                       
                   
                    
                   
                     ( 
                     54 
                     ) 
                   
                    
                   
                       
                   
                    
                   give 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       E 
                       T 
                     
                      
                     
                       ( 
                       
                         
                           mol 
                           . 
                           atom 
                         
                         , 
                         
                           msp 
                           3 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         E 
                         T 
                       
                        
                       
                         ( 
                         
                           
                             C 
                             ethane 
                           
                           , 
                           
                             2 
                              
                             
                               sp 
                               3 
                             
                           
                         
                         ) 
                       
                     
                     = 
                     
                       
                         - 
                         151.61569 
                       
                        
                       
                           
                       
                        
                       eV 
                     
                   
                 
               
               
                 
                   ( 
                   64 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Using Eqs. (55-65), the final values of r C2sp     3   , E Coulomb (C2sp 3 ), and E(C2sp 3 ), and the resulting E T (C BO —C,C2sp 3 ) of the MO due to charge donation from the HO to the MO where C BO —C refers to the bond order of the carbon-carbon bond for different values of the parameter s are given in Table 4. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 The final values of r C2sp   3 , E Coulomb (C2sp 3 ), and E(C2sp 3 ) and the resulting 
               
               
                 E T (C BO —C,C2sp 3 ) of the MO due to charge donation from the HO to the 
               
               
                 MO where C BO —C refers to the bond order of the carbon-carbon bond. 
               
             
          
           
               
                 MO 
                   
                   
                   
                   
                   
                   
               
               
                 Bond 
                   
                   
                   
                 E Coulomb (C2sp 3 ) 
                 E(C2sp 3 ) 
               
               
                 Order 
                   
                   
                 r C2sp   3 (a 0 ) 
                 (eV) 
                 (eV) 
                 E T (C BO —C,C2sp 3 ) 
               
               
                 (BO) 
                 s 1   
                 s 2   
                 Final 
                 Final 
                 Final 
                 (eV) 
               
               
                   
               
             
          
           
               
                 I 
                 1 
                 0 
                 0.87495 
                 −15.55033 
                 −15.35946 
                 −0.72457 
               
               
                 II 
                 2 
                 0 
                 0.85252 
                 −15.95955 
                 −15.76868 
                 −1.13379 
               
               
                 III 
                 3 
                 0 
                 0.83008 
                 −16.39089 
                 −16.20002 
                 −1.56513 
               
               
                 IV 
                 4 
                 0 
                 0.80765 
                 −16.84619 
                 −16.65532 
                 −2.02043 
               
               
                   
               
             
          
         
       
     
         [0148]    In another generalized case of the basis of forming a minimum-energy bond with the constraint that it must meet the energy matching condition for all MOs at all HOs or AOs, the energy E(mol.atom,msp 3 ) of the outer electron of the atom msp 3  shell of each bonding atom must be the average of E(mol.atom,msp 3 ) for two different values of s: 
         [0000]    
       
         
           
             
               
                 
                   
                     E 
                      
                     
                       ( 
                       
                         
                           mol 
                           . 
                           atom 
                         
                         , 
                         
                           msp 
                           3 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           
                             
                               E 
                                
                               
                                 ( 
                                 
                                   
                                     mol 
                                     . 
                                     
                                       atom 
                                        
                                       
                                         ( 
                                         
                                           s 
                                           1 
                                         
                                         ) 
                                       
                                     
                                   
                                   , 
                                   
                                     msp 
                                     3 
                                   
                                 
                                 ) 
                               
                             
                             + 
                           
                         
                       
                       
                         
                           
                             E 
                              
                             
                               ( 
                               
                                 
                                   mol 
                                   . 
                                   
                                     atom 
                                      
                                     
                                       ( 
                                       
                                         s 
                                         2 
                                       
                                       ) 
                                     
                                   
                                 
                                 , 
                                 
                                   msp 
                                   3 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                     2 
                   
                 
               
               
                 
                   ( 
                   65 
                   ) 
                 
               
             
           
         
       
     
         [0000]    In this case, E T (atom-atom,msp 3 ), the energy change of each atom msp 3  shell with the formation of each atom-atom-bond MO, is average for two different values of s: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       E 
                       T 
                     
                      
                     
                       ( 
                       
                         
                           atom 
                           - 
                           atom 
                         
                         , 
                         
                           msp 
                           3 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           
                             
                               
                                 E 
                                 T 
                               
                                
                               
                                 ( 
                                 
                                   
                                     atom 
                                     - 
                                     
                                       atom 
                                        
                                       
                                         ( 
                                         
                                           s 
                                           1 
                                         
                                         ) 
                                       
                                     
                                   
                                   , 
                                   
                                     msp 
                                     3 
                                   
                                 
                                 ) 
                               
                             
                             + 
                           
                         
                       
                       
                         
                           
                             
                               E 
                               T 
                             
                              
                             
                               ( 
                               
                                 
                                   atom 
                                   - 
                                   
                                     atom 
                                      
                                     
                                       ( 
                                       
                                         s 
                                         2 
                                       
                                       ) 
                                     
                                   
                                 
                                 , 
                                 
                                   msp 
                                   3 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                     2 
                   
                 
               
               
                 
                   ( 
                   66 
                   ) 
                 
               
             
           
         
       
     
         [0149]    Consider an aromatic molecule such as benzene given in the Benzene Molecule section of Ref. [1]. Each C═C double bond comprises a linear combination of a factor of 0.75 of four paired electrons (three electrons) from two sets of two C2sp 3  HOs of the participating carbon atoms. Each C—H bond of CH having two spin-paired electrons, one from an initially unpaired electron of the carbon atom and the other from the hydrogen atom, comprises the linear combination of 75% H 2 -type ellipsoidal MO and 25% C2sp 3  HO as given by Eq. (13.439). However, E T (atom-atom, msp 3 ) of the C—H-bond MO is given by 0.5E T (C═C,2sp 3 ) (Eq. (14.247)) corresponding to one half of a double bond that matches the condition for a single-bond order for C—H that is lowered in energy due to the aromatic character of the bond. 
         [0150]    A further general possibility is that a minimum-energy bond is achieved with satisfaction of the potential, kinetic, and orbital energy relationships by the formation of an MO comprising an allowed multiple of a linear combination of H 2 -type ellipsoidal MOs and corresponding HOs or AOs that contribute a corresponding allowed multiple (e.g. 0.5, 0.75, 1) of the bond order given in Table 4. For example, the alkane MO given in the Continuous-Chain Alkanes section of Ref. [1] comprises a linear combination of factors of 0.5 of a single bond and 0.5 of a double bond. 
         [0151]    Consider a first MO and its HOs comprising a linear combination of bond orders and a second MO that shares a HO with the first. In addition to the mutual HO, the second MO comprises another AO or HO having a single bond order or a mixed bond order. Then, in order for the two MOs to be energy matched, the bond order of the second MO and its HOs or its HO and AO is a linear combination of the terms corresponding to the bond order of the mutual HO and the bond order of the independent HO or AO. Then, in general, E T (atom-atom,msp 3 ), the energy change of each atom msp 3  shell with the formation of each atom-atom-bond MO, is a weighted linear sum for different values of s that matches the energy of the bonded MOs, HOs, and AOs: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       E 
                       T 
                     
                      
                     
                       ( 
                       
                         
                           atom 
                           - 
                           atom 
                         
                         , 
                         
                           msp 
                           3 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         n 
                         = 
                         1 
                       
                       N 
                     
                      
                     
                       
                         c 
                         
                           s 
                           n 
                         
                       
                        
                       
                         
                           E 
                           T 
                         
                          
                         
                           ( 
                           
                             
                               atom 
                               - 
                               
                                 atom 
                                  
                                 
                                   ( 
                                   
                                     s 
                                     n 
                                   
                                   ) 
                                 
                               
                             
                             , 
                             
                               msp 
                               3 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   67 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where c s     n    is the multiple of the BO of s n . The radius r msp     3    of the atom msp 3  shell of each bonding atom is given by the Coulombic energy using the initial energy E Coulomb  (atom,msp 3 ) and E T (atom-atom,msp 3 ), the energy change of each atom msp 3  shell with the formation of each atom-atom-bond MO: 
         [0000]    
       
         
           
             
               
                 
                   
                     r 
                     
                       msp 
                       3 
                     
                   
                   = 
                   
                     
                       - 
                       
                          
                         2 
                       
                     
                     
                       8 
                        
                       
                         πɛ 
                         0 
                       
                        
                       
                         
                           a 
                           0 
                         
                          
                         
                           ( 
                           
                             
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         
                                           E 
                                           Coulonb 
                                         
                                          
                                         atom 
                                       
                                       , 
                                       
                                         msp 
                                         3 
                                       
                                     
                                     ) 
                                   
                                   + 
                                 
                               
                             
                             
                               
                                 
                                   
                                     E 
                                     T 
                                   
                                    
                                   
                                     ( 
                                     
                                       
                                         atom 
                                         - 
                                         atom 
                                       
                                       , 
                                       
                                         msp 
                                         3 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   68 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where E Coulomb (C2sp 3 )=−14.825751 eV. The Coulombic energy E Coulomb (mol.atom,msp 3 ) of the outer electron of the atom msp 3  shell is given by Eq. (56). In the case that during hybridization, at least one of the spin-paired AO electrons is unpaired in the hybridized orbital (HO), the energy change for the promotion to the unpaired state is the magnetic energy E(magnetic) (Eq. (52)) at the initial radius r of the AO electron. Then, the energy E(mol.atom,msp 3 ) of the outer electron of the atom msp 3  shell is given by the sum of E Coulomb (mol.atom,msp 3 ) and E(magnetic) (Eq. (57)). E T (atom-atom,msp 3 ), the energy change of each atom msp 3  shell with the formation of the atom-atom-bond MO is given by the difference between E(mol.atom,msp 3 ) and E(atom,msp 3 ) given by Eq. (58). Using Eq. (60) for E Coulomb (C,2sp 3 ) in Eq. (68), the single bond order energies given by Eqs. (55-64) and shown in Table 4, and the linear combination energies (Eqs. (65-67)), the parameters of linear combinations of bond orders and linear combinations of mixed bond orders are given in Table 5. 
         [0152]    Table 5. The final values of r C2sp     3   , E Coulomb (C2sp 3 ), and E(C2sp 3 ) and the resulting E T (C BO —C, C2sp 3 ) of the MO comprising a linear combination of H 2 -type ellipsoidal MOs and corresponding HOs of single or mixed bond order where c s     n    is the multiple of the bond order parameter E T (atom-atom(s n ),msp 3 ) given in Table 4. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                 The final value of r C2sp     3   , E Coulomb (C2sp 3 ), and E(C2sp 3 ) and the 
               
               
                 resulting E T (C BO —C,C2sp 3 ) of the MO comprising a linear combination of 
               
               
                 H 2 -type ellipsoidal MOs and corresponding HOs of single or mixed bond under where c s     n    is the 
               
               
                 multiple bond order parameter E T (atom - atom(s n ), msp 3 ) given in Table 4. 
               
             
          
           
               
                 MO 
                   
                   
                   
                   
                   
                   
                   
                 E Coulomb (C2sp 3 ) 
                 E(C2sp 3 ) 
                   
               
               
                 Bond Order 
                   
                   
                   
                   
                   
                   
                 r C2sp     3   (a 0 ) 
                 (eV) 
                 (eV) 
                 E T (C BO —C,C2sp 3 ) 
               
               
                 (BO) 
                 s 1   
                 c s     1     
                 s 2   
                 c s     2     
                 s 3   
                 c s     3     
                 Final 
                 Final 
                 Final 
                 (eV) 
               
               
                   
               
             
          
           
               
                 1/2I 
                 1 
                 0.5 
                 0 
                 0 
                 0 
                 0 
                 0.89582 
                 −15.18804 
                 −14.99717 
                 −0.36228 
               
               
                 1/2II 
                 2 
                 0.5 
                 0 
                 0 
                 0 
                 0 
                 0.88392 
                 −15.39265 
                 −15.20178 
                 −0.56689 
               
               
                 1/2I + 1/4II 
                 1 
                 0.5 
                 2 
                 0.25 
                 0 
                 0 
                 0.87941 
                 −15.47149 
                 −15.28062 
                 −0.64573 
               
               
                 1/4II + 1/4(I + 
                 2 
                 0.25 
                 1 
                 0.25 
                 2 
                 0.25 
                 0.87363 
                 −15.57379 
                 −15.38293 
                 −0.74804 
               
               
                 II) 
               
               
                 3/4II 
                 2 
                 0.75 
                 0 
                 0 
                 0 
                 0 
                 0.86793 
                 −15.67610 
                 −15.48523 
                 −0.85034 
               
               
                 1/2I + 1/2II 
                 1 
                 0.5 
                 2 
                 0.5 
                 0 
                 0 
                 0.86359 
                 −15.75493 
                 −15.56407 
                 −0.92918 
               
               
                 1/2I + 1/2III 
                 1 
                 0.5 
                 3 
                 0.5 
                 0 
                 0 
                 0.85193 
                 −15.97060 
                 −15.77974 
                 −1.14485 
               
               
                 1/2I + 1/2IV 
                 1 
                 0.5 
                 4 
                 0.5 
                 0 
                 0 
                 0.83995 
                 −16.19826 
                 −16.00739 
                 −1.37250 
               
               
                 1/2II + 1/2III 
                 2 
                 0.5 
                 3 
                 0.5 
                 0 
                 0 
                 0.84115 
                 −16.17521 
                 −15.98435 
                 −1.34946 
               
               
                 1/2II + 1/2IV 
                 2 
                 0.5 
                 4 
                 0.5 
                 0 
                 0 
                 0.82948 
                 −16.40286 
                 −16.21200 
                 −1.57711 
               
               
                 I + 1/2(I + II) 
                 1 
                 1 
                 1 
                 0.5 
                 2 
                 0.5 
                 0.82562 
                 −16.47951 
                 −16.28865 
                 −1.65376 
               
               
                 1/2III + 1/2IV 
                 3 
                 0.5 
                 4 
                 0.5 
                 0 
                 0 
                 0.81871 
                 −16.61853 
                 −16.42767 
                 −1.79278 
               
               
                 1/2IV + 1/2IV 
                 4 
                 0.5 
                 4 
                 0.5 
                 0 
                 0 
                 0.80765 
                 −16.84619 
                 −16.65532 
                 −2.02043 
               
               
                 1/2(I + II) + II 
                 1 
                 0.5 
                 2 
                 0.5 
                 2 
                 1 
                 0.80561 
                 −16.88873 
                 −16.69786 
                 −2.06297 
               
               
                   
               
             
          
         
       
     
         [0153]    Consider next the radius of the AO or HO due to the contribution of charge to more than one bond. The energy contribution due to the charge donation at each atom such as carbon superimposes linearly. In general, the radius r mol2sp     3    of the C2sp 3  HO of a carbon atom of a given molecule is calculated using Eq. (14.514) by considering ΣE T     mol   (MO,2sp 3 ), the total energy donation to all bonds with which it participates in bonding. The general equation for the radius is given by 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           
                             mo 
                              
                             
                                 
                             
                              
                             l 
                              
                             
                                 
                             
                              
                             2 
                              
                             
                               sp 
                               3 
                             
                           
                         
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       E 
                                       Coulomb 
                                     
                                      
                                     
                                       ( 
                                       
                                         C 
                                         , 
                                         
                                           2 
                                            
                                           
                                             sp 
                                             3 
                                           
                                         
                                       
                                       ) 
                                     
                                   
                                   + 
                                   
                                     ∑ 
                                     
                                       
                                         E 
                                         
                                           T 
                                           
                                             mo 
                                              
                                             
                                                 
                                             
                                              
                                             l 
                                           
                                         
                                       
                                        
                                       
                                         ( 
                                         
                                           MO 
                                           , 
                                           
                                             2 
                                              
                                             
                                               sp 
                                               3 
                                             
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                              
                             2 
                           
                           
                             8 
                              
                             
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 ( 
                                 
                                   
                                     e 
                                      
                                     
                                         
                                     
                                      
                                     14.825751 
                                      
                                     
                                         
                                     
                                      
                                     eV 
                                   
                                   + 
                                   
                                     ∑ 
                                     
                                        
                                       
                                         
                                           E 
                                           
                                             T 
                                             
                                               mo 
                                                
                                               
                                                   
                                               
                                                
                                               l 
                                             
                                           
                                         
                                          
                                         
                                           ( 
                                           
                                             MO 
                                             , 
                                             
                                               2 
                                                
                                               
                                                 sp 
                                                 3 
                                               
                                             
                                           
                                           ) 
                                         
                                       
                                        
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   69 
                   ) 
                 
               
             
           
         
       
     
         [0154]    The Coulombic energy E Coulomb (mol.atom,msp 3 ) of the outer electron of the atom msp 3  shell is given by Eq. (56). In the case that during hybridization, at least one of the spin-paired AO electrons is unpaired in the hybridized orbital (HO), the energy change for the promotion to the unpaired state is the magnetic energy E(magnetic) (Eq. (52)) at the initial radius r of the AO electron. Then, the energy E(mol.atom,msp 3 ) of the outer electron of the atom msp 3  shell is given by the sum of E Coulomb (mol.atom,msp 3 ) and E(magnetic) (Eq. (57)). 
         [0155]    For example, the C2sp 3  HO of each methyl group of an alkane contributes −0.92918 eV (Eq. (14.513)) to the corresponding single C—C bond; thus, the corresponding C2sp 3  HO radius is given by Eq. (14.514). The C2sp 3  HO of each methylene group of C n H 2n+2  contributes −0.92918 eV to each of the two corresponding C—C bond MOs. Thus, the radius (Eq. (69)), the Coulombic energy (Eq. (56)), and the energy (Eq. (57)) of each alkane methylene group are 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           
                             
                               alkaneC 
                               methylene 
                             
                              
                             2 
                              
                             
                               sp 
                               3 
                             
                           
                         
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       
                                         
                                           
                                             E 
                                             Coulomb 
                                           
                                            
                                           
                                             ( 
                                             
                                               C 
                                               , 
                                               
                                                 2 
                                                  
                                                 
                                                   sp 
                                                   3 
                                                 
                                               
                                             
                                             ) 
                                           
                                         
                                         + 
                                       
                                     
                                   
                                   
                                     
                                       
                                         ∑ 
                                         
                                           
                                             E 
                                             
                                               T 
                                               alkane 
                                             
                                           
                                            
                                           
                                             ( 
                                             
                                               
                                                 
                                                   
                                                     
                                                       
                                                         methylene 
                                                          
                                                         
                                                             
                                                         
                                                          
                                                         C 
                                                       
                                                       - 
                                                       C 
                                                     
                                                     , 
                                                   
                                                 
                                               
                                               
                                                 
                                                   
                                                     2 
                                                      
                                                     
                                                       sp 
                                                       3 
                                                     
                                                   
                                                 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                              
                             2 
                           
                           
                             8 
                              
                             
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       
                                         
                                           
                                             
                                               
                                                 e 
                                                  
                                                 
                                                     
                                                 
                                                  
                                                 14.825751 
                                                  
                                                 
                                                     
                                                 
                                                  
                                                 eV 
                                               
                                               + 
                                             
                                           
                                         
                                         
                                           
                                             
                                               
                                                 e 
                                                  
                                                 
                                                     
                                                 
                                                  
                                                 0.92918 
                                                  
                                                 
                                                     
                                                 
                                                  
                                                 eV 
                                               
                                               + 
                                             
                                           
                                         
                                       
                                     
                                   
                                   
                                     
                                       
                                         e 
                                          
                                         
                                             
                                         
                                          
                                         0.92918 
                                          
                                         
                                             
                                         
                                          
                                         eV 
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           0.81549 
                            
                           
                             a 
                             0 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   70 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             Coulomb 
                           
                            
                           
                             ( 
                             
                               
                                 C 
                                 methylene 
                               
                                
                               2 
                                
                               
                                 sp 
                                 3 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 ( 
                                 
                                   0.81549 
                                    
                                   
                                     a 
                                     0 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             16.68412 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   71 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           E 
                            
                           
                             ( 
                             
                               
                                 C 
                                 methylene 
                               
                                
                               2 
                                
                               
                                 sp 
                                 3 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               - 
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               
                                 
                                   πɛ 
                                   0 
                                 
                                  
                                 
                                   ( 
                                   
                                     0.81549 
                                      
                                     
                                       a 
                                       0 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           + 
                           
                             
                               2 
                                
                               
                                 πμ 
                                 0 
                               
                                
                               
                                  
                                 2 
                               
                                
                               
                                 ℏ 
                                 2 
                               
                             
                             
                               
                                 
                                   m 
                                   e 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     0.84317 
                                      
                                     
                                       a 
                                       0 
                                     
                                   
                                   ) 
                                 
                               
                               3 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             16.49325 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   72 
                   ) 
                 
               
             
           
         
       
     
         [0156]    In the determination of the parameters of functional groups, heteroatoms bonding to C2sp 3  HOs to form MOs are energy matched to the C2sp 3  HOs. Thus, the radius and the energy parameters of a bonding heteroatom are given by the same equations as those for C2sp 3  HOs. Using Eqs. (52), (56-57), (61), and (69) in a generalized fashion, the final values of the radius of the HO or AO, r Atom,HO,AO , E Coulomb (mol.atom,msp3), and E(C mol 2sp 3 ) are calculated using ΣE T     group   (MO,2sp 3 ), the total energy donation to each bond with which an atom participates in bonding corresponding to the values of E T (C BO —C,C2sp 3 ) of the MO due to charge donation from the AO or HO to the MO given in Tables 4 and 5. 
         [0157]    The energy of the MO is matched to each of the participating outermost atomic or hybridized orbitals of the bonding atoms wherein the energy match includes the energy contribution due to the AO or HO&#39;s donation of charge to the MO. The force constant k′ (Eq. (38)) is used to determine the ellipsoidal parameter c′ (Eq. (39)) of the each H 2 -type-ellipsoidal-MO in terms of the central force of the foci. Then, c′ is substituted into the energy equation (from Eq. (48))) which is set equal to n 1  times the total energy of H 2  where n 1  is the number of equivalent bonds of the MO and the energy of H 2 , −31.63536831 eV, Eq. (11.212) is the minimum energy possible for a prolate spheroidal MO. From the energy equation and the relationship between the axes, the dimensions of the MO are solved. The energy equation has the semimajor axis a as it only parameter. The solution of the semimajor axis a then allows for the solution of the other axes of each prolate spheroid and eccentricity of each MO (Eqs. (40-42)). The parameter solutions then allow for the component and total energies of the MO to be determined. 
         [0158]    The total energy, E T (H 2 MO), is given by the sum of the energy terms (Eqs. (43-48)) plus E T (AO/HO): 
         [0000]    
       
         
           
             
               
                 
                   
                     E 
                     
                       T 
                       
                         ( 
                         
                           
                             H 
                             2 
                           
                            
                           MO 
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       V 
                       e 
                     
                     + 
                     T 
                     + 
                     
                       V 
                       m 
                     
                     + 
                     
                       V 
                       p 
                     
                     + 
                     
                       
                         E 
                         T 
                       
                        
                       
                         ( 
                         
                           AO 
                           / 
                           HO 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   73 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           E 
                           
                             T 
                             
                               ( 
                               
                                 
                                   H 
                                   2 
                                 
                                  
                                 MO 
                               
                               ) 
                             
                           
                         
                         = 
                           
                          
                         
                           
                             - 
                             
                               
                                 
                                   
                                     n 
                                     1 
                                   
                                    
                                   
                                      
                                     2 
                                   
                                 
                                 
                                   8 
                                    
                                   
                                     πɛ 
                                     o 
                                   
                                    
                                   
                                     
                                       
                                         a 
                                         2 
                                       
                                       - 
                                       
                                         b 
                                         2 
                                       
                                     
                                   
                                 
                               
                                
                               
                                 [ 
                                 
                                   
                                     
                                       
                                         
                                           c 
                                           1 
                                         
                                          
                                         
                                           
                                             c 
                                             2 
                                           
                                            
                                           
                                             ( 
                                             
                                               2 
                                               - 
                                               
                                                 
                                                   a 
                                                   0 
                                                 
                                                 a 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                   
                                   
                                     
                                       
                                         
                                           ln 
                                            
                                           
                                             
                                               
                                                   
                                               
                                                
                                               
                                                 a 
                                                 + 
                                                 
                                                   
                                                     
                                                       a 
                                                       2 
                                                     
                                                     - 
                                                     
                                                       b 
                                                       2 
                                                     
                                                   
                                                 
                                               
                                             
                                             
                                               a 
                                               - 
                                               
                                                 
                                                   
                                                     a 
                                                     2 
                                                   
                                                   - 
                                                   
                                                     b 
                                                     2 
                                                   
                                                 
                                               
                                             
                                           
                                         
                                         - 
                                         1 
                                       
                                     
                                   
                                 
                                 ] 
                               
                             
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             E 
                             T 
                           
                            
                           
                             ( 
                             
                               AO 
                               / 
                               HO 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             
                               
                                 
                                   
                                     n 
                                     1 
                                   
                                    
                                   
                                      
                                     2 
                                   
                                 
                                 
                                   8 
                                    
                                   
                                     πɛ 
                                     0 
                                   
                                    
                                   
                                     c 
                                     ′ 
                                   
                                 
                               
                                
                               
                                 [ 
                                 
                                   
                                     
                                       c 
                                       1 
                                     
                                      
                                     
                                       
                                         c 
                                         2 
                                       
                                        
                                       
                                         ( 
                                         
                                           2 
                                           - 
                                           
                                             
                                               a 
                                               0 
                                             
                                             a 
                                           
                                         
                                         ) 
                                       
                                     
                                      
                                     ln 
                                      
                                     
                                         
                                     
                                      
                                     
                                       
                                         a 
                                         + 
                                         
                                           c 
                                           ′ 
                                         
                                       
                                       
                                         a 
                                         - 
                                         
                                           c 
                                           ′ 
                                         
                                       
                                     
                                   
                                   - 
                                   1 
                                 
                                 ] 
                               
                             
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             E 
                             T 
                           
                            
                           
                             ( 
                             
                               AO 
                               / 
                               HO 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   74 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where n 1  is the number of equivalent bonds of the MO, c 1  is the fraction of the H 2 -type ellipsoidal MO basis function of a chemical bond of the group, c 2  is the factor that results in an equipotential energy match of the participating at least two atomic orbitals of each chemical bond, and E T (AO/HO) is the total energy comprising the difference of the energy E(AO/HO) of at least one atomic or hybrid orbital to which the MO is energy matched and any energy component ΔE H     2     MO (AO/HO) due to the AO or HO&#39;s charge donation to the MO. 
         [0000]        E   T ( AO/HO )= E ( AO/HO )−ΔE H     2     MO ( AO/HO )   (75) 
         [0159]    To solve the bond parameters and energies, 
         [0000]    
       
         
           
             
               
                 
                   
                     c 
                     ′ 
                   
                   = 
                   
                     
                       a 
                        
                       
                         
                           
                             
                               ℏ 
                               2 
                             
                              
                             4 
                              
                             
                               πɛ 
                               0 
                             
                           
                           
                             
                               m 
                               e 
                             
                              
                             
                                
                               2 
                             
                              
                             2 
                              
                             
                               C 
                               1 
                             
                              
                             
                               C 
                               2 
                             
                              
                             a 
                           
                         
                       
                     
                     = 
                     
                       
                         
                           aa 
                           0 
                         
                         
                           2 
                            
                           
                             C 
                             1 
                           
                            
                           
                             C 
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                      
                     
                       ( 
                       39 
                       ) 
                     
                   
                   ) 
                 
               
             
           
         
       
     
         [0000]    is substituted into E T  (H 2 MO) to give 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           E 
                           
                             T 
                             
                               ( 
                               
                                 
                                   H 
                                   2 
                                 
                                  
                                 MO 
                               
                               ) 
                             
                           
                         
                         = 
                           
                          
                         
                           
                             - 
                             
                               
                                 
                                   
                                     n 
                                     1 
                                   
                                    
                                   
                                      
                                     2 
                                   
                                 
                                 
                                   8 
                                    
                                   
                                     πɛ 
                                     o 
                                   
                                    
                                   
                                     
                                       
                                         a 
                                         2 
                                       
                                       - 
                                       
                                         b 
                                         2 
                                       
                                     
                                   
                                 
                               
                                
                               
                                 [ 
                                 
                                   
                                     
                                       
                                         
                                           c 
                                           1 
                                         
                                          
                                         
                                           
                                             c 
                                             2 
                                           
                                            
                                           
                                             ( 
                                             
                                               2 
                                               - 
                                               
                                                 
                                                   a 
                                                   0 
                                                 
                                                 a 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                   
                                   
                                     
                                       
                                         
                                           ln 
                                            
                                           
                                               
                                           
                                            
                                           
                                             
                                               a 
                                               + 
                                               
                                                 
                                                   
                                                     a 
                                                     2 
                                                   
                                                   - 
                                                   
                                                     b 
                                                     2 
                                                   
                                                 
                                               
                                             
                                             
                                               a 
                                               - 
                                               
                                                 
                                                   
                                                     a 
                                                     2 
                                                   
                                                   - 
                                                   
                                                     b 
                                                     2 
                                                   
                                                 
                                               
                                             
                                           
                                         
                                         - 
                                         1 
                                       
                                     
                                   
                                 
                                 ] 
                               
                             
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             E 
                             T 
                           
                            
                           
                             ( 
                             
                               AO 
                               / 
                               HO 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             
                               
                                 
                                   
                                     n 
                                     1 
                                   
                                    
                                   
                                      
                                     2 
                                   
                                 
                                 
                                   8 
                                    
                                   
                                     πɛ 
                                     0 
                                   
                                    
                                   
                                     c 
                                     ′ 
                                   
                                 
                               
                                
                               
                                 [ 
                                 
                                   
                                     
                                       
                                         
                                           c 
                                           1 
                                         
                                          
                                         
                                           
                                             c 
                                             2 
                                           
                                            
                                           
                                             ( 
                                             
                                               2 
                                               - 
                                               
                                                 
                                                   a 
                                                   0 
                                                 
                                                 a 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                   
                                   
                                     
                                       
                                         
                                           ln 
                                            
                                           
                                               
                                           
                                            
                                           
                                             
                                               a 
                                               + 
                                               
                                                 c 
                                                 ′ 
                                               
                                             
                                             
                                               a 
                                               - 
                                               
                                                 c 
                                                 ′ 
                                               
                                             
                                           
                                         
                                         - 
                                         1 
                                       
                                     
                                   
                                 
                                 ] 
                               
                             
                           
                           + 
                           
                             
                               E 
                               T 
                             
                              
                             
                               ( 
                               
                                 AO 
                                 / 
                                 HO 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             
                               
                                 
                                   
                                     n 
                                     1 
                                   
                                    
                                   
                                      
                                     2 
                                   
                                 
                                 
                                   8 
                                    
                                   
                                     πɛ 
                                     0 
                                   
                                    
                                   
                                     
                                       
                                         aa 
                                         0 
                                       
                                       
                                         2 
                                          
                                         
                                           C 
                                           1 
                                         
                                          
                                         
                                           C 
                                           2 
                                         
                                       
                                     
                                   
                                 
                               
                                
                               
                                 [ 
                                 
                                   
                                     
                                       
                                         
                                           c 
                                           1 
                                         
                                          
                                         
                                           
                                             c 
                                             2 
                                           
                                            
                                           
                                             ( 
                                             
                                               2 
                                               - 
                                               
                                                 
                                                   a 
                                                   0 
                                                 
                                                 a 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                   
                                   
                                     
                                       
                                         
                                           ln 
                                            
                                           
                                               
                                           
                                            
                                           
                                             
                                               a 
                                               + 
                                               
                                                 
                                                   
                                                     aa 
                                                     0 
                                                   
                                                   
                                                     2 
                                                      
                                                     
                                                       C 
                                                       1 
                                                     
                                                      
                                                     
                                                       C 
                                                       2 
                                                     
                                                   
                                                 
                                               
                                             
                                             
                                               a 
                                               - 
                                               
                                                 
                                                   
                                                     aa 
                                                     0 
                                                   
                                                   
                                                     2 
                                                      
                                                     
                                                       C 
                                                       1 
                                                     
                                                      
                                                     
                                                       C 
                                                       2 
                                                     
                                                   
                                                 
                                               
                                             
                                           
                                         
                                         - 
                                         1 
                                       
                                     
                                   
                                 
                                 ] 
                               
                             
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             E 
                             T 
                           
                            
                           
                             ( 
                             
                               AO 
                               / 
                               HO 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   76 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The total energy is set equal to E (basis energies) which in the most general case is given by the sum of a first integer n 1  times the total energy of H 2  minus a second integer n 2  times the total energy of H, minus a third integer n 3  times the valence energy of E(AO) (e.g. E(N)=−14.53414 eV) where the first integer can be 1, 2, 3 . . . , and each of the second and third integers can be 0,1,2,3. 
         [0000]        E (basis energies)= n   1 (−31.63536831 eV)− n   2  (−13.605804 eV)− n   3   E ( AO )   (77) 
         [0000]    In the case that the MO bonds two atoms other than hydrogen, E(basis energies) is n 1  times the total energy of H 2  where n 1  is the number of equivalent bonds of the MO and the energy of H 2 , −31.63536831 eV, Eq. (11.212) is the minimum energy possible for a prolate spheroidal MO: 
         [0000]        E (basis energies)= n   1 (−31.63536831 eV)   (78) 
         [0160]    E T (H 2 MO), is set equal to E(basis energies), and the semimajor axis a is solved. Thus, the semimajor axis a is solved from the equation of the form: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       - 
                       
                         
                           
                             
                               n 
                               1 
                             
                              
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             
                               
                                 
                                   aa 
                                   0 
                                 
                                 
                                   2 
                                    
                                   
                                     C 
                                     1 
                                   
                                    
                                   
                                     C 
                                     2 
                                   
                                 
                               
                             
                           
                         
                         [ 
                         
                           
                             
                               c 
                               1 
                             
                              
                             
                               
                                 c 
                                 2 
                               
                                
                               
                                 ( 
                                 
                                   2 
                                   - 
                                   
                                     
                                       a 
                                       0 
                                     
                                     a 
                                   
                                 
                                 ) 
                               
                             
                              
                             ln 
                              
                             
                                 
                             
                              
                             
                               
                                 a 
                                 + 
                                 
                                   
                                     
                                       aa 
                                       0 
                                     
                                     
                                       2 
                                        
                                       
                                         C 
                                         
                                           
                                               
                                           
                                            
                                           1 
                                         
                                       
                                        
                                       
                                         C 
                                         2 
                                       
                                     
                                   
                                 
                               
                               
                                 a 
                                 - 
                                 
                                   
                                     
                                       aa 
                                       0 
                                     
                                     
                                       2 
                                        
                                       
                                         C 
                                         1 
                                       
                                        
                                       
                                         C 
                                         2 
                                       
                                     
                                   
                                 
                               
                             
                           
                           - 
                           1 
                         
                         ] 
                       
                     
                     + 
                     
                       
                         E 
                         T 
                       
                        
                       
                         ( 
                         
                           AO 
                           / 
                           HO 
                         
                         ) 
                       
                     
                   
                   = 
                   
                     E 
                      
                     
                       ( 
                       
                         basis 
                          
                         
                             
                         
                          
                         energies 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   79 
                   ) 
                 
               
             
           
         
       
     
         [0161]    The distance from the origin of the H 2 -type-ellipsoidal-MO to each focus c′, the internuclear distance 2c′, and the length of the semiminor axis of the prolate spheroidal H 2 -type MO b=c are solved from the semimajor axis a using Eqs. (39-41). Then, the component energies are given by Eqs. (43-46) and (76). 
         [0162]    The total energy of the MO of the functional group, E T (MO), is the sum of the total energy of the components comprising the energy contribution of the MO formed between the participating atoms and E T (atom-atom,msp 3 .AO), the change in the energy of the AOs or HOs upon forming the bond. From Eqs. (76-77), E T (MO) is 
         [0000]        E   T ( MO )= E (basis energies)+ E   T (atom-atom,msp 3   .AO )   (80) 
         [0163]    During bond formation, the electrons undergo a reentrant oscillatory orbit with vibration of the nuclei, and the corresponding energy Ē osc  is the sum of the Doppler, Ē D , and average vibrational kinetic energies, Ē Kvib : 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       E 
                       _ 
                     
                     osc 
                   
                   = 
                   
                     
                       
                         n 
                         1 
                       
                        
                       
                         ( 
                         
                           
                             
                               E 
                               _ 
                             
                             D 
                           
                           + 
                           
                             
                               E 
                               _ 
                             
                             Kvib 
                           
                         
                         ) 
                       
                     
                     = 
                     
                       
                         n 
                         1 
                       
                        
                       
                         ( 
                         
                           
                             
                               E 
                               hv 
                             
                              
                             
                               
                                 
                                   2 
                                    
                                   
                                     
                                       E 
                                       _ 
                                     
                                     K 
                                   
                                 
                                 
                                   
                                     m 
                                     e 
                                   
                                    
                                   
                                     c 
                                     2 
                                   
                                 
                               
                             
                           
                           + 
                           
                             
                               1 
                               2 
                             
                              
                             ℏ 
                              
                             
                               
                                 k 
                                 μ 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   81 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where n 1  is the number of equivalent bonds of the MO, k is the spring constant of the equivalent harmonic oscillator, and μ is the reduced mass. The angular frequency of the reentrant oscillation in the transition state corresponding to Ē D  is determined by the force between the central field and the electrons in the transition state. The force and its derivative are given by 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       f 
                        
                       
                         ( 
                         R 
                         ) 
                       
                     
                     = 
                     
                       - 
                       
                         
                           
                             C 
                             
                               1 
                                
                               o 
                             
                           
                            
                           
                             C 
                             
                               2 
                                
                               o 
                             
                           
                            
                           
                              
                             2 
                           
                         
                         
                           4 
                            
                           
                             πɛ 
                             0 
                           
                            
                           
                             R 
                             3 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   and 
                 
               
               
                 
                   ( 
                   82 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       f 
                       ′ 
                     
                      
                     
                       ( 
                       a 
                       ) 
                     
                   
                   = 
                   
                     2 
                      
                     
                       
                         
                           C 
                           
                             1 
                              
                             o 
                           
                         
                          
                         
                           C 
                           
                             2 
                              
                             o 
                           
                         
                          
                         
                            
                           2 
                         
                       
                       
                         4 
                          
                         
                           πɛ 
                           0 
                         
                          
                         
                           R 
                           3 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   83 
                   ) 
                 
               
             
           
         
       
     
         [0000]    such that the angular frequency of the oscillation in the transition state is given by 
         [0000]    
       
         
           
             
               
                 
                   ω 
                   = 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 
                                   - 
                                   3 
                                 
                                 a 
                               
                                
                               
                                 f 
                                  
                                 
                                   ( 
                                   a 
                                   ) 
                                 
                               
                             
                             - 
                             
                               
                                 f 
                                 ′ 
                               
                                
                               
                                 ( 
                                 a 
                                 ) 
                               
                             
                           
                           ] 
                         
                         
                           m 
                           e 
                         
                       
                     
                     = 
                     
                       
                         
                           k 
                           
                             m 
                             e 
                           
                         
                       
                       = 
                       
                         
                           
                             
                               
                                 C 
                                 
                                   1 
                                    
                                   o 
                                 
                               
                                
                               
                                 C 
                                 
                                   2 
                                    
                                   o 
                                 
                               
                                
                               
                                  
                                 2 
                               
                             
                             
                               4 
                                
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 R 
                                 3 
                               
                             
                           
                           
                             m 
                             e 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   84 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where R is the semimajor axis a or the semiminor axis b depending on the eccentricity of the bond that is most representative of the oscillation in the transition state. C 1o  is the fraction of the H 2 -type ellipsoidal MO basis function of the oscillatory transition state of a chemical bond of the group, and C 2o  is the factor that results in an equipotential energy match of the participating at least two atomic orbitals of the transition state of the chemical bond. Typically, C 1o =C 1  and C 2o =C 2 . The kinetic energy, E K , corresponding to Ē D  is given by Planck&#39;s equation for functional groups: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       E 
                       _ 
                     
                     K 
                   
                   = 
                   
                     ℏω 
                     = 
                     
                       ℏ 
                        
                       
                         
                           
                             
                               
                                 C 
                                 
                                   1 
                                    
                                   o 
                                 
                               
                                
                               
                                 C 
                                 
                                   2 
                                    
                                   o 
                                 
                               
                                
                               
                                  
                                 2 
                               
                             
                             
                               4 
                                
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 R 
                                 3 
                               
                             
                           
                           
                             m 
                             e 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   85 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The Doppler energy of the electrons of the reentrant orbit is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         E 
                         _ 
                       
                       D 
                     
                     ≅ 
                     
                       
                         E 
                         hv 
                       
                        
                       
                         
                           
                             2 
                              
                             
                               
                                 E 
                                 _ 
                               
                               K 
                             
                           
                           
                             
                               
                                 m 
                                 e 
                               
                                
                               
                                 c 
                                 2 
                               
                             
                              
                             
                                 
                             
                           
                         
                       
                     
                   
                   = 
                   
                     
                       E 
                       hv 
                     
                      
                     
                       
                         
                           2 
                            
                           ℏ 
                            
                           
                             
                               
                                 
                                   
                                     C 
                                     
                                       1 
                                        
                                       o 
                                     
                                   
                                    
                                   
                                     C 
                                     
                                       2 
                                        
                                       o 
                                     
                                   
                                    
                                   
                                      
                                     2 
                                   
                                 
                                 
                                   4 
                                    
                                   
                                     πɛ 
                                     0 
                                   
                                    
                                   
                                     R 
                                     3 
                                   
                                 
                               
                               
                                 m 
                                 e 
                               
                             
                           
                         
                         
                           
                             m 
                             e 
                           
                            
                           
                             c 
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   86 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Ē osc  given by the sum of Ē D  and Ē Kvib  is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       E 
                       _ 
                     
                     
                       osc 
                       
                         ( 
                         group 
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         n 
                         1 
                       
                        
                       
                         ( 
                         
                           
                             
                               E 
                               _ 
                             
                             D 
                           
                           + 
                           
                             
                               E 
                               _ 
                             
                             Kvib 
                           
                         
                         ) 
                       
                     
                     = 
                     
                       
                         n 
                         1 
                       
                       ( 
                       
                         
                           
                             E 
                             hv 
                           
                            
                           
                             
                               
                                 2 
                                  
                                 ℏ 
                                  
                                 
                                   
                                     
                                       
                                         
                                           C 
                                           
                                             1 
                                              
                                             o 
                                           
                                         
                                          
                                         
                                           C 
                                           
                                             2 
                                              
                                             o 
                                           
                                         
                                          
                                         
                                            
                                           2 
                                         
                                       
                                       
                                         4 
                                          
                                         
                                           πɛ 
                                           0 
                                         
                                          
                                         
                                           R 
                                           3 
                                         
                                       
                                     
                                     
                                       m 
                                       e 
                                     
                                   
                                 
                               
                               
                                 
                                   m 
                                   e 
                                 
                                  
                                 
                                   c 
                                   2 
                                 
                               
                             
                           
                         
                         + 
                         
                           E 
                           vib 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   87 
                   ) 
                 
               
             
           
         
       
     
         [0000]    E hv  of a group having n, bonds is given by E T (MO)/n 1  such that 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       E 
                       _ 
                     
                     osc 
                   
                   = 
                   
                     
                       
                         n 
                         1 
                       
                        
                       
                         ( 
                         
                           
                             
                               E 
                               _ 
                             
                             D 
                           
                           + 
                           
                             
                               E 
                               _ 
                             
                             Kvib 
                           
                         
                         ) 
                       
                     
                     = 
                     
                       
                         n 
                         1 
                       
                        
                       
                         ( 
                         
                           
                             
                               
                                 E 
                                 
                                   T 
                                   
                                     ( 
                                     MO 
                                     ) 
                                   
                                 
                               
                               / 
                               
                                 n 
                                 1 
                               
                             
                              
                             
                               
                                 
                                   2 
                                    
                                   
                                     
                                       E 
                                       _ 
                                     
                                     K 
                                   
                                 
                                 
                                   M 
                                    
                                   
                                       
                                   
                                    
                                   
                                     c 
                                     2 
                                   
                                 
                               
                             
                           
                           + 
                           
                             
                               1 
                               2 
                             
                              
                             ℏ 
                              
                             
                               
                                 k 
                                 μ 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   88 
                   ) 
                 
               
             
           
         
       
     
         [0000]    E T+osc (Group) is given by the sum of E T (MO) (Eq. (79)) and Ē osc  (Eq. (88)): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           E 
                           
                             T 
                             + 
                             
                               osc 
                               
                                 ( 
                                 Group 
                                 ) 
                               
                             
                           
                         
                         = 
                           
                          
                         
                           
                             E 
                             
                               T 
                               
                                 ( 
                                 MO 
                                 ) 
                               
                             
                           
                           + 
                           
                             
                               E 
                               _ 
                             
                             osc 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           ( 
                           
                             
                               
                                 
                                   ( 
                                   
                                     
                                       
                                         
                                           
                                             
                                               
                                                 - 
                                                 
                                                   
                                                     
                                                       n 
                                                       1 
                                                     
                                                      
                                                     
                                                        
                                                       2 
                                                     
                                                   
                                                   
                                                     8 
                                                      
                                                     
                                                       πɛ 
                                                       0 
                                                     
                                                      
                                                     
                                                       
                                                         
                                                           aa 
                                                           0 
                                                         
                                                         
                                                           2 
                                                            
                                                           
                                                             C 
                                                             1 
                                                           
                                                            
                                                           
                                                             C 
                                                             2 
                                                           
                                                         
                                                       
                                                     
                                                   
                                                 
                                               
                                             
                                           
                                           
                                             
                                               
                                                 
                                                   [ 
                                                   
                                                     
                                                       
                                                         c 
                                                         1 
                                                       
                                                        
                                                       
                                                         
                                                           c 
                                                           2 
                                                         
                                                          
                                                         
                                                           ( 
                                                           
                                                             2 
                                                             - 
                                                             
                                                             
                                                             a 
                                                             0 
                                                             
                                                             a 
                                                             
                                                           
                                                           ) 
                                                         
                                                       
                                                        
                                                       ln 
                                                        
                                                       
                                                           
                                                       
                                                        
                                                       
                                                         
                                                           a 
                                                           + 
                                                           
                                                             
                                                             
                                                             aa 
                                                             0 
                                                             
                                                             
                                                             2 
                                                              
                                                             
                                                             C 
                                                             1 
                                                             
                                                              
                                                             
                                                             C 
                                                             2 
                                                             
                                                             
                                                             
                                                           
                                                         
                                                         
                                                           a 
                                                           - 
                                                           
                                                             
                                                             
                                                             aa 
                                                             0 
                                                             
                                                             
                                                             2 
                                                              
                                                             
                                                             C 
                                                             1 
                                                             
                                                              
                                                             
                                                             C 
                                                             2 
                                                             
                                                             
                                                             
                                                           
                                                         
                                                       
                                                     
                                                     - 
                                                     1 
                                                   
                                                   ] 
                                                 
                                                 + 
                                               
                                             
                                           
                                         
                                       
                                     
                                     
                                       
                                         
                                           
                                             
                                               E 
                                               T 
                                             
                                              
                                             
                                               ( 
                                               
                                                 AO 
                                                  
                                                 
                                                   / 
                                                 
                                                  
                                                 HO 
                                               
                                               ) 
                                             
                                           
                                           + 
                                           
                                             
                                               E 
                                               T 
                                             
                                              
                                             
                                               ( 
                                               
                                                 
                                                   atom 
                                                   - 
                                                   atom 
                                                 
                                                 , 
                                                 
                                                   
                                                     msp 
                                                     3 
                                                   
                                                   . 
                                                   AO 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 
                                   
                                     [ 
                                     
                                       1 
                                       + 
                                       
                                         
                                           
                                             2 
                                              
                                             ℏ 
                                              
                                             
                                               
                                                 
                                                   
                                                     
                                                       C 
                                                       
                                                         1 
                                                          
                                                         o 
                                                       
                                                     
                                                      
                                                     
                                                       C 
                                                       
                                                         2 
                                                          
                                                         o 
                                                       
                                                     
                                                      
                                                     
                                                        
                                                       2 
                                                     
                                                   
                                                   
                                                     4 
                                                      
                                                     
                                                       πɛ 
                                                       o 
                                                     
                                                      
                                                     
                                                       R 
                                                       3 
                                                     
                                                   
                                                 
                                                 
                                                   m 
                                                   e 
                                                 
                                               
                                             
                                           
                                           
                                             
                                               m 
                                               e 
                                             
                                              
                                             
                                               c 
                                               2 
                                             
                                           
                                         
                                       
                                     
                                     ] 
                                   
                                   + 
                                   
                                     
                                       n 
                                       1 
                                     
                                      
                                     
                                       1 
                                       2 
                                     
                                      
                                     ℏ 
                                      
                                     
                                       
                                         k 
                                         μ 
                                       
                                     
                                   
                                 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           ( 
                           
                             
                               E 
                                
                               
                                 ( 
                                 
                                   basis 
                                    
                                   
                                       
                                   
                                    
                                   energies 
                                 
                                 ) 
                               
                             
                             + 
                             
                               
                                 E 
                                 T 
                               
                                
                               
                                 ( 
                                 
                                   
                                     atom 
                                     - 
                                     atom 
                                   
                                   , 
                                   
                                     
                                       msp 
                                       3 
                                     
                                     . 
                                     AO 
                                   
                                 
                                 ) 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             [ 
                             
                               1 
                               + 
                               
                                 
                                   
                                     2 
                                      
                                     ℏ 
                                      
                                     
                                       
                                         
                                           
                                             
                                               C 
                                               
                                                 1 
                                                  
                                                 o 
                                               
                                             
                                              
                                             
                                               C 
                                               
                                                 2 
                                                  
                                                 o 
                                               
                                             
                                              
                                             
                                                
                                               2 
                                             
                                           
                                           
                                             4 
                                              
                                             
                                               πɛ 
                                               o 
                                             
                                              
                                             
                                               R 
                                               3 
                                             
                                           
                                         
                                         
                                           m 
                                           e 
                                         
                                       
                                     
                                   
                                   
                                     
                                       m 
                                       e 
                                     
                                      
                                     
                                       c 
                                       2 
                                     
                                   
                                 
                               
                             
                             ] 
                           
                           + 
                           
                             
                               n 
                               1 
                             
                              
                             
                               1 
                               2 
                             
                              
                             ℏ 
                              
                             
                               
                                 k 
                                 μ 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   89 
                   ) 
                 
               
             
           
         
       
     
         [0164]    The total energy of the functional group E T (group) is the sum of the total energy of the components comprising the energy contribution of the MO formed between the participating atoms, E(basis energies), the change in the energy of the AOs or HOs upon forming the bond (E T (atom-atom,msp 3 .AO)), the energy of oscillation in the transition state, and the change in magnetic energy with bond formation, E mag . From Eq. (89), the total energy of the group 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       E 
                       
                         T 
                         
                           ( 
                           Group 
                           ) 
                         
                       
                     
                      
                     
                         
                     
                      
                     is 
                   
                    
                   
                     
 
                   
                    
                   
                     
                       E 
                       
                         T 
                         
                           ( 
                           Group 
                           ) 
                         
                       
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     
                                       
                                         E 
                                          
                                         
                                           ( 
                                           
                                             basis 
                                              
                                             
                                                 
                                             
                                              
                                             energies 
                                           
                                           ) 
                                         
                                       
                                       + 
                                     
                                   
                                 
                                 
                                   
                                     
                                       
                                         E 
                                         T 
                                       
                                        
                                       
                                         ( 
                                         
                                           
                                             atom 
                                             - 
                                             atom 
                                           
                                           , 
                                           
                                             
                                               msp 
                                               3 
                                             
                                             . 
                                             AO 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                         
                           
                             
                               
                                 [ 
                                 
                                   1 
                                   + 
                                   
                                     
                                       
                                         2 
                                          
                                         ℏ 
                                          
                                         
                                           
                                             
                                               
                                                 
                                                   C 
                                                   
                                                     1 
                                                      
                                                     o 
                                                   
                                                 
                                                  
                                                 
                                                   C 
                                                   
                                                     2 
                                                      
                                                     o 
                                                   
                                                 
                                                  
                                                 
                                                    
                                                   2 
                                                 
                                               
                                               
                                                 4 
                                                  
                                                 
                                                   πɛ 
                                                   o 
                                                 
                                                  
                                                 
                                                   R 
                                                   3 
                                                 
                                               
                                             
                                             
                                               m 
                                               e 
                                             
                                           
                                         
                                       
                                       
                                         
                                           m 
                                           e 
                                         
                                          
                                         
                                           c 
                                           2 
                                         
                                       
                                     
                                   
                                 
                                 ] 
                               
                               + 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   n 
                                   1 
                                 
                                  
                                 
                                   
                                     E 
                                     _ 
                                   
                                   Kvib 
                                 
                               
                               + 
                               
                                 E 
                                 mag 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   90 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The change in magnetic energy E mag  which arises due to the formation of unpaired electrons in the corresponding fragments relative to the bonded group is given by 
         [0000]    
       
         
           
             
               
                 
                   
                     E 
                     mag 
                   
                   = 
                   
                     
                       
                         c 
                         3 
                       
                        
                       
                         
                           2 
                            
                           
                             πμ 
                             0 
                           
                            
                           
                              
                             2 
                           
                            
                           
                             ℏ 
                             2 
                           
                         
                         
                           
                             m 
                             e 
                             2 
                           
                            
                           
                             r 
                             3 
                           
                         
                       
                     
                     = 
                     
                       
                         c 
                         3 
                       
                        
                       
                         
                           8 
                            
                           
                             πμ 
                             o 
                           
                            
                           
                             μ 
                             B 
                             2 
                           
                         
                         
                           r 
                           3 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   91 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where r 3  is the radius of the atom that reacts to form the bond and c 3  is the number of electron pairs. 
         [0000]    
       
         
           
             
               
                 
                   
                     E 
                     
                       T 
                       
                         ( 
                         Group 
                         ) 
                       
                     
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       E 
                                        
                                       
                                         ( 
                                         
                                           basis 
                                            
                                           
                                               
                                           
                                            
                                           energies 
                                         
                                         ) 
                                       
                                     
                                     + 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       E 
                                       T 
                                     
                                      
                                     
                                       ( 
                                       
                                         
                                           atom 
                                           - 
                                           atom 
                                         
                                         , 
                                         
                                           
                                             msp 
                                             3 
                                           
                                           . 
                                           AO 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             
                               [ 
                               
                                 1 
                                 + 
                                 
                                   
                                     
                                       2 
                                        
                                       ℏ 
                                        
                                       
                                         
                                           
                                             
                                               
                                                 C 
                                                 
                                                   1 
                                                    
                                                   o 
                                                 
                                               
                                                
                                               
                                                 C 
                                                 
                                                   2 
                                                    
                                                   o 
                                                 
                                               
                                                
                                               
                                                  
                                                 2 
                                               
                                             
                                             
                                               4 
                                                
                                               
                                                 πɛ 
                                                 o 
                                               
                                                
                                               
                                                 R 
                                                 3 
                                               
                                             
                                           
                                           
                                             m 
                                             e 
                                           
                                         
                                       
                                     
                                     
                                       
                                         m 
                                         e 
                                       
                                        
                                       
                                         c 
                                         2 
                                       
                                     
                                   
                                 
                               
                               ] 
                             
                             + 
                           
                         
                       
                       
                         
                           
                             
                               
                                 n 
                                 1 
                               
                                
                               
                                 
                                   E 
                                   _ 
                                 
                                 Kvib 
                               
                             
                             + 
                             
                               
                                 c 
                                 3 
                               
                                
                               
                                 
                                   8 
                                    
                                   
                                     πμ 
                                     o 
                                   
                                    
                                   
                                     μ 
                                     B 
                                     2 
                                   
                                 
                                 
                                   r 
                                   3 
                                 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   92 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The total bond energy of the group E D (Group) is the negative difference of the total energy of the group (Eq. (92)) and the total energy of the starting species given by the sum of c 4 E initial  (c 4  AO/HO) and c 5 E initia (c 5  AO/HO): 
         [0000]    
       
         
           
             
               
                 
                   
                     E 
                     
                       D 
                       
                         ( 
                         Group 
                         ) 
                       
                     
                   
                   = 
                   
                     - 
                     
                       ( 
                       
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     
                                       
                                         E 
                                          
                                         
                                           ( 
                                           
                                             basis 
                                              
                                             
                                                 
                                             
                                              
                                             energies 
                                           
                                           ) 
                                         
                                       
                                       + 
                                     
                                   
                                 
                                 
                                   
                                     
                                       
                                         E 
                                         T 
                                       
                                        
                                       
                                         ( 
                                         
                                           
                                             atom 
                                             - 
                                             atom 
                                           
                                           , 
                                           
                                             
                                               msp 
                                               3 
                                             
                                             . 
                                             AO 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                         
                           
                             
                               
                                 [ 
                                 
                                   1 
                                   + 
                                   
                                     
                                       
                                         2 
                                          
                                         ℏ 
                                          
                                         
                                           
                                             
                                               
                                                 C 
                                                 
                                                   1 
                                                    
                                                   o 
                                                 
                                               
                                                
                                               
                                                 C 
                                                 
                                                   2 
                                                    
                                                   o 
                                                 
                                               
                                                
                                               
                                                  
                                                 2 
                                               
                                             
                                             
                                               4 
                                                
                                               
                                                 πɛ 
                                                 o 
                                               
                                                
                                               
                                                 R 
                                                 3 
                                               
                                             
                                           
                                           
                                             m 
                                             e 
                                           
                                         
                                       
                                       
                                         
                                           m 
                                           e 
                                         
                                          
                                         
                                           c 
                                           2 
                                         
                                       
                                     
                                   
                                 
                                 ] 
                               
                               + 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   n 
                                   1 
                                 
                                  
                                 
                                   
                                     E 
                                     _ 
                                   
                                   Kvib 
                                 
                               
                               + 
                               
                                 
                                   c 
                                   3 
                                 
                                  
                                 
                                   
                                     8 
                                      
                                     
                                       πμ 
                                       o 
                                     
                                      
                                     
                                       μ 
                                       B 
                                       2 
                                     
                                   
                                   
                                     r 
                                     n 
                                     3 
                                   
                                 
                               
                               - 
                             
                           
                         
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     
                                       
                                         
                                           c 
                                           4 
                                         
                                          
                                         
                                           
                                             E 
                                             initial 
                                           
                                            
                                           
                                             ( 
                                             
                                               AO 
                                                
                                               
                                                 / 
                                               
                                                
                                               HO 
                                             
                                             ) 
                                           
                                         
                                       
                                       + 
                                     
                                   
                                 
                                 
                                   
                                     
                                       
                                         c 
                                         5 
                                       
                                        
                                       
                                         
                                           E 
                                           initial 
                                         
                                          
                                         
                                           ( 
                                           
                                             
                                               c 
                                               5 
                                             
                                              
                                             AO 
                                              
                                             
                                               / 
                                             
                                              
                                             HO 
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   93 
                   ) 
                 
               
             
           
         
       
     
         [0000]    In the case of organic molecules, the atoms of the functional groups are energy matched to the C2sp 3  HO such that 
         [0000]        E ( AO/HO )=−14.63489 eV   (94) 
         [0000]    For example, of E mag  of the C2sp 3  HO is: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             mag 
                           
                            
                           
                             ( 
                             
                               C 
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                   
                               
                                
                               
                                 sp 
                                 3 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             c 
                             3 
                           
                            
                           
                             
                               8 
                                
                               
                                 πμ 
                                 o 
                               
                                
                               
                                 μ 
                                 B 
                                 2 
                               
                             
                             
                               r 
                               3 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             c 
                             3 
                           
                            
                           
                             
                               8 
                                
                               
                                 πμ 
                                 o 
                               
                                
                               
                                 μ 
                                 B 
                                 2 
                               
                             
                             
                               
                                 ( 
                                 
                                   0.91771 
                                    
                                   
                                     a 
                                     0 
                                   
                                 
                                 ) 
                               
                               3 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             c 
                             3 
                           
                            
                           0.14803 
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   95 
                   ) 
                 
               
             
           
         
       
     
         [0165]    Each molecule, independently of its complexity and size, is comprised of functional groups wherein each present occurs an integer number of times in the molecule. The total bond energy of the molecule is then given by the integer-weighted sum of the energies of the functions groups corresponding to the composition of the molecule. Thus, integer formulas can be constructed easily for molecules for a given class such as straight-chain hydrocarbons considered as an example infra. The results demonstrate how simply and instantaneously molecules are solved using the classical exact solutions. In contrast, quantum mechanics requires that wavefunction are nonlinear, and any sum must be squared. The results of Millsian disprove quantum mechanics in this regard, and the linearity and superposition properties of Millsian represent a breakthrough with orders of magnitude reduction in complexity in solving molecules as well as being accurate physical representations rather than pure mathematical curve-fits devoid of a connection to reality. 
       C. Total Energy of Continuous-Chain Alkanes 
       [0166]    E D (C n H 2n+2 ), the total bond dissociation energy of C n H 2n+2 , is given as the sum of the energy components due to the two methyl groups, n-2 methylene groups, and n-1 C—C bonds where each energy component is given by Eqs. (14.590), (14.625), and (14.641), respectively. Thus, the total bond dissociation energy of C n H 2n+2  is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             D 
                           
                            
                           
                             ( 
                             
                               
                                 C 
                                 n 
                               
                                
                               
                                 H 
                                 
                                   
                                     2 
                                      
                                     n 
                                   
                                   + 
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               
                                 E 
                                 D 
                               
                                
                               
                                 ( 
                                 
                                   C 
                                   - 
                                   C 
                                 
                                 ) 
                               
                             
                             
                               n 
                               - 
                               1 
                             
                           
                           + 
                           
                             2 
                              
                             
                               
                                 
                                   E 
                                   D 
                                 
                                 alkane 
                               
                                
                               
                                 ( 
                                 
                                   CH 
                                   3 
                                   
                                       
                                   
                                     
                                     
                                   12 
                                 
                                 ) 
                               
                             
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             ( 
                             
                               n 
                               - 
                               2 
                             
                             ) 
                           
                            
                           
                             
                               E 
                               
                                 D 
                                 alkane 
                               
                             
                              
                             
                               ( 
                               
                                 CH 
                                 2 
                                   
                                   
                                   
                                 12 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               ( 
                               
                                 n 
                                 - 
                                 1 
                               
                               ) 
                             
                              
                             
                               ( 
                               
                                 4.32754 
                                  
                                 
                                     
                                 
                                  
                                 eV 
                               
                               ) 
                             
                           
                           + 
                           
                             2 
                              
                             
                               ( 
                               
                                 12.49186 
                                  
                                 
                                     
                                 
                                  
                                 eV 
                               
                               ) 
                             
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             ( 
                             
                               n 
                               - 
                               2 
                             
                             ) 
                           
                            
                           
                             ( 
                             
                               7.83016 
                                
                               
                                   
                               
                                
                               eV 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   96 
                   ) 
                 
               
             
           
         
       
     
         [0167]    The experimental total bond dissociation energy of C n H 2n+2 , E D     exp   (C n H 2n+2 ), is given by the negative difference between the enthalpy of its formation (ΔH f (C n H 2n+2 (gas))) and the sum of the enthalpy of the formation of the reactant gaseous carbons (ΔH f (C(gas))) and hydrogen (ΔH f (H (gas))) atoms: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             
                               D 
                               
                                 ex 
                                  
                                 
                                     
                                 
                                  
                                 p 
                               
                             
                           
                            
                           
                             ( 
                             
                               
                                 C 
                                 n 
                               
                                
                               
                                 H 
                                 
                                   
                                     2 
                                      
                                     n 
                                   
                                   + 
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           - 
                           
                             { 
                             
                               
                                 
                                   
                                     
                                       Δ 
                                        
                                       
                                           
                                       
                                        
                                       
                                         
                                           H 
                                           f 
                                         
                                          
                                         
                                           ( 
                                           
                                             
                                               C 
                                               n 
                                             
                                              
                                             
                                               
                                                 H 
                                                 
                                                   
                                                     2 
                                                      
                                                     n 
                                                   
                                                   + 
                                                   2 
                                                 
                                               
                                                
                                               
                                                 ( 
                                                 gas 
                                                 ) 
                                               
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     - 
                                   
                                 
                               
                               
                                 
                                   
                                     [ 
                                     
                                       
                                         
                                           
                                             
                                               n 
                                                
                                               
                                                   
                                               
                                                
                                               Δ 
                                                
                                               
                                                   
                                               
                                                
                                               
                                                 
                                                   H 
                                                   f 
                                                 
                                                  
                                                 
                                                   ( 
                                                   
                                                     C 
                                                      
                                                     
                                                       ( 
                                                       gas 
                                                       ) 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                             
                                             + 
                                           
                                         
                                       
                                       
                                         
                                           
                                             
                                               ( 
                                               
                                                 
                                                   2 
                                                    
                                                   n 
                                                 
                                                 + 
                                                 2 
                                               
                                               ) 
                                             
                                              
                                             Δ 
                                              
                                             
                                                 
                                             
                                              
                                             
                                               
                                                 H 
                                                 f 
                                               
                                                
                                               
                                                 ( 
                                                 
                                                   H 
                                                    
                                                   
                                                     ( 
                                                     gas 
                                                     ) 
                                                   
                                                 
                                                 ) 
                                               
                                             
                                           
                                         
                                       
                                     
                                     ] 
                                   
                                 
                               
                             
                             } 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           - 
                           
                             { 
                             
                               
                                 
                                   
                                     
                                       Δ 
                                        
                                       
                                           
                                       
                                        
                                       
                                         
                                           H 
                                           f 
                                         
                                          
                                         
                                           ( 
                                           
                                             
                                               C 
                                               n 
                                             
                                              
                                             
                                               
                                                 H 
                                                 
                                                   
                                                     2 
                                                      
                                                     n 
                                                   
                                                   + 
                                                   2 
                                                 
                                               
                                                
                                               
                                                 ( 
                                                 gas 
                                                 ) 
                                               
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     - 
                                   
                                 
                               
                               
                                 
                                   
                                     [ 
                                     
                                       
                                         
                                           
                                             
                                               n 
                                                
                                               
                                                   
                                               
                                                
                                               7.42774 
                                                
                                               
                                                   
                                               
                                                
                                               eV 
                                             
                                             + 
                                           
                                         
                                       
                                       
                                         
                                           
                                             
                                               ( 
                                               
                                                 
                                                   2 
                                                    
                                                   n 
                                                 
                                                 + 
                                                 2 
                                               
                                               ) 
                                             
                                              
                                             2.259353 
                                              
                                             
                                                 
                                             
                                              
                                             eV 
                                           
                                         
                                       
                                     
                                     ] 
                                   
                                 
                               
                             
                             } 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   97 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where the heats of formation atomic carbon and hydrogen gas are given by [32-33] 
         [0000]      Δ H   f (C(gas))=716.68 kJ/mole (7.42774 eV/molecule)   (98) 
         [0000]      Δ H   f (H(gas))=217.998 kJ/mole (2.259353 eV/molecule)   (99) 
         [0168]    The comparison of the results predicted by Eq. (96) and the experimental values given by using Eqs. (97-99) with the data from Refs. [32-33] is given in Table 6. 
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 6 
               
             
             
               
                   
               
               
                 Summary results of n-alkanes. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 3 H 8   
                 Propane 
                 41.46896 
                 41.434 
                 −0.00085 
               
               
                 C 4 H 10   
                 Butane 
                 53.62666 
                 53.61 
                 −0.00036 
               
               
                 C 5 H 12   
                 Pentane 
                 65.78436 
                 65.77 
                 −0.00017 
               
               
                 C 6 H 14   
                 Hexane 
                 77.94206 
                 77.93 
                 −0.00019 
               
               
                 C 7 H 16   
                 Heptane 
                 90.09976 
                 90.09 
                 −0.00013 
               
               
                 C 8 H 18   
                 Octane 
                 102.25746 
                 102.25 
                 −0.00006 
               
               
                 C 9 H 20   
                 Nonane 
                 114.41516 
                 114.40 
                 −0.00012 
               
               
                 C 10 H 22   
                 Decane 
                 126.57286 
                 126.57 
                 −0.00003 
               
               
                 C 11 H 24   
                 Undecane 
                 138.73056 
                 138.736 
                 0.00004 
               
               
                 C 12 H 26   
                 Dodecane 
                 150.88826 
                 150.88 
                 −0.00008 
               
               
                 C 18 H 38   
                 Octadecane 
                 223.83446 
                 223.85 
                 0.00008 
               
               
                   
               
             
          
         
       
     
         [0169]    The following list of references, which are also incorporated herein by reference in their entirety, are referred to in the above sections using [brackets]: 
       REFERENCES 
       [0000]    
       
         
           
             1. R. Mills,  The Grand Unified Theory of Classical Physics;  June 2008 Edition, posted at http://www.blacklightpower.com/theory/bookdownload.shtml. 
             2. R. L. Mills, B. Holverstott, B. Good, N. Hogle, A. Makwana, J. Paulus, “Total Bond Energies of Exact Classical Solutions of Molecules Generated by Millsian 1.0 Compared to Those Computed Using Modern 3-21G and 6-31G* Basis Sets”, submitted. 
             3. R. L. Mills, “Classical Quantum Mechanics”, Physics Essays, Vol. 16, No. 4, December, (2003), pp. 433-498. 
             4. R. Mills, “Physical Solutions of the Nature of the Atom, Photon, and Their Interactions to Form Excited and Predicted Hydrino States”, in press. 
             5. R. L. Mills, “Exact Classical Quantum Mechanical Solutions for One- Through Twenty-Electron Atoms”, Physics Essays, Vol. 18, (2005), pp. 321-361. 
             6. R. L. Mills, “The Nature of the Chemical Bond Revisited and an Alternative Maxwellian Approach”, Physics Essays, Vol. 17, (2004), pp. 342-389. 
             7. R. L. Mills, “Maxwell&#39;s Equations and QED: Which is Fact and Which is Fiction”, Vol. 19, (2006), pp. 225-262. 
             8. R. L. Mills, “Exact Classical Quantum Mechanical Solution for Atomic Helium Which Predicts Conjugate Parameters from a Unique Solution for the First Time”, in press. 
             9. R. L. Mills, “The Fallacy of Feynman&#39;s Argument on the Stability of the Hydrogen Atom According to Quantum Mechanics,” Annales de la Fondation Louis de Broglie, Vol. 30, No. 2, (2005), pp. 129-151. 
             10. R. Mills, “The Grand Unified Theory of Classical Quantum Mechanics”, Int. J. Hydrogen Energy, Vol. 27, No. 5, (2002), pp. 565-590. 
             11. R. Mills, The Nature of Free Electrons in Superfluid Helium—a Test of Quantum Mechanics and a Basis to Review its Foundations and Make a Comparison to Classical Theory, Int. J. Hydrogen Energy, Vol. 26, No. 10, (2001), pp. 1059-1096. 
             12. R. Mills, “The Hydrogen Atom Revisited”, Int. J. of Hydrogen Energy, Vol. 25, Issue 12, December, (2000), pp. 1171-1183. 
             13. R. Mills, “The Grand Unified Theory of Classical Quantum Mechanics”, Global Foundation, Inc. Orbis Scientiae entitled  The Role of Attractive and Repulsive Gravitational Forces in Cosmic Acceleration of Particles The Origin of the Cosmic Gamma  Ray Bursts, (29th Conference on High Energy Physics and Cosmology Since 1964) Dr. Behram N. Kursunoglu, Chairman, Dec. 14-17, 2000, Lago Mar Resort, Fort Lauderdale, Fla., Kluwer Academic/Plenum Publishers, New York, pp. 243-258. 
             14. P. Pearle, Foundations of Physics, “Absence of radiationless motions of relativistically rigid classical electron”, Vol. 7, Nos. 11/12, (1977), pp. 931-945. 
             15. V. F. Weisskopf, Reviews of Modern Physics, Vol. 21, No. 2, (1949), pp. 305-315. 
             16. A. Einstein, B. Podolsky, N. Rosen, Phys. Rev., Vol. 47, (1935), p. 777. 
             17. H. Wergeland, “The Klein Paradox Revisited”,  Old and New Questions in Physics, Cosmology, Philosophy, and Theoretical Biology,  A. van der Merwe, Editor, Plenum Press, New York, (1983), pp. 503-515. 
             18. F. Laloë, Do we really understand quantum mechanics? Strange correlations, paradoxes, and theorems, Am. J. Phys. 69 (6), June 2001, 655-701. 
             19. F. Dyson, “Feynman&#39;s proof of Maxwell equations”, Am. J. Phys., Vol. 58, (1990), pp. 209-211. 
             20. H. A. Haus, “On the radiation from point charges”, American Journal of Physics, Vol. 54, (1986), 1126-1129. 
             21. J. D. Jackson,  Classical Electrodynamics,  Second Edition, John Wiley &amp; Sons, New York, (1975), pp. 739-779. 
             22. J. D. Jackson,  Classical Electrodynamics,  Second Edition, John Wiley &amp; Sons, New York, (1975), p. 111. 
             23. T. A. Abbott and D. J. Griffiths, Am. J. Phys., Vol. 153, No. 12, (1985), pp. 1203-1211. 
             24. G. Goedecke, Phys. Rev 135B, (1964), p. 281. 
             25. http://www.blacklightpower.com/theory/theory.shtml. 
             26. W. J. Nellis, “Making Metallic Hydrogen,” Scientific American, May, (2000), pp. 84-90. 
             27. J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, D. M. Villeneuve, “Tomographic imaging of molecular orbitals”, Nature, Vol. 432, (2004), pp. 867-871. 
             28. J. A. Stratton,  Electromagnetic Theory  (McGraw-Hill Book Company, 1941), p. 195. 
             29. J. D. Jackson,  Classical Electrodynamics,  2 nd  Edition (John Wiley &amp; Sons, New York, (1975), pp. 17-22. 
             30. H. A. Haus, J. R. Melcher, “Electromagnetic Fields and Energy,” Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, (1985), Sec. 5.3. 
             31. NIST Computational Chemistry Comparison and Benchmark Data Base, NIST Standard Reference Database Number 101, Release 14, Sept., (2006), Editor R. D. Johnson III, http://srdata.nist.gov/cccbdb. 
             32. D. R. Lide,  CRC Handbook of Chemistry and Physics,  79th Edition, CRC Press, Boca Raton, Fla., (1998-9), pp. 9-63. 
             33. D. R. Lide,  CRC Handbook of Chemistry and Physics,  79th Edition, CRC Press, Boca Raton, Fla., (1998-9), pp. 5-1 to 5-60. 
           
         
       
     
         [0203]    The equation numbers and sections referenced herein infra. are those disclosed in R. Mills,  The Grand Unified Theory of Classical Physics;  June 2008 Edition, posted at http://www.blacklightpower.com/theory/bookdownload.shtml which is herein incorporated by reference in its entirety. 
         [0204]    The following represents prophetic examples that support the foregoing various embodiments according to the present disclosure. 
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 7 
               
               
                   
               
               
                 The final values of r Atom.HO.AO , E Coulomb  (mol.atom, msp 3 ), and E(C mol C2sp 3 ) calculated 
               
               
                 using the values of E T (C BO -C, C2sp 3 ) given in Tables 4 and 5. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Atom 
                   
                   
                   
                   
               
               
                 Hybridization 
               
               
                 Designation 
                 E T (C BO -C, C2sp 3 ) 
                 E T (C BO -C, C2sp 3 ) 
                 E T (C BO -C, C2sp 3 ) 
                 E T (C BO -C, C2sp 3 ) 
               
               
                   
               
               
                 1 
                 0 
                 0 
                 0 
                 0 
               
               
                 2 
                 −0.36229 
                 0 
                 0 
                 0 
               
               
                 3 
                 −0.46459 
                 0 
                 0 
                 0 
               
               
                 4 
                 −0.56689 
                 0 
                 0 
                 0 
               
               
                 5 
                 −0.72457 
                 0 
                 0 
                 0 
               
               
                 6 
                 −0.85034 
                 0 
                 0 
                 0 
               
               
                 7 
                 −0.92918 
                 0 
                 0 
                 0 
               
               
                 8 
                 −0.54343 
                 −0.54343 
                 0 
                 0 
               
               
                 9 
                 −0.18114 
                 −0.92918 
                 0 
                 0 
               
               
                 10 
                 −1.13379 
                 0 
                 0 
                 0 
               
               
                 11 
                 −1.14485 
                 0 
                 0 
                 0 
               
               
                 12 
                 −0.46459 
                 −0.82688 
                 0 
                 0 
               
               
                 13 
                 −1.34946 
                 0 
                 0 
                 0 
               
               
                 14 
                 −1.3725 
                 0 
                 0 
                 0 
               
               
                 15 
                 −0.46459 
                 −0.92918 
                 0 
                 0 
               
               
                 16 
                 −0.72457 
                 −0.72457 
                 0 
                 0 
               
               
                 17 
                 −0.5669 
                 −0.92918 
                 0 
                 0 
               
               
                 18 
                 −0.82688 
                 −0.72457 
                 0 
                 0 
               
               
                 19 
                 −1.56513 
                 0 
                 0 
                 0 
               
               
                 20 
                 −0.64574 
                 −0.92918 
                 0 
                 0 
               
               
                 21 
                 −1.57711 
                 0 
                 0 
                 0 
               
               
                 22 
                 −0.72457 
                 −0.92918 
                 0 
                 0 
               
               
                 23 
                 −0.85035 
                 −0.85035 
                 0 
                 0 
               
               
                 24 
                 −1.79278 
                 0 
                 0 
                 0 
               
               
                 25 
                 −1.13379 
                 −0.72457 
                 0 
                 0 
               
               
                 26 
                 −0.92918 
                 −0.92918 
                 0 
                 0 
               
               
                 27 
                 −0.56690 
                 −0.54343 
                 −0.85034 
                 0 
               
               
                 28 
                 −2.02043 
                 0 
                 0 
                 0 
               
               
                 29 
                 −1.13379 
                 −0.92918 
                 0 
                 0 
               
               
                 30 
                 −0.56690 
                 −0.56690 
                 −0.92918 
                 0 
               
               
                 31 
                 −0.85035 
                 −0.85035 
                 −0.46459 
                 0 
               
               
                 32 
                 −0.85035 
                 −0.42517 
                 −0.92918 
                 0 
               
               
                 33 
                 −0.5669 
                 −0.72457 
                 −0.92918 
                 0 
               
               
                 34 
                 −1.13379 
                 −1.13379 
                 0 
                 0 
               
               
                 35 
                 −1.34946 
                 −0.92918 
                 0 
                 0 
               
               
                 36 
                 −0.46459 
                 −0.92918 
                 −0.92918 
                 0 
               
               
                 37 
                 −0.64574 
                 −0.85034 
                 −0.85034 
                 0 
               
               
                 38 
                 −0.85035 
                 −0.5669 
                 −0.92918 
                 0 
               
               
                 39 
                 −0.72457 
                 −0.72457 
                 −0.92918 
                 0 
               
               
                 40 
                 −0.75586 
                 −0.75586 
                 −0.92918 
                 0 
               
               
                 41 
                 −0.74804 
                 −0.85034 
                 −0.85034 
                 0 
               
               
                 42 
                 −0.82688 
                 −0.72457 
                 −0.92918 
                 0 
               
               
                 43 
                 −0.72457 
                 −0.92918 
                 −0.92918 
                 0 
               
               
                 44 
                 −0.92918 
                 −0.72457 
                 −0.92918 
                 0 
               
               
                 45 
                 −0.54343 
                 −0.54343 
                 −0.5669 
                 −0.92918 
               
               
                 46 
                 −0.92918 
                 −0.85034 
                 −0.85034 
                 0 
               
               
                 47 
                 −0.42517 
                 −0.42517 
                 −0.85035 
                 −0.92918 
               
               
                 48 
                 −0.82688 
                 −0.92918 
                 −0.92918 
                 0 
               
               
                 49 
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
               
               
                 50 
                 −0.85035 
                 −0.54343 
                 −0.5669 
                 −0.92918 
               
               
                 51 
                 −1.34946 
                 −0.64574 
                 −0.92918 
                 0 
               
               
                 52 
                 −0.85034 
                 −0.54343 
                 −0.60631 
                 −0.92918 
               
               
                 53 
                 −1.1338 
                 −0.92918 
                 −0.92918 
                 0 
               
               
                 54 
                 −0.46459 
                 −0.85035 
                 −0.85035 
                 −0.92918 
               
               
                 55 
                 −0.82688 
                 −1.34946 
                 −0.92918 
                 0 
               
               
                 56 
                 −0.92918 
                 −1.34946 
                 −0.92918 
                 0 
               
               
                 57 
                 −1.13379 
                 −1.13379 
                 −1.13379 
                 0 
               
               
                 58 
                 −1.79278 
                 −0.92918 
                 −0.92918 
                 0 
               
               
                   
               
             
          
           
               
                 Atom 
                   
                   
                 E Coulomb (mol.atom, msp 3 ) 
                 E(C mol 2sp 3 ) 
               
               
                 Hybridization 
                   
                 r Atom.HO.AO   
                 (eV) 
                 (eV) 
               
               
                 Designation 
                 E T (C BO -C, C2sp 3 ) 
                 Final 
                 Final 
                 Final 
               
               
                   
               
               
                 1 
                 0 
                 0.91771 
                 −14.82575 
                 −14.63489 
               
               
                 2 
                 0 
                 0.89582 
                 −15.18804 
                 −14.99717 
               
               
                 3 
                 0 
                 0.88983 
                 −15.29034 
                 −15.09948 
               
               
                 4 
                 0 
                 0.88392 
                 −15.39265 
                 −15.20178 
               
               
                 5 
                 0 
                 0.87495 
                 −15.55033 
                 −15.35946 
               
               
                 6 
                 0 
                 0.86793 
                 −15.6761 
                 −15.48523 
               
               
                 7 
                 0 
                 0.86359 
                 −15.75493 
                 −15.56407 
               
               
                 8 
                 0 
                 0.85503 
                 −15.91261 
                 −15.72175 
               
               
                 9 
                 0 
                 0.85377 
                 −15.93607 
                 −15.74521 
               
               
                 10 
                 0 
                 0.85252 
                 −15.95955 
                 −15.76868 
               
               
                 11 
                 0 
                 0.85193 
                 −15.9706 
                 −15.77974 
               
               
                 12 
                 0 
                 0.84418 
                 −16.11722 
                 −15.92636 
               
               
                 13 
                 0 
                 0.84115 
                 −16.17521 
                 −15.98435 
               
               
                 14 
                 0 
                 0.83995 
                 −16.19826 
                 −16.00739 
               
               
                 15 
                 0 
                 0.83885 
                 −16.21952 
                 −16.02866 
               
               
                 16 
                 0 
                 0.836 
                 −16.2749 
                 −16.08404 
               
               
                 17 
                 0 
                 0.8336 
                 −16.32183 
                 −16.13097 
               
               
                 18 
                 0 
                 0.83078 
                 −16.37721 
                 −16.18634 
               
               
                 19 
                 0 
                 0.83008 
                 −16.39089 
                 −16.20002 
               
               
                 20 
                 0 
                 0.82959 
                 −16.40067 
                 −16.20981 
               
               
                 21 
                 0 
                 0.82948 
                 −16.40286 
                 −16.212 
               
               
                 22 
                 0 
                 0.82562 
                 −16.47951 
                 −16.28865 
               
               
                 23 
                 0 
                 0.82327 
                 −16.52645 
                 −16.33559 
               
               
                 24 
                 0 
                 0.81871 
                 −16.61853 
                 −16.42767 
               
               
                 25 
                 0 
                 0.81549 
                 −16.68411 
                 −16.49325 
               
               
                 26 
                 0 
                 0.81549 
                 −16.68412 
                 −16.49325 
               
               
                 27 
                 0 
                 0.81052 
                 −16.78642 
                 −16.59556 
               
               
                 28 
                 0 
                 0.80765 
                 −16.84619 
                 −16.65532 
               
               
                 29 
                 0 
                 0.80561 
                 −16.88872 
                 −16.69786 
               
               
                 30 
                 0 
                 0.80561 
                 −16.88873 
                 −16.69786 
               
               
                 31 
                 0 
                 0.80076 
                 −16.99104 
                 −16.80018 
               
               
                 32 
                 0 
                 0.79891 
                 −17.03045 
                 −16.83959 
               
               
                 33 
                 0 
                 0.78916 
                 −17.04641 
                 −16.85554 
               
               
                 34 
                 0 
                 0.79597 
                 −17.09334 
                 −16.90248 
               
               
                 35 
                 0 
                 0.79546 
                 −17.1044 
                 −16.91353 
               
               
                 36 
                 0 
                 0.79340 
                 −17.14871 
                 −16.95784 
               
               
                 37 
                 0 
                 0.79232 
                 −17.17217 
                 −16.98131 
               
               
                 38 
                 0 
                 0.79232 
                 −17.17218 
                 −16.98132 
               
               
                 39 
                 0 
                 0.79085 
                 −17.20408 
                 −17.01322 
               
               
                 40 
                 0 
                 0.78798 
                 17.26666 
                 17.07580 
               
               
                 41 
                 0 
                 0.78762 
                 17.27448 
                 17.08362 
               
               
                 42 
                 0 
                 0.78617 
                 −17.30638 
                 −17.11552 
               
               
                 43 
                 0 
                 0.78155 
                 −17.40868 
                 −17.21782 
               
               
                 44 
                 0 
                 0.78155 
                 −17.40869 
                 −17.21783 
               
               
                 45 
                 0 
                 0.78155 
                 −17.40869 
                 −17.21783 
               
               
                 46 
                 0 
                 0.77945 
                 −17.45561 
                 −17.26475 
               
               
                 47 
                 0 
                 0.77945 
                 −17.45563 
                 −17.26476 
               
               
                 48 
                 0 
                 0.77699 
                 −17.51099 
                 −17.32013 
               
               
                 49 
                 0 
                 0.77247 
                 −17.6133 
                 −17.42244 
               
               
                 50 
                 0 
                 0.76801 
                 −17.71561 
                 −17.52475 
               
               
                 51 
                 0 
                 0.76652 
                 −17.75013 
                 −17.55927 
               
               
                 52 
                 0 
                 0.76631 
                 −17.75502 
                 −17.56415 
               
               
                 53 
                 0 
                 0.7636 
                 −17.81791 
                 −17.62705 
               
               
                 54 
                 0 
                 0.75924 
                 −17.92022 
                 −17.72936 
               
               
                 55 
                 0 
                 0.75877 
                 −17.93128 
                 −17.74041 
               
               
                 56 
                 0 
                 0.75447 
                 −18.03358 
                 −17.84272 
               
               
                 57 
                 0 
                 0.74646 
                 −18.22712 
                 −18.03626 
               
               
                 58 
                 0 
                 0.73637 
                 −18.47690 
                 −18.28604 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 8 
               
               
                   
               
               
                 The final values of r Atom.HO.AO , E Coulomb  (mol.atom, msp 3 ), and E(C mol C2sp 3 ) calculated 
               
               
                 for heterocyclic groups using the values of E T (C BO -C, C2sp 3 ) given in Tables 4 and 5. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Atom 
                   
                   
                   
                   
               
               
                 Hybridization 
               
               
                 Designation 
                 E T (C BO -C, C2sp 3 ) 
                 E T (C BO -C, C2sp 3 ) 
                 E T (C BO -C, C2sp 3 ) 
                 E T (C BO -C, C2sp 3 ) 
               
               
                   
               
               
                 1 
                 0 
                 0 
                 0 
                 0 
               
               
                 2 
                 −0.56690 
                 0 
                 0 
                 0 
               
               
                 3 
                 −0.72457 
                 0 
                 0 
                 0 
               
               
                 4 
                 −0.92918 
                 0 
                 0 
                 0 
               
               
                 5 
                 −0.54343 
                 −0.54343 
                 0 
                 0 
               
               
                 6 
                 −1.13379 
                 0 
                 0 
                 0 
               
               
                 7 
                 −0.60631 
                 −0.60631 
                 0 
                 0 
               
               
                 8 
                 −1.34946 
                 0 
                 0 
                 0 
               
               
                 9 
                 −0.46459 
                 −0.92918 
                 0 
                 0 
               
               
                 10 
                 −0.72457 
                 −0.72457 
                 0 
                 0 
               
               
                 11 
                 0.00000 
                 −0.92918 
                 −0.56690 
                 0 
               
               
                 12 
                 −0.92918 
                 −0.60631 
                 0 
                 0 
               
               
                 13 
                 0 
                 −1.13379 
                 −0.46459 
                 0 
               
               
                 14 
                 −0.92918 
                 −0.72457 
                 0 
                 0 
               
               
                 15 
                 −0.85035 
                 −0.85035 
                 0 
                 0 
               
               
                 16 
                 −0.82688 
                 0 
                 0 
                 0 
               
               
                 17 
                 −0.92918 
                 −0.92918 
                 0 
                 0 
               
               
                 18 
                 −1.13379 
                 −0.72457 
                 0 
                 0 
               
               
                 19 
                 −0.92918 
                 −0.56690 
                 −0.46459 
                 0 
               
               
                 20 
                 −1.13379 
                 −0.92918 
                 0 
                 0 
               
               
                 21 
                 −0.85035 
                 −0.85035 
                 −0.46459 
                 0 
               
               
                 22 
                 0 
                 −1.34946 
                 −0.82688 
                 0 
               
               
                 23 
                 −0.85034 
                 −0.85034 
                 −0.56690 
                 0 
               
               
                 24 
                 −1.13379 
                 −1.13380 
                 0 
                 0 
               
               
                 25 
                 −1.34946 
                 −0.92918 
                 0 
                 0 
               
               
                 26 
                 −0.85035 
                 −0.54343 
                 0.00000 
                 −0.92918 
               
               
                 27 
                 −0.85035 
                 −0.56690 
                 −0.92918 
                 0 
               
               
                 28 
                 −0.56690 
                 −0.92918 
                 −0.92918 
                 0 
               
               
                 29 
                 −0.46459 
                 −1.13380 
                 −0.92918 
                 0 
               
               
                 30 
                 −0.54343 
                 −0.54343 
                 −0.56690 
                 −0.92918 
               
               
                 31 
                 −0.85034 
                 −0.28345 
                 −0.54343 
                 −0.92918 
               
               
                 32 
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
               
               
                 33 
                 −0.85034 
                 −0.54343 
                 −0.56690 
                 −0.92918 
               
               
                 34 
                 −0.85034 
                 −0.54343 
                 −0.60631 
                 −0.92918 
               
               
                 35 
                 −1.13379 
                 −0.92918 
                 −0.92918 
                 0 
               
               
                 36 
                 −1.13379 
                 −1.13380 
                 −0.72457 
                 0 
               
               
                 37 
                 −0.46459 
                 −0.85035 
                 −0.85035 
                 −0.92918 
               
               
                 38 
                 −0.92918 
                 −1.34946 
                 −0.82688 
                 0 
               
               
                 39 
                 −0.85034 
                 −0.54343 
                 −0.60631 
                 −1.13379 
               
               
                 40 
                 −1.13380 
                 −1.13379 
                 −0.92918 
                 0 
               
               
                 41 
                 −1.13379 
                 −1.13379 
                 −1.13379 
                 0 
               
               
                   
               
             
          
           
               
                 Atom 
                   
                   
                 E Coulomb  (mol.atom, msp 3 ) 
                   
               
               
                 Hybridization 
                   
                 r Atom.HO.AO   
                 (eV) 
                 E(C mol  2sp 3 ) (eV) 
               
               
                 Designation 
                 E T (C BO -C, 2sp 3 ) 
                 Final 
                 Final 
                 Final 
               
               
                   
               
               
                 1 
                 0 
                 0.91771 
                 −14.82575 
                 −14.63489 
               
               
                 2 
                 0 
                 0.88392 
                 −15.39265 
                 −15.20178 
               
               
                 3 
                 0 
                 0.87495 
                 −15.55033 
                 −15.35946 
               
               
                 4 
                 0 
                 0.86359 
                 −15.75493 
                 −15.56407 
               
               
                 5 
                 0 
                 0.85503 
                 −15.91261 
                 −15.72175 
               
               
                 6 
                 0 
                 0.85252 
                 −15.95954 
                 −15.76868 
               
               
                 7 
                 0 
                 0.84833 
                 −16.03838 
                 −15.84752 
               
               
                 8 
                 0 
                 0.84115 
                 −16.17521 
               
               
                 9 
                 0 
                 0.83885 
                 −16.21953 
                 −16.02866 
               
               
                 10 
                 0 
                 0.83600 
                 −16.27490 
                 −16.08404 
               
               
                 11 
                 0 
                 0.83360 
                 −16.32183 
                 −16.13097 
               
               
                 12 
                 0 
                 0.83159 
                 −16.36125 
                 −16.17038 
               
               
                 13 
                 0 
                 0.82840 
                 −16.42413 
                 −16.23327 
               
               
                 14 
                 0 
                 0.82562 
                 −16.47951 
                 −16.28864 
               
               
                 15 
                 0 
                 0.82327 
                 −16.52644 
                 −16.33558 
               
               
                 16 
                 0 
                 0.82053 
                 −16.58181 
                 −16.39095 
               
               
                 17 
                 0 
                 0.81549 
                 −16.68411 
                 −16.49325 
               
               
                 18 
                 0 
                 0.81549 
                 −16.68412 
                 −16.49325 
               
               
                 19 
                 0 
                 0.81052 
                 −16.78642 
                 −16.59556 
               
               
                 20 
                 0 
                 0.80561 
                 −16.88873 
                 −16.69786 
               
               
                 21 
                 0 
                 0.80076 
                 −16.99103 
                 −16.80017 
               
               
                 22 
                 0 
                 0.80024 
                 −17.00209 
                 −16.81123 
               
               
                 23 
                 0 
                 0.79597 
                 −17.09334 
                 −16.90247 
               
               
                 24 
                 0 
                 0.79597 
                 −17.09334 
                 −16.90248 
               
               
                 25 
                 0 
                 0.79546 
                 −17.10440 
                 −16.91353 
               
               
                 26 
                 0 
                 0.79340 
                 −17.14871 
                 −16.95785 
               
               
                 27 
                 0 
                 0.79232 
                 −17.17218 
                 −16.98132 
               
               
                 28 
                 0 
                 0.78870 
                 −17.25101 
                 −17.06015 
               
               
                 29 
                 0 
                 0.78405 
                 −17.35332 
                 −17.16246 
               
               
                 30 
                 0 
                 0.78155 
                 −17.40869 
                 −17.21783 
               
               
                 31 
                 0 
                 0.78050 
                 −17.43216 
                 −17.24130 
               
               
                 32 
                 0 
                 0.77247 
                 −17.61330 
                 −17.42243 
               
               
                 33 
                 0 
                 0.76801 
                 −17.71560 
                 −17.52474 
               
               
                 34 
                 0 
                 0.76631 
                 −17.75502 
                 −17.56416 
               
               
                 35 
                 0 
                 0.76360 
                 −17.81791 
                 −17.62704 
               
               
                 36 
                 0 
                 0.76360 
                 −17.81791 
                 −17.62705 
               
               
                 37 
                 0 
                 0.75924 
                 −17.92022 
                 −17.72935 
               
               
                 38 
                 0 
                 0.75878 
                 −17.93127 
                 −17.74041 
               
               
                 39 
                 0 
                 0.75758 
                 −17.95963 
                 −17.76877 
               
               
                 40 
                 0 
                 0.75493 
                 −18.02252 
                 −17.83166 
               
               
                 41 
                 0 
                 0.74646 
                 −18.22713 
                 −18.03627 
               
               
                   
               
             
          
         
       
     
         [0205]    Halobenzenes 
         [0206]    Halobenzenes have the formula C 6 H 6-m X m X═F, Cl, Br, I and comprise the benzene molecule with at least one hydrogen atom replaced by a halogen atom corresponding to a C—X functional group. The aromatic C 3e ═C and C—H functional groups are equivalent to those of benzene given in Aromatic and Heterocyclic Compounds section. The hybridization factors of the aryl C—X functional groups are equivalent to those of the corresponding alkyl halides as given in Tables 15.30, 15.36, 15.42, and 15.48, and are solved using the same principles as those used to solve the alkyl halide functional groups as given in the corresponding sections. In each case, the 2s and 2p AOs of each C hybridize to form a single 2sp 3  shell as an energy minimum, and the sharing of electrons between the C2sp 3  HO and X AO to form a MO permits each participating hybridized orbital to decrease in radius and energy. Therefore, the MO is energy matched to the C2sp 3  HO such that E(AO/HO) in Eq. (15.51) is −14.63489 eV. E T (atom-atom,msp 3 .AO) of each C—X functional group given in Table 12 that achieves matching of the energies of the AOs and HOs within the functional groups of the MOs are those of alkanes and alkenes given in Tables 4 and 5. To further match energies within each MO that bridges the halogen AO and aromatic carbon C2sp 3  HO, ΔE H     2     MO  (AO/HO) in Eq. (15.51) is E T (atom-atom,msp 3 .AO) of the alkene C═C function group, −2.26759 eV given by Eq. (14.247), plus the maximum possible contribution of E T (atom-atom,msp 3 .AO) of the C—X functional group to minimize the energy of the MO as given in Table 12. E initial (c 4  AO/HO) is −14.63489 eV (Eq. (15.25)), except for C—I due to the low ionization potential of the I AO. In order to achieve an energy minimum with energy matching within iodo-aryl molecules, E initial (c 4  AO/HO) of the C—I functional group is −15.76868 eV (Eq. (14.246)), and E T (atom-atom,msp 3 .AO) is −1.65376 eV given by the linear combination of −0.72457 eV (Eq. (14.151)) and −0.92918 eV (Eq. (14.513)), respectively. 
         [0207]    The small differences between energies of ortho, meta, and para-dichlorobenzene is due to differences in the energies of vibration in the transition state that contribute to E osc . Two types of C—Cl functional groups can be identified based on symmetry that determine the parameter R in Eq. (15.57). One corresponds to the special case of 1,3,5 substitution and the other corresponds to other cases of single or multiple substitutions of Cl for H. P-dichlorobenzene is representative of the bonding with R=a. 1,2,3-trichlorbenzene is the particular case wherein R=b. Also, beyond the binding of three chlorides E mag  is subtracted for each additional Cl due to the formation of an unpaired electrons on each C—Cl bond. 
         [0208]    The symbols of the functional groups of halobenzenes are given in Table 9. The geometrical (Eqs. (15.1-15.5) and (15.51)), intercept (Eqs. (15.80-15.87)), and energy (Eqs. (15.6-15.11), (15.17-15.65), and (15.165-15.166)) parameters of halobenzenes are given in Tables 10, 11, and 12, respectively. The total energy of each halobenzene given in Table 13 was calculated as the sum over the integer multiple of each E D (Group) of Table 12 corresponding to functional-group composition of the molecule. For each set of unpaired electrons created by bond breakage, the C2sp 3  HO magnetic energy E mag  that is subtracted from the weighted sum of the E D (Group) (eV) values based on composition is given by Eq. (15.67). The bond angle parameters of halobenzenes determined using Eqs. (15.88-15.117) are given in Table 14. The color scale, translucent view of the charge-density of chlorobenzene comprising the concentric shells of atoms with the outer shell bridged by one or more H 2 -type ellipsoidal MOs or joined with one or more hydrogen MOs is shown in  FIG. 5 . 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 9 
               
             
             
               
                   
               
               
                 The symbols of functional groups of halobenzenes. 
               
             
          
           
               
                   
                 Functional Group 
                 Group Symbol 
               
               
                   
                   
               
               
                   
                 CC (aromatic bond) 
                 C 3e ═C 
               
               
                   
                 CH (aromatic) 
                 CH (i) 
               
               
                   
                 F—C (F to aromatic bond) 
                 C—F 
               
               
                   
                 Cl—C (Cl to aromatic bond) 
                 C—Cl (a) 
               
               
                   
                 Cl—C (Cl to aromatic bond of 1,3,5- 
                 C—Cl (b) 
               
               
                   
                 trichlorbenzene) 
               
               
                   
                 Br—C (Br to aromatic bond) 
                 C—Br 
               
               
                   
                 I—C (I to aromatic bond) 
                 C—I 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 10 
               
             
             
               
                   
               
               
                 The geometrical bond parameters of halobenzenes and experimental values [1]. 
               
             
          
           
               
                   
                 C 3e ═C 
                 CH (i) 
                 C—F 
                 C—Cl (a) 
                 C—Cl (b) 
                 C—Br 
                 C—I 
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 1.47348 
                 1.60061 
                 1.60007 
                 2.20799 
                 2.20799 
                 2.30810 
                 2.50486 
               
               
                 c′ (a 0 ) 
                 1.31468 
                 1.03299 
                 1.26494 
                 1.64782 
                 1.64782 
                 1.76512 
                 1.95501 
               
               
                 Bond Length 
                 1.39140 
                 1.09327 
                 1.33875 
                 1.74397 
                 1.74397 
                 1.86812 
                 2.06909 
               
               
                 2c′ (Å) 
               
               
                 Exp. Bond Length 
                 1.400 
                 1.083 
                 1.356 [54] 
                 1.737 
                 1.737 
                 1.8674 [55] 
                 2.08 [56] 
               
               
                 (Å) 
                 (chlorobenzene) 
                 (chlorobenzene) 
                 (fluorobenzene) 
                 (chlorobenzene) 
                 (chlorobenzene) 
                 (bromobenzene) 
                 (iodobenzene) 
               
               
                 b, c (a 0 ) 
                 0.66540 
                 1.22265 
                 0.97987 
                 1.46967 
                 1.46967 
                 1.48718 
                 1.56597 
               
               
                 e 
                 0.89223 
                 0.64537 
                 0.79055 
                 0.74630 
                 0.74630 
                 0.76475 
                 0.78049 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 11 
               
               
                   
               
               
                 The MO to HO intercept geometrical bond parameters of halobenzenes. 
               
               
                 E T  is E T (atom - atom, msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                 E T   
                 E T   
                 E T   
                 E T   
                 Final Total Energy 
                   
                   
               
               
                   
                   
                 (eV) 
                 (eV) 
                 (eV) 
                 (eV) 
                 C2sp 3   
                 r initial   
                 r final   
               
               
                 Bond 
                 Atom 
                 Bond 1 
                 Bond 2 
                 Bond 3 
                 Bond 4 
                 (eV) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 C—H (C b H) 
                 C b   
                 −0.85035 
                 −0.85035 
                 −0.56690 
                 0 
                 −153.88327 
                 0.91771 
                 0.79597 
               
               
                 C 3e ═HC b   3e ═C 
                 C b   
                 −0.85035 
                 −0.85035 
                 −0.56690 
                 0 
                 −153.88327 
                 0.91771 
                 0.79597 
               
               
                 (C 3e ═) 2 C a —F 
                 C a   
                 −1.03149 
                 −0.85035 
                 −0.85035 
                 0 
                 −154.34787 
                 0.91771 
                 0.77491 
               
               
                 (C 3e ═) 2 C a —F 
                 F 
                 −1.03149 
                 0 
                 0 
                 0 
                   
                 0.78069 
                 0.85802 
               
               
                 (C 3e ═) 2 C a —Cl 
                 C a   
                 −0.36229 
                 −0.85035 
                 −0.85035 
                 0 
                 −153.67867 
                 0.91771 
                 0.80561 
               
               
                 (C 3e ═) 2 C a —Cl 
                 Cl 
                 −0.36229 
                 0 
                 0 
                 0 
                   
                 1.05158 
                 0.89582 
               
               
                 C b   3e ═(Cl)C a   3e ═C b   
                 C b   
                 −0.36229 
                 −0.85035 
                 −0.85035 
                 0 
                 −153.67867 
                 0.91771 
                 0.80561 
               
               
                 (C b  bound to Cl) 
               
               
                 (C 3e ═) 2 C a —Br 
                 C a   
                 −0.18114 
                 −0.85035 
                 −0.85035 
                 0 
                 −153.49753 
                 0.91771 
                 0.81435 
               
               
                 (C 3e ═) 2 C a —Br 
                 Br 
                 −0.18114 
                 0 
                 0 
                 0 
                   
                 1.15169 
                 0.90664 
               
               
                 (C 3e ═) 2 C a —I 
                 C a   
                 −0.82688 
                 −0.85035 
                 −0.85035 
                 0 
                 −154.14326 
                 0.91771 
                 0.78405 
               
               
                 (C 3e ═) 2 C a —I 
                 I 
                 −0.82688 
                 0 
                 0 
                 0 
                   
                 1.30183 
                 0.86923 
               
               
                   
               
             
          
           
               
                   
                   
                 E(C2sp 3 ) 
                   
                   
                   
                   
                   
               
               
                   
                 E Coulomb (C2sp 3 )(eV) 
                 (eV) 
                 θ′ 
                 θ 1   
                 θ 2   
                 d 1   
                 d 2   
               
               
                 Bond 
                 Final 
                 Final 
                 (°) 
                 (°) 
                 (°) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 C—H (C b H) 
                 −17.09334 
                 −16.90248 
                 74.42 
                 105.58 
                 38.84 
                 1.24678 
                 0.21379 
               
               
                 C 3e ═HC b   3e ═C 
                 −17.09334 
                 −16.90248 
                 134.24 
                 45.76 
                 58.98 
                 0.75935 
                 0.55533 
               
               
                 (C 3e ═) 2 C a —F 
                 −17.55793 
                 −17.36707 
                 106.58 
                 73.42 
                 49.28 
                 1.04378 
                 0.22116 
               
               
                 (C 3e ═) 2 C a —F 
                 −15.85724 
                   
                 112.35 
                 67.65 
                 54.08 
                 0.93865 
                 0.32629 
               
               
                 (C 3e ═) 2 C a —Cl 
                 −16.88873 
                 −16.69786 
                 73.32 
                 106.68 
                 31.67 
                 1.87911 
                 0.23129 
               
               
                 (C 3e ═) 2 C a —Cl 
                 15.18804 
                   
                 82.92 
                 97.08 
                 37.22 
                 1.75824 
                 0.11042 
               
               
                 C b   3e ═Cl)C a   3e ═C b   
                 −16.88873 
                 −16.69786 
                 134.65 
                 45.35 
                 59.47 
                 0.74854 
                 0.56614 
               
               
                 (C b  bound to Cl) 
               
               
                 (C 3e ═) 2 C a —Br 
                 −16.70759 
                 −16.51672 
                 76.64 
                 103.36 
                 32.19 
                 1.95326 
                 0.18814 
               
               
                 (C 3e ═) 2 C a —Br 
                 −15.00689 
                   
                 85.73 
                 94.27 
                 37.44 
                 1.83258 
                 0.06746 
               
               
                 (C 3e ═) 2 C a —I 
                 −17.35332 
                 −17.16246 
                 71.42 
                 108.58 
                 28.33 
                 2.20480 
                 0.24979 
               
               
                 (C 3e ═) 2 C a —I 
                 −15.65263 
                   
                 80.69 
                 99.31 
                 33.21 
                 2.09565 
                 0.14064 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 12 
               
             
             
               
                   
               
               
                 The energy parameters (eV) of functional groups of halobenzenes. 
               
             
          
           
               
                   
                 C 3e ═C 
                 CH (i) 
                 C—F 
                 C—Cl (a) 
                 C—Cl (b) 
                 C—Br 
                 C—I 
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
             
          
           
               
                 f 1   
                 0.75 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 n 1   
                 2 
                 1 
                 1 
                 1 
                 1 
                 2 
                 2 
               
               
                 n 2   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.5 
                 0.75 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
               
               
                 C 2   
                 0.85252 
                 1 
                 1 
                 0.81317 
                 0.81317 
                 0.74081 
                 0.65537 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 2   
                 0.85252 
                 0.91771 
                 0.77087 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 3   
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 c 4   
                 3 
                 1 
                 2 
                 2 
                 2 
                 2 
                 2 
               
               
                 c 5   
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1o   
                 0.5 
                 0.75 
                 1 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
               
               
                 C 2o   
                 0.85252 
                 1 
                 0.5 
                 0.81317 
                 0.81317 
                 0.74081 
                 0.65537 
               
               
                 V e  (eV) 
                 −101.12679 
                 −37.10024 
                 −35.58388 
                 −31.85648 
                 −31.85648 
                 −31.06557 
                 −29.13543 
               
               
                 V p  (eV) 
                 20.69825 
                 13.17125 
                 10.75610 
                 8.25686 
                 8.25686 
                 7.70816 
                 6.95946 
               
               
                 T (eV) 
                 34.31559 
                 11.58941 
                 11.11948 
                 7.21391 
                 7.21391 
                 6.72969 
                 5.81578 
               
               
                 V m  (eV) 
                 −17.15779 
                 −5.79470 
                 −5.55974 
                 −3.60695 
                 −3.60695 
                 −3.36484 
                 −2.90789 
               
               
                 E(AO/HO) (eV) 
                 0 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −2.99216 
                 −2.26759 
               
               
                 ΔE H     2     MO (AO/HO) (eV) 
                 0 
                 −1.13379 
                 −2.26759 
                 −2.99216 
                 −2.99216 
                 −14.63489 
                 −14.63489 
               
               
                 E T (AO/HO) (eV) 
                 0 
                 −13.50110 
                 −12.36730 
                 −11.64273 
                 −11.64273 
                 −11.64273 
                 −12.36730 
               
               
                 E T (H 2 MO) (eV) 
                 −63.27075 
                 −31.63539 
                 −31.63535 
                 −31.63539 
                 −31.63539 
                 −31.63530 
                 −31.63538 
               
               
                 E T (atom - atom, msp 3 .AO) (eV) 
                 −2.26759 
                 −0.56690 
                 −2.06297 
                 −0.72457 
                 −0.72457 
                 −0.36229 
                 1.65376 
               
               
                 E T (MO) (eV) 
                 −65.53833 
                 −32.20226 
                 −33.69834 
                 −32.35994 
                 −32.35994 
                 −31.99766 
                 −33.28912 
               
               
                 ω(10 15  rad/s) 
                 49.7272 
                 26.4826 
                 14.4431 
                 8.03459 
                 14.7956 
                 7.17533 
                 12.0764 
               
               
                 E K  (eV) 
                 32.73133 
                 17.43132 
                 9.50672 
                 5.28851 
                 9.73870 
                 4.72293 
                 7.94889 
               
               
                 Ē D  (eV) 
                 −0.35806 
                 −0.26130 
                 −0.20555 
                 −0.14722 
                 −0.19978 
                 −0.13757 
                 −0.18568 
               
               
                 Ē Kvib  (eV) 
                 0.19649 [49] 
                 0.35532 
                 0.10911 [11] 
                 0.08059 [12] 
                 0.08059 [12] 
                 0.08332 [15] 
                 0.06608 [16] 
               
               
                   
                   
                 Eq. (13.458) 
               
               
                 Ē osc  (eV) 
                 −0.25982 
                 −0.08364 
                 −0.15100 
                 −0.10693 
                 −0.15949 
                 −0.09591 
                 −0.15264 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                 E T (Group) (eV) 
                 −49.54347 
                 −32.28590 
                 −33.84934 
                 −32.46687 
                 −32.51943 
                 −32.09357 
                 −33.44176 
               
               
                 E initial (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −15.76868 
               
               
                 E initial (c 5  AO/HO) (eV) 
                 0 
                 −13.59844 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 E D (Group) (eV) 
                 5.63881 
                 3.90454 
                 4.57956 
                 3.19709 
                 3.24965 
                 2.82379 
                 1.90439 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 13 
               
               
                   
               
               
                 The total bond energies of halobenzenes calculated using the functional group 
               
               
                 composition and the energies of Table 15.234 compared to the experimental values 
               
               
                 [3]. The magnetic energy E mag  that is subtracted from the weighted 
               
               
                 sum of the E D (Group) (eV) values based on composition is given by (15.58). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                 C—F 
                 C—Cl (a) 
                 C—Cl (b) 
                 C—Br 
               
               
                 Formula 
                 Name 
                 C 3e ═C 
                 CH (i) 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 C 6 H 5 Cl 
                 Fluorobenzene 
                 6 
                 5 
                 1 
                 0 
                 0 
                 0 
               
               
                 C 6 H 5 Cl 
                 Chlorobenzene 
                 6 
                 5 
                   
                 1 
                 0 
               
               
                 C 6 H 4 Cl 2   
                 m-dichlorobenzene 
                 6 
                 4 
                   
                 2 
                 0 
               
               
                 C 6 H 3 Cl 3   
                 1,2,3-trichlorobenzene 
                 6 
                 3 
                   
                 3 
                 0 
               
               
                 C 6 H 3 Cl 3   
                 1,3,5-trichlorbenzene 
                 6 
                 3 
                   
                 0 
                 3 
               
               
                 C 6 Cl 6   
                 Hexachlorobenzene 
                 6 
                 0 
                   
                 6 
                 0 
               
               
                 C 6 H 5 Br 
                 Bromobenzene 
                 6 
                 5 
                 0 
                 0 
                 0 
                 1 
               
               
                 C 6 H 5 I 
                 Iodobenzene 
                 6 
                 5 
                 0 
                 0 
                 0 
                 0 
               
               
                   
               
             
          
           
               
                   
                   
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 C—I 
                   
                 Total Bond 
                 Total Bond 
               
               
                 Formula 
                 Name 
                 Group 
                 E mag   
                 Energy (eV) 
                 Energy (eV) 
                 Relative Error 
               
               
                   
               
               
                 C 6 H 5 Cl 
                 Fluorobenzene 
                 0 
                 0 
                 57.93510 
                 57.887 
                 −0.00083 
               
               
                 C 6 H 5 Cl 
                 Chlorobenzene 
                   
                 0 
                 56.55263 
                 56.581 
                 0.00051 
               
               
                 C 6 H 4 Cl 2   
                 m-dichlorobenzene 
                   
                 0 
                 55.84518 
                 55.852 
                 0.00012 
               
               
                 C 6 H 3 Cl 3   
                 1,2,3-trichlorobenzene 
                   
                 0 
                 55.13773 
                 55.077 
                 −0.00111 
               
               
                 C 6 H 3 Cl 3   
                 1,3,5-trichlorbenzene 
                   
                 0 
                 55.29542 
                 55.255 
                 −0.00073 
               
               
                 C 6 Cl 6   
                 Hexachlorobenzene 
                   
                 3 
                 52.57130 
                 52.477 
                 −0.00179 
               
               
                 C 6 H 5 Br 
                 Bromobenzene 
                 0 
                 0 
                 56.17932 
                 56.391 a   
                 0.00376 
               
               
                 C 6 H 5 I 
                 Iodobenzene 
                 1 
                 0 
                 55.25993 
                 55.261 
                 0.00001 
               
               
                   
               
               
                   a Liquid. 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 14 
               
               
                   
               
               
                 The bond angle parameters of halobenzenes and experimental values [1]. 
               
               
                 E T  is E T (atom - atom, msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                 2c′ 
                   
                 Atom 1 
                   
                 Atom 2 
                   
                   
               
               
                   
                 2c′ 
                 2c′ 
                 Terminal 
                   
                 Hybridization 
                   
                 Hybridization 
               
               
                 Atoms of 
                 Bond 1 
                 Bond 2 
                 Atoms 
                 E Coulombic   
                 Designation 
                 E Coulombic   
                 Designation 
                 c 2   
                 c 2   
               
               
                 Angle 
                 (a 0 ) 
                 (a 0 ) 
                 (a 0 ) 
                 Atom 1 
                 (Table 7) 
                 Atom 2 
                 (Table 7) 
                 Atom 1 
                 Atom 2 
               
               
                   
               
               
                 ∠CCC 
                 2.62936 
                 2.62936 
                 4.5585 
                 −17.17218 
                 38 
                 −17.17218 
                 38 
                 0.79232 
                 0.79232 
               
               
                 (aromatic) 
               
               
                 ∠CCH 
               
               
                 ∠CCX 
               
               
                 (aromatic) 
               
               
                   
               
             
          
           
               
                 Atoms of 
                   
                   
                   
                   
                 E T   
                 θ v   
                 θ 1   
                 θ 2   
                 Cal. θ 
                 Exp. θ 
               
               
                 Angle 
                 C 1   
                 C 2   
                 c 1   
                 c 2 ′ 
                 (eV) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
               
               
                   
               
               
                 ∠CCC 
                 1 
                 1 
                 1 
                 0.79232 
                 −1.85836 
                   
                   
                   
                 120.19 
                 120   
               
               
                 (aromatic) 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (∠CC(H)C chlorobenzene) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 121.7 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (∠CC(Cl)C chlorobenzene) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 120 [50-52] 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (benzene) 
               
               
                 ∠CCH 
                   
                   
                   
                   
                   
                   
                 120.19 
                   
                 119.91 
                 120 [50-52] 
               
               
                 ∠CCX 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (benzene) 
               
               
                 (aromatic) 
               
               
                   
               
             
          
         
       
     
         [0209]    Adenine 
         [0210]    Adenine having the formula C 5 H 5 N 5  comprises a pyrimidine moiety with an aniline-type moiety and a conjugated five-membered ring, which comprises imidazole except that one of the double bonds is part of the aromatic ring. The structure is shown in  FIG. 6 . The aromatic C 3e ═C, C—H, and C 3e ═N functional groups of the pyrimidine moiety are equivalent to those of pyrimidine as given in the corresponding section. The CH, NH, C d —N e , and N e ═C e  groups of the imidazole-type ring are equivalent to the corresponding groups of imidazole as given in the corresponding section. The C—N—C functional group of the imidazole-type ring is equivalent to the corresponding group of indole having the same structure with the C—N—C group bonding to aryl and alkenyl groups. The NH 2  and C a —N a  functional groups of the aniline-type moiety are equivalent to those of aniline as given in the corresponding section except that ΔE H     2     MO  (AO/HO) of the C a —N a  group is equal to twice E T (atom-atom, msp 3 .AO), and to meet the equipotential condition of the union of the C—N H 2 -type-ellipsoidal-MO with these orbitals, the hybridization factor c 2  of Eq. (15.60) for the C—N-bond MO given by Eqs. (15.77), (15.79), and (15.162) is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             c 
                             2 
                           
                            
                           
                             ( 
                             
                               arylC 
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                                
                               
                                   
                               
                                
                               to 
                                
                               
                                   
                               
                                
                               N 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               E 
                                
                               
                                 ( 
                                 N 
                                 ) 
                               
                             
                             
                               E 
                                
                               
                                 ( 
                                 
                                   C 
                                   , 
                                   
                                     2 
                                      
                                     
                                       sp 
                                       3 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                            
                           
                             
                               c 
                               2 
                             
                              
                             
                               ( 
                               
                                 arylC 
                                  
                                 
                                     
                                 
                                  
                                 2 
                                  
                                 
                                   sp 
                                   3 
                                 
                                  
                                 HO 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               
                                 - 
                                 14.53414 
                               
                                
                               
                                   
                               
                                
                               eV 
                             
                             
                               
                                 - 
                                 15.95955 
                               
                                
                               
                                   
                               
                                
                               eV 
                             
                           
                            
                           
                             ( 
                             0.8252 
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         0.77638 
                       
                     
                   
                 
               
               
                 
                   ( 
                   15.173 
                   ) 
                 
               
             
           
         
       
     
         [0211]    The symbols of the functional groups of adenine are given in Table 15. The geometrical (Eqs. (15.1-15.5) and (15.51)), intercept (Eqs. (15.80-15.87)), and energy (Eqs. (15.6-15.11) and (15.17-15.65)) parameters of adenine are given in Tables 16, 17, and 18, respectively. The total energy of adenine given in Table 19 was calculated as the sum over the integer multiple of each E D  (Group) of Table 18 corresponding to functional-group composition of the molecule. The bond angle parameters of adenine determined using Eqs. (15.88-15.117) are given in Table 20. The color scale, charge-density of adenine comprising atoms with the outer shell bridged by one or more H 2 -type ellipsoidal MOs or joined with one or more hydrogen MOs is shown in  FIG. 7 . 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 15 
               
             
             
               
                   
               
               
                 The symbols of functional groups of adenine. 
               
             
          
           
               
                   
                 Functional Group 
                 Group Symbol 
               
               
                   
                   
               
               
                   
                 CC (aromatic bond) 
                 C 3e ═C 
               
               
                   
                 CH (aromatic) 
                 CH (i) 
               
               
                   
                 C b,c   3e ═N c  C a,b   3e ═N b   
                 C 3e ═N 
               
               
                   
                 C a —N a   
                 C—N (a) 
               
               
                   
                 NH 2  group 
                 NH 2   
               
               
                   
                 N e ═C e  double bond 
                 N═C 
               
               
                   
                 C d —N e   
                 C—N (b) 
               
               
                   
                 N d H group 
                 NH 
               
               
                   
                 CH 
                 CH (ii) 
               
               
                   
                 C c —N d —C e   
                 C—N—C 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 16 
               
               
                   
               
               
                 The geometrical bond parameters of adenine and experimental values [1]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 C 3e ═C 
                 CH (i) 
                 C 3e ═N 
                 C—N (a) 
                 NH 2   
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 1.47348 
                 1.60061 
                 1.47169 
                 1.61032 
                 1.24428 
               
               
                 c′ (a 0 ) 
                 1.31468 
                 1.03299 
                 1.27073 
                 1.26898 
                 0.94134 
               
               
                 Bond Length 
                 1.39140 
                 1.09327 
                 1.34489 
                 1.34303 
                 0.99627 
               
               
                 2c′ (Å) 
               
               
                 Exp. Bond Length 
                 1.393 
                 1.084 
                 1.340 
                 1.34 [64] 
                 0.998 
               
               
                 (Å) 
                 (pyrimidine) 
                 (pyridine) 
                 (pyrimidine) 
                 (adenine) 
                 (aniline) 
               
               
                 b, c (a 0 ) 
                 0.66540 
                 1.22265 
                 0.74237 
                 0.99137 
                 0.81370 
               
               
                 e 
                 0.89223 
                 0.64537 
                 0.86345 
                 0.78803 
                 0.75653 
               
               
                   
               
             
          
           
               
                   
                 N═C 
                 C—N (b) 
                 NH 
                 CH (ii) 
                 C—N—C 
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 1.44926 
                 1.82450 
                 1.24428 
                 1.53380 
                 1.44394 
               
               
                 c′ (a 0 ) 
                 1.30383 
                 1.35074 
                 0.94134 
                 1.01120 
                 1.30144 
               
               
                 Bond Length 
                 1.37991 
                 1.42956 
                 0.996270 
                 1.07021 
                 1.37738 
               
               
                 2c′ (Å) 
               
               
                 Exp. Bond Length 
                   
                   
                 0.996 
                 1.076 
                 1.370 
               
               
                 (Å) 
                   
                   
                 (pyrrole) 
                 (pyrrole) 
                 (pyrrole) 
               
               
                 b, c (a 0 ) 
                 0.63276 
                 1.22650 
                 0.81370 
                 1.15326 
                 0.62548 
               
               
                 e 
                 0.89965 
                 0.74033 
                 0.75653 
                 0.65928 
                 0.90131 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 17 
               
               
                   
               
               
                 The MO to HO intercept geometrical bond parameters of adenine. R 1  is an alkyl group and R, 
               
               
                 R′, R″ are H or alkyl groups. E T  is E T (atom - atom, msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 Final Total 
                   
                   
               
               
                   
                   
                 E T   
                 E T   
                 E T   
                 E T   
                 Energy 
               
               
                   
                   
                 (eV) 
                 (eV) 
                 (eV) 
                 (eV) 
                 C2sp 3   
                 r initial   
                 r final   
               
               
                 Bond 
                 Atom 
                 Bond 1 
                 Bond 2 
                 Bond 3 
                 Bond 4 
                 (eV) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 C d (N b )C a N a H—H 
                 N a   
                 −0.56690 
                 0 
                 0 
                 0 
                   
                 0.93084 
                 0.88392 
               
               
                 C d (N b )C a —N a H 2   
                 C a   
                 −0.56690 
                 −0.54343 
                 −0.85035 
                 0 
                 −153.57636 
                 0.91771 
                 0.81052 
               
               
                 C d (N b )C a —N a H 2   
                 N a   
                 −0.56690 
                 0 
                 0 
                 0 
                   
                 0.93084 
                 0.88392 
               
               
                 C—H (C b H) 
                 C b   
                 −0.54343 
                 −0.54343 
                 −0.56690 
                 0 
                 −153.26945 
                 0.91771 
                 0.82562 
               
               
                 C—H (C e H) 
                 C e   
                 −0.92918 
                 −0.60631 
                 0 
                 0 
                 −153.15119 
                 0.91771 
                 0.83159 
               
               
                 N—H (N d H) 
                 N 
                 −0.60631 
                 −0.60631 
                 0 
                 0 
                   
                 0.93084 
                 0.84833 
               
               
                 C d (NH 2 )C a   3e ═N b C b   
                 C a   
                 −0.85035 
                 −0.54343 
                 −0.56690 
                 0 
                 −153.57636 
                 0.91771 
                 0.81052 
               
               
                 C d (NH 2 )C a   3e ═N b C b   
                 N b   
                 −0.54343 
                 −0.54343 
                 0 
                 0 
                   
                 0.93084 
                 0.85503 
               
               
                 N b C b   3e ═N c C c   
                 N c   
               
               
                 N b C b   3e ═N c C c   
                 C b   
                 −0.54343 
                 −0.54343 
                 −0.56690 
                 0 
                 −153.26945 
                 0.91771 
                 0.82562 
               
               
                 C a N b   3e ═C b N c   
               
               
                 C d (N d H)C c   3e ═N c C b   
                 C c   
                 −0.85035 
                 −0.54343 
                 −0.60631 
                 0 
                 −153.61578 
                 0.91771 
                 0.80863 
               
               
                 N b (N a H 2 )C a   3e ═C d (N e )C c   
                 C a   
                 −0.85035 
                 −0.54343 
                 −0.56690 
                 0 
                 −153.57636 
                 0.91771 
                 0.81052 
               
               
                 N b (N a H 2 )C a   3e ═C d (N e )C c   
                 C d   
                 −0.85035 
                 −0.85035 
                 −0.46459 
                 0 
                 −153.78097 
                 0.91771 
                 0.80076 
               
               
                 C a (N e )C d   3e ═C c (N d H)N c   
               
               
                 C a (N e )C d   3e ═C c (N d H)N c   
                 C c   
                 −0.85035 
                 −0.54343 
                 −0.60631 
                 0 
                 −153.61578 
                 0.91771 
                 0.80863 
               
               
                 C d (N c )C c —N d H 
                 C c   
                 −0.85035 
                 −0.54343 
                 −0.60631 
                 0 
                 −153.61578 
                 0.91771 
                 0.80863 
               
               
                 C e (H)N d —C c (N c )C d   
                 N d   
                 −0.60631 
                 −0.60631 
                 0 
                 0 
                   
                 0.93084 
                 0.84833 
               
               
                 N e (H)C e —N d (H)C c   
               
               
                 N e (H)C e —N d (H)C c   
                 C e   
                 −0.60631 
                 −0.92918 
                 0 
                 0 
                 −153.15119 
                 0.91771 
                 0.83159 
               
               
                 C d N e ═C e (H)N d H 
                 C e   
                 −0.92918 
                 −0.60631 
                 0 
                 0 
                 −153.15119 
                 0.91771 
                 0.83159 
               
               
                 C d N e ═C e (H)N d H 
                 N e   
                 −0.92918 
                 −0.46459 
                 0 
                 0 
                   
                 0.93084 
                 0.83885 
               
               
                 C a (C c )C d —N e C e   
                 N e   
                 −0.46459 
                 −0.92918 
                 0 
                 0 
                   
                 0.93084 
                 0.83885 
               
               
                 C a (C c )C d —N e C e   
                 C d   
                 −0.46459 
                 −0.85035 
                 −0.85035 
                 0 
                 −153.78097 
                 0.91771 
                 0.80076 
               
               
                   
               
             
          
           
               
                   
                 E Coulomb (C2sp           
                 E(C2sp 3 ) 
                   
                   
                   
                   
                   
               
               
                   
                 (eV) 
                 (eV) 
                 θ′ 
                 θ 1   
                 θ 2   
                 d 1   
                 d 2   
               
               
                 Bond 
                 Final 
                 Final 
                 (°) 
                 (°) 
                 (°) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 C d (N b )C a N a H—H 
                 −15.39265 
                   
                 121.74 
                 58.26 
                 67.49 
                 0.47634 
                 0.46500 
               
               
                 C d (N b )C a —N a H 2   
                 −16.78642 
                 −16.59556 
                 108.27 
                 71.73 
                 50.93 
                 1.01493 
                 0.25406 
               
               
                 C d (N b )C a —N a H 2   
                 −15.39265 
                   
                 113.13 
                 66.87 
                 55.08 
                 0.92180 
                 0.34719 
               
               
                 C—H (C b H) 
                 −16.47951 
                 −16.28864 
                 78.27 
                 101.73 
                 41.39 
                 1.20084 
                 0.16785 
               
               
                 C—H (C e H) 
                 −16.36125 
                 −16.17038 
                 86.28 
                 93.72 
                 46.02 
                 1.06512 
                 0.05392 
               
               
                 N—H (N d H) 
                 −16.03838 
                   
                 119.52 
                 60.48 
                 65.13 
                 0.52338 
                 0.41796 
               
               
                 C d (NH 2 )C a   3e ═N b C b   
                 −16.78642 
                 −16.59556 
                 128.54 
                 51.46 
                 58.65 
                 0.76572 
                 0.50501 
               
               
                 C d (NH 2 )C a   3e ═N b C b   
                 −15.91261 
                   
                 130.61 
                 49.39 
                 60.97 
                 0.71418 
                 0.55656 
               
               
                 N b C b   3e ═N c C c   
               
               
                 N b C b   3e ═N c C c   
                 −16.47951 
                 −16.28865 
                 129.26 
                 50.74 
                 59.44 
                 0.74824 
                 0.52249 
               
               
                 C a N b   3e ═C b N c   
               
               
                 C d (N d H)C c   3e ═N c C b   
                 −16.82584 
                 −16.63498 
                 128.45 
                 51.55 
                 58.55 
                 0.76792 
                 0.50281 
               
               
                 N b (N a H 2 )C a   3e ═C d (N e )C c   
                 −16.78642 
                 −16.59556 
                 134.85 
                 45.15 
                 59.72 
                 0.74304 
                 0.57165 
               
               
                 N b (N a H 2 )C a   3e ═C d (N e )C c   
                 −16.99103 
                 −16.80017 
                 134.44 
                 45.56 
                 59.22 
                 0.75398 
                 0.56071 
               
               
                 C a (N e )C d   3e ═C c (N d H)N c   
               
               
                 C a (N e )C d   3e ═C c (N d H)N c   
                 −16.82584 
                 −16.63498 
                 134.77 
                 45.23 
                 59.62 
                 0.74516 
                 0.56952 
               
               
                 C d (N c )C c —N d H 
                 −16.82584 
                 −16.63498 
                 137.54 
                 42.46 
                 60.78 
                 0.70488 
                 0.59656 
               
               
                 C e (H)N d —C c (N c )C d   
                 −16.03838 
                   
                 139.04 
                 40.96 
                 62.76 
                 0.66083 
                 0.64061 
               
               
                 N e (H)C e —N d (H)C c   
               
               
                 N e (H)C e —N d (H)C c   
                 −16.36125 
                 −16.17039 
                 138.42 
                 41.58 
                 61.93 
                 0.67940 
                 0.62203 
               
               
                 C d N e ═C e (H)N d H 
                 −16.36125 
                 −16.17039 
                 137.93 
                 42.07 
                 61.72 
                 0.68657 
                 0.61726 
               
               
                 C d N e ═C e (H)N d H 
                 −16.21952 
                   
                 138.20 
                 41.80 
                 62.08 
                 0.67849 
                 0.62534 
               
               
                 C a (C c )C d —N e C e   
                 −16.21952 
                   
                 91.32 
                 88.68 
                 43.14 
                 1.33135 
                 0.01939 
               
               
                 C a (C c )C d —N e C e   
                 −16.99103 
                 −16.80017 
                 87.71 
                 92.29 
                 40.72 
                 1.38280 
                 0.03206 
               
               
                   
               
               
                             indicates data missing or illegible when filed 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 18 
               
               
                   
               
               
                 The energy parameters (eV) of functional groups of adenine. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 C 3e ═C 
                 CH (i) 
                 C 3e ═N 
                 C—N (a) 
                 NH 2   
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 f 1   
                 0.75 
                 1 
                 0.75 
                 1 
                 1 
               
               
                 n 1   
                 2 
                 1 
                 2 
                 1 
                 2 
               
               
                 n 2   
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 1 
               
               
                 C 1   
                 0.5 
                 0.75 
                 0.5 
                 0.5 
                 0.75 
               
               
                 C 2   
                 0.85252 
                 1 
                 0.91140 
                 1 
                 0.93613 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 0.75 
               
               
                 c 2   
                 0.85252 
                 0.91771 
                 0.91140 
                 0.84665 
                 0.92171 
               
               
                 c 3   
                 0 
                 1 
                 0 
                 0 
                 0 
               
               
                 c 4   
                 3 
                 1 
                 3 
                 2 
                 1 
               
               
                 c 5   
                 0 
                 1 
                 0 
                 0 
                 2 
               
               
                 C 1o   
                 0.5 
                 0.75 
                 0.5 
                 0.5 
                 1.5 
               
               
                 C 2o   
                 0.85252 
                 1 
                 0.91140 
                 1 
                 1 
               
               
                 V e  (eV) 
                 −101.12679 
                 −37.10024 
                 −102.01431 
                 −35.50149 
                 −78.97795 
               
               
                 V p  (eV) 
                 20.69825 
                 13.17125 
                 21.41410 
                 10.72181 
                 28.90735 
               
               
                 T (eV) 
                 34.31559 
                 11.58941 
                 34.65890 
                 11.02312 
                 31.73641 
               
               
                 V m  (eV) 
                 −17.15779 
                 −5.79470 
                 −17.32945 
                 −5.51156 
                 −15.86820 
               
               
                 E (AO/HO) (eV) 
                 0 
                 −14.63489 
                 0 
                 −14.63489 
                 −14.53414 
               
               
                 ΔE H   2 MO (AO/HO) (eV) 
                 0 
                 −1.13379 
                 0 
                 −2.26759 
                 0 
               
               
                 E T  (AO/HO) (eV) 
                 0 
                 −13.50110 
                 0 
                 −12.36730 
                 −14.53414 
               
               
                 E (n 3  AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 −14.53414 
               
               
                 E T  (H 2 MO) (eV) 
                 −63.27075 
                 −31.63539 
                 −63.27076 
                 −31.63543 
                 −48.73654 
               
               
                 E T  (atom-atom, msp 3 .AO) (eV) 
                 −2.26759 
                 −0.56690 
                 −1.44915 
                 −1.13379 
                 0 
               
               
                 E T  (MO) (eV) 
                 −65.53833 
                 −32.20226 
                 −64.71988 
                 −32.76916 
                 −48.73660 
               
               
                 ω (10 15  rad/s) 
                 49.7272 
                 26.4826 
                 43.6311 
                 14.3055 
                 68.9812 
               
               
                 E K  (eV) 
                 32.73133 
                 17.43132 
                 28.71875 
                 9.41610 
                 45.40465 
               
               
                 Ē D  (eV) 
                 −0.35806 
                 −0.26130 
                 −0.33540 
                 −0.19893 
                 −0.42172 
               
               
                 Ē Kvib  (eV) 
                 0.19649 [49] 
                 0.35532 
                 0.19649 [49] 
                 0.15498 [57] 
                 0.40929 [22] 
               
               
                   
                   
                 Eq. (13.458) 
               
               
                 Ē osc  (eV) 
                 −0.25982 
                 −0.08364 
                 −0.23715 
                 −0.12144 
                 −0.21708 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.09457 
                 0.14803 
                 0.14803 
               
               
                 E T  (Group) (eV) 
                 −49.54347 
                 −32.28590 
                 −48.82472 
                 −32.89060 
                 −49.17075 
               
               
                 E initial  (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.53414 
               
               
                 E initial  (c 5  AO/HO) (eV) 
                 0 
                 −13.59844 
                 0 
                 0 
                 −13.59844 
               
               
                 E D  (Group) (eV) 
                 5.63881 
                 3.90454 
                 4.92005 
                 3.62082 
                 7.43973 
               
               
                   
               
               
                   
                 N═C 
                 C—N (b) 
                 NH 
                 CH (ii) 
                 C—N—C 
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 f 1   
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 n 1   
                 2 
                 1 
                 1 
                 1 
                 2 
               
               
                 n 2   
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.5 
                 0.5 
                 0.75 
                 0.75 
                 0.5 
               
               
                 C 2   
                 0.85252 
                 1 
                 0.93613 
                 1 
                 0.85252 
               
               
                 c 1   
                 1 
                 1 
                 0.75 
                 1 
                 1 
               
               
                 c 2   
                 0.84665 
                 0.84665 
                 0.92171 
                 0.91771 
                 0.84665 
               
               
                 c 3   
                 0 
                 0 
                 1 
                 1 
                 0 
               
               
                 c 4   
                 4 
                 2 
                 1 
                 1 
                 4 
               
               
                 c 5   
                 0 
                 0 
                 1 
                 1 
                 0 
               
               
                 C 1o   
                 0.5 
                 0.5 
                 0.75 
                 0.75 
                 0.5 
               
               
                 C 2o   
                 0.85252 
                 1 
                 1 
                 1 
                 0.85252 
               
               
                 V e  (eV) 
                 −103.92756 
                 −32.44864 
                 −39.48897 
                 −39.09538 
                 −104.73877 
               
               
                 V p  (eV) 
                 20.87050 
                 10.07285 
                 14.45367 
                 13.45505 
                 20.90891 
               
               
                 T (eV) 
                 35.85539 
                 8.89248 
                 15.86820 
                 12.74462 
                 36.26840 
               
               
                 V m  (eV) 
                 −17.92770 
                 −4.44624 
                 −7.93410 
                 −6.37231 
                 −18.13420 
               
               
                 E (AO/HO) (eV) 
                 0 
                 −14.63489 
                 −14.53414 
                 −14.63489 
                 0 
               
               
                 ΔE H   2 MO (AO/HO) (eV) 
                 −1.85836 
                 −0.92918 
                 0 
                 −2.26758 
                 −2.42526 
               
               
                 E T  (AO/HO) (eV) 
                 1.85836 
                 −13.70571 
                 −14.53414 
                 −12.36731 
                 2.42526 
               
               
                 E (n 3  (AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 E T  (H 2 MO) (eV) 
                 −63.27100 
                 −31.63527 
                 −31.63534 
                 −31.63533 
                 −63.27040 
               
               
                 E T  (atom-atom, msp 3 .AO) (eV) 
                 −1.85836 
                 −0.92918 
                 0 
                 0 
                 −2.42526 
               
               
                 E T  (MO) (eV) 
                 −65.12910 
                 −32.56455 
                 −31.63537 
                 −31.63537 
                 −65.69600 
               
               
                 ω (10 15  rad/s) 
                 15.4704 
                 21.5213 
                 48.7771 
                 28.9084 
                 54.5632 
               
               
                 E K  (eV) 
                 10.18290 
                 14.16571 
                 32.10594 
                 19.02803 
                 35.91442 
               
               
                 Ē D  (eV) 
                 −0.20558 
                 −0.24248 
                 −0.35462 
                 −0.27301 
                 −0.38945 
               
               
                 Ē Kvib  (eV) 
                 0.20768 [61] 
                 0.12944 [23] 
                 0.40696 [24] 
                 0.39427 [59] 
                 0.11159 [12] 
               
               
                 Ē osc  (eV) 
                 −0.10174 
                 −0.17775 
                 −0.15115 
                 −0.07587 
                 −0.33365 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                 E T  (Group) (eV) 
                 −65.33259 
                 −32.74230 
                 −31.78651 
                 −31.71124 
                 −66.36330 
               
               
                 E initial  (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.53414 
                 −14.63489 
                 −14.63489 
               
               
                 E initial  (c 5  AO/HO) (eV) 
                 0 
                 0 
                 −13.59844 
                 −13.59844 
                 0 
               
               
                 E D  (Group) (eV) 
                 6.79303 
                 3.47253 
                 3.51208 
                 3.32988 
                 7.82374 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 19 
               
               
                   
               
               
                 The total bond energies of adenine calculated using the functional group 
               
               
                 composition and the energies of Table 18 compared to the experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                 C 3e ═N 
                 C—N (a) 
                 NH 2   
                   
                   
               
               
                 Formula 
                 Name 
                 C 3e ═C 
                 CH (i) 
                 Group 
                 Group 
                 Group 
                 N═C 
                 C—N (b) 
               
               
                   
               
               
                 C 5 H 5 N 5   
                 Adenine 
                 2 
                 1 
                 4 
                 1 
                 1 
                 1 
                 1 
               
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                   
                   
                   
                 Total Bond 
                 Total Bond 
               
               
                 Formula 
                 Name 
                 NH 
                 CH (ii) 
                 C—N—C 
                 Energy (eV) 
                 Energy (eV) 
                 Relative Error 
               
               
                   
               
               
                 C 5 H 5 N 5   
                 Adenine 
                 1 
                 1 
                 1 
                 70.85416 
                 70.79811 
                 −0.00079 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 20 
               
               
                   
               
               
                 The bond angle parameters of adenine and experimental values [65]. In the calculation of θ v , the 
               
               
                 parameters from the preceding angle were used. E T  is E T  (atom-atom, msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                 2c′ 
                   
                 Atom 1 
                   
                 Atom 2 
                   
                   
               
               
                   
                 2c′ 
                 2c′ 
                 Terminal 
                   
                 Hybridization 
                   
                 Hybridization 
               
               
                 Atoms of 
                 Bond 1 
                 Bond 2 
                 Atoms 
                 E Coulombic   
                 Designation 
                 E Coulombic   
                 Designation 
                 c 2   
                 c 2   
               
               
                 Angle 
                 (a 0 ) 
                 (a 0 ) 
                 (a 0 ) 
                 Atom 1 
                 (Table 8) 
                 Atom 2 
                 (Table 8) 
                 Atom 1 
                 Atom 2 
               
               
                   
               
               
                 ∠HNH 
                 1.88268 
                 1.88268 
                 3.1559 
                 −14.53414 
                 N 
                 H 
                 H 
                 0.93613 
                 1 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Eq. 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 (13.248) 
               
               
                 ∠C a NH 
                 2.53797 
                 1.88268 
                 3.8123 
                 −16.78642 
                 19 
                 −14.53414 
                 N 
                 0.81052 
                 0.77638 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Eq. 
                 Eq. 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 (15.71) 
                 (15.173) 
               
               
                 ∠N b C b N c   
                 2.54147 
                 2.54147 
                 4.5826 
                 −15.55033 
                  3 
                 −15.55033 
                 3 
                 0.87495 
                 0.87495 
               
               
                 ∠H b C b N b   
               
               
                 ∠H b C b N c   
               
               
                 ∠H e C e N e   
                 2.02241 
                 2.60766 
                 4.0661 
                 −16.36125 
                 12 
                 −14.53414 
                 N 
                 0.83159 
                 0.84665 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Eq. 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (15.171) 
               
               
                 ∠N e C e N d   
                 2.60766 
                 2.60287 
                 4.3359 
                 −16.21952 
                  9 
                 −16.03838 
                 7 
                 0.83885 
                 0.84833 
               
               
                 ∠N c C c N d   
                 2.54147 
                 2.60287 
                 4.6260 
                 −14.53414 
                 N 
                 −14.53414 
                 N 
                 0.91140 
                 0.84665 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Eq. 
                 Eq. 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 (15.135) 
                 (15.171) 
               
               
                 ∠H e C e N d   
               
               
                 ∠H d N d C e   
                 1.88268 
                 2.60287 
                 4.0166 
                 −14.53414 
                 N 
                 −15.95955 
                 6 
                 0.84665 
                 0.85252 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Eq. 
                 Eq. 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 (15.171) 
                 (15.162) 
               
               
                 ∠C c N d C e   
                 2.60287 
                 2.60287 
                 4.1952 
                 −17.95963 
                 39 
                 −17.95963 
                 39  
                 0.75758 
                 0.75758 
               
               
                 ∠H d N d C c   
               
               
                 ∠N a C a C d   
                 2.53797 
                 2.62936 
                 4.5387 
                 −14.53414 
                 N 
                 −16.52644 
                 15  
                 0.91140 
                 0.82327 
               
               
                   
                   
                   
                   
                   
                   
                 C d   
                   
                 Eq. 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 (15.135) 
               
               
                 ∠N b C a C d   
                 2.54147 
                 2.62936 
                 4.4272 
                 −14.53414 
                 N 
                 −16.99103 
                 21  
                 0.91140 
                 0.80076 
               
               
                   
                   
                   
                   
                   
                   
                 C d   
                   
                 Eq. 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 (15.135) 
               
               
                 ∠N b C a N a   
               
               
                 ∠N e C d C c   
                 2.70148 
                 2.62936 
                 4.3818 
                 −14.53414 
                 N 
                 −15.95955 
                 6 
                 0.84665 
                 0.85252 
               
               
                   
                   
                   
                   
                   
                   
                 C c   
                   
                 Eq. 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 (15.171) 
               
               
                 ∠N d C c C d   
                 2.60287 
                 2.62936 
                 4.1952 
                 −14.53414 
                 N 
                 −16.99103 
                 21  
                 0.84665 
                 0.80076 
               
               
                   
                   
                   
                   
                   
                   
                 C d   
                   
                 Eq. 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 (15.171) 
               
               
                 ∠N c C c C d   
                 2.54147 
                 2.62936 
                 4.6043 
                 −14.53414 
                 N 
                 −16.52644 
                 15  
                 0.84665 
                 0.82327 
               
               
                   
                   
                   
                   
                   
                   
                 C d   
                   
                 Eq. 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 (15.171) 
               
               
                 ∠N e C d C a   
                 2.70148 
                 2.62936 
                 4.8580 
                 −14.53414 
                 N 
                 −16.78642 
                 1 
                 0.91140 
                 0.81052 
               
               
                   
                   
                   
                   
                   
                   
                 C a   
                   
                 Eq. 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 (15.135) 
               
               
                 ∠C d N e C e   
                 2.70148 
                 2.60766 
                 4.2661 
                 −17.92022 
                 37 
                 −17.92022 
                 37  
                 0.75924 
                 0.75924 
               
               
                 ∠C b N c C c   
                 2.54147 
                 2.54147 
                 4.1952 
                 −17.95963 
                 39 
                 −17.95963 
                 39  
                 0.75758 
                 0.75758 
               
               
                 ∠C a N b C b   
                 2.54147 
                 2.54147 
                 4.3704 
                 −17.71560 
                 33 
                 −17.40869 
                 30  
                 0.76801 
                 0.78155 
               
               
                 ∠C a C d C c   
                 2.62936 
                 2.62936 
                 4.4721 
                 −17.71560 
                 33 
                 −17.14871 
                 26  
                 0.76801 
                 0.79340 
               
               
                   
               
             
          
           
               
                   
                 Atoms of 
                   
                   
                   
                   
                 E T   
                 θ v   
                 θ 1   
                 θ 2   
                 Cal. θ 
                 Exp. θ 
               
               
                   
                 Angle 
                 C 1   
                 C 2   
                 c 1   
                 c 2 ′ 
                 (eV) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
               
               
                   
                   
               
               
                   
                 ∠HNH 
                 1 
                 1 
                 0.75 
                 1.06823 
                 0 
                   
                   
                   
                 113.89 
                 113.9 [1] 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (aniline) 
               
               
                   
                 ∠C a NH 
                 0.75 
                 1 
                 0.75 
                 0.95787 
                 0 
                   
                   
                   
                 118.42 
                 118 
               
               
                   
                 ∠N b C b N c   
                 1 
                 1 
                 1 
                 0.87495 
                 −1.44915 
                   
                   
                   
                 128.73 
                 128.9 
               
               
                   
                 ∠H b C b N b   
                   
                   
                   
                   
                   
                   
                   
                 128.73 
                 115.64 
                 115 
               
               
                   
                 ∠H b C b N c   
                   
                   
                   
                   
                   
                   
                   
                   
                 Eq. 
                 116 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (15.109) 
               
               
                   
                 ∠H e C e N e   
                 0.75 
                 1 
                 0.75 
                 1.01811 
                 0 
                   
                   
                   
                 122.35 
                 126 
               
               
                   
                 ∠N e C e N d   
                 1 
                 1 
                 1 
                 0.84359 
                 −1.44915 
                   
                   
                   
                 112.64 
                 114.4 
               
               
                   
                 ∠N c C c N d   
                 1 
                 1 
                 1 
                 0.87902 
                 −1.44915 
                   
                   
                   
                 128.11 
                 127.8 
               
               
                   
                 ∠H e C e N d   
                   
                   
                   
                   
                   
                   
                 122.35 
                 112.64 
                 125.02 
                 119 
               
               
                   
                 ∠H d N d C e   
                 0.75 
                 1 
                 0.75 
                 1.00693 
                 0 
                   
                   
                   
                 126.39 
                 127 
               
               
                   
                 ∠C c N d C e   
                 1 
                 1 
                 1 
                 0.75758 
                 −1.85836 
                   
                   
                   
                 107.39 
                 106.1 
               
               
                   
                 ∠H d N d C c   
                   
                   
                   
                   
                   
                   
                 126.39 
                 107.39 
                 126.22 
                 127 
               
               
                   
                 ∠N a C a C d   
                 1 
                 1 
                 1 
                 0.86734 
                 −1.44915 
                   
                   
                   
                 122.88 
                 122.1 
               
               
                   
                 ∠N b C a C d   
                 1 
                 1 
                 1 
                 0.85608 
                 −1.44915 
                   
                   
                   
                 117.77 
                 118.2 
               
               
                   
                 ∠N b C a N a   
                   
                   
                   
                   
                   
                   
                 122.88 
                 117.77 
                 119.35 
                 119.4 
               
               
                   
                 ∠N e C d C c   
                 1 
                 1 
                 1 
                 0.84958 
                 −1.44915 
                   
                   
                   
                 110.56 
                 110.4 
               
               
                   
                 ∠N d C c C d   
                 1 
                 1 
                 1 
                 0.82371 
                 −1.44915 
                   
                   
                   
                 106.60 
                 105.9 
               
               
                   
                 ∠N c C c C d   
                 1 
                 1 
                 1 
                 0.83496 
                 −1.65376 
                   
                   
                   
                 125.85 
                 126.4 
               
               
                   
                 ∠N e C d C a   
                 1 
                 1 
                 1 
                 0.86096 
                 −1.65376 
                   
                   
                   
                 131.37 
                 132.8 
               
               
                   
                 ∠C d N e C e   
                 1 
                 1 
                 1 
                 0.75924 
                 −1.85836 
                   
                   
                   
                 106.93 
                 103.3 
               
               
                   
                 ∠C b N c C c   
                 1 
                 1 
                 1 
                 0.75758 
                 −1.85836 
                   
                   
                   
                 111.25 
                 111.3 
               
               
                   
                 ∠C a N b C b   
                 1 
                 1 
                 1 
                 0.77478 
                 −1.85836 
                   
                   
                   
                 118.59 
                 118.6 
               
               
                   
                 ∠C a C d C c   
                 1 
                 1 
                 1 
                 0.78071 
                 −1.85836 
                   
                   
                   
                 116.52 
                 116.7 
               
               
                   
                   
               
             
          
         
       
     
         [0212]    Thymine 
         [0213]    Thymine having the formula C 5 H 6 N 2 O 2  is a pyrimidine with carbonyl substitutions at positions C a  and C b  and a methyl substitution at position C d  further comprising a vinyl group as shown in  FIG. 8 . Each C═O, adjacent C—N, and NH functional group is equivalent to the corresponding group of alkyl amides. The methyl-vinyl moiety is equivalent to the CH 3 , —C(C)═C, CH, and C═C functional groups of alkenes. Thymine further comprises N b H and C b —N c —C c  groups that are equivalent to the corresponding groups of imidazole as given in the corresponding section. The C a —C d  bond comprises another functional group that is equivalent to the C a —C d  group of guanine. 
         [0214]    The symbols of the functional groups of thymine are given in Table 21. The geometrical (Eqs. (15.1-15.5) and (15.51)), intercept (Eqs. (15.80-15.87)), and energy (Eqs. (15.6-15.11) and (15.17-15.65)) parameters of thymine are given in Tables 22, 23, and 24, respectively. The total energy of thymine given in Table 25 was calculated as the sum over the integer multiple of each E D (Group) of Table 24 corresponding to functional-group composition of the molecule. The bond angle parameters of thymine determined using Eqs. (15.88-15.117) are given in Table 26. The color scale, charge-density of thymine comprising atoms with the outer shell bridged by one or more H 2 -type ellipsoidal MOs or joined with one or more hydrogen MOs is shown in  FIG. 9 . 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 21 
               
             
             
               
                   
               
               
                 The symbols of functional groups of thymine. 
               
             
          
           
               
                   
                 Functional Group 
                 Group Symbol 
               
               
                   
                   
               
               
                   
                 C a ═O C b ═O (alkyl amide) 
                 C═O 
               
               
                   
                 C a —N b  C b —N b  amide 
                 C—N 
               
               
                   
                 N b H amide group 
                 NH (i) 
               
               
                   
                 CH 3  group 
                 C—H (CH 3 ) 
               
               
                   
                 C c ═C d  double bond 
                 C═C 
               
               
                   
                 C d —C e   
                 C—C (i) 
               
               
                   
                 C a —C d   
                 C—C (ii) 
               
               
                   
                 C b —N c —C c   
                 C—N—C 
               
               
                   
                 N c H group 
                 NH (ii) 
               
               
                   
                 C c H 
                 CH 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 22 
               
               
                   
               
               
                 The geometrical bond parameters of thymine and experimental values [1]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 C═O 
                 C—N 
                 NH (i) 
                 C—H (CH 3 ) 
                 C═C 
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 1.29907 
                 1.75370 
                 1.28620 
                 1.64920 
                 1.47228 
               
               
                 c′ (a 0 ) 
                 1.13977 
                 1.32427 
                 0.95706 
                 1.04856 
                 1.26661 
               
               
                 Bond Length 2c′ (Å) 
                 1.20628 
                 1.40155 
                 1.01291 
                 1.10974 
                 1.34052 
               
               
                 Exp. Bond Length 
                 1.220 
                 1.380 
                   
                 1.107 
                 1.34 [64] 
               
               
                 (Å) 
                 (acetamide) 
                 (acetamide) 
                   
                 (C—H propane) 
                 (thymine) 
               
               
                   
                 1.225 
                   
                   
                 1.117 
                 1.342 
               
               
                   
                 (N-methylacetamide) 
                   
                   
                 (C—H butane) 
                 (2-methylpropene) 
               
               
                   
                   
                   
                   
                   
                 1.346 
               
               
                   
                   
                   
                   
                   
                 (2-butene) 
               
               
                   
                   
                   
                   
                   
                 1.349 
               
               
                   
                   
                   
                   
                   
                 (1,3-butadiene) 
               
               
                 b, c (a 0 ) 
                 0.62331 
                 1.14968 
                 0.85927 
                 1.27295 
                 0.75055 
               
               
                 e 
                 0.87737 
                 0.75513 
                 0.74410 
                 0.63580 
                 0.86030 
               
               
                   
               
             
          
           
               
                   
                   
                 C—C (i) 
                 C—C (ii) 
                 C—N—C 
                 NH (ii) 
                 CH 
               
               
                   
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
                   
               
               
                   
                 a (a 0 ) 
                 2.04740 
                 1.88599 
                 1.43222 
                 1.24428 
                 1.53380 
               
               
                   
                 c′ (a 0 ) 
                 1.43087 
                 1.37331 
                 1.29614 
                 0.94134 
                 1.01120 
               
               
                   
                 Bond Length 2c′ (Å) 
                 1.51437 
                 1.45345 
                 1.37178 
                 0.996270 
                 1.07021 
               
               
                   
                 Exp. Bond Length 
                   
                 1.43 [64] 
                 1.370 
                 0.996 
                 1.076 
               
               
                   
                 (Å) 
                   
                 (thymine) 
                 (pyrrole) 
                 (pyrrole) 
                 (pyrrole) 
               
               
                   
                 b, c (a 0 ) 
                 1.46439 
                 1.29266 
                 0.60931 
                 0.81370 
                 1.15326 
               
               
                   
                 e 
                 0.69887 
                 0.72817 
                 0.90499 
                 0.75653 
                 0.65928 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 23 
               
               
                   
               
               
                 The MO to HO intercept geometrical bond parameters of thymine. R 1  is an alkyl group 
               
               
                 and R, R′, R″ are H or alkyl groups. E T  is E T (atom - atom, msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 Final Total 
                   
                   
               
               
                   
                   
                 E T   
                 E T   
                 E T   
                 E T   
                 Energy 
               
               
                   
                   
                 (eV) 
                 (eV) 
                 (eV) 
                 (eV) 
                 C2sp 3   
                 r initial   
                 r final   
               
               
                 Bond 
                 Atom 
                 Bond 1 
                 Bond 2 
                 Bond 3 
                 Bond 4 
                 (eV) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 N b (C d )C a ═O 
                 O a   
                 −1.34946 
                 0 
                 0 
                 0 
                   
                 1.00000 
                 0.84115 
               
               
                 N b (C d )C a ═O 
                 C a   
                 −1.34946 
                 −0.82688 
                 0 
                 0 
                 −153.79203 
                 0.91771 
                 0.80024 
               
               
                 N—H (N b H) 
                 N b   
                 −0.82688 
                 −0.82688 
                 0 
                 0 
                   
                 0.93084 
                 0.82562 
               
               
                 C d (O)C a —N b H(C b ) 
                 N b   
                 −0.82688 
                 −0.82688 
                 0 
                 0 
                   
                 0.93084 
                 0.82562 
               
               
                 C d (O)C a —N b H(C b ) 
                 C a   
                 −0.82688 
                 −1.34946 
                 0 
                 0 
                 −153.79203 
                 0.91771 
                 0.80024 
               
               
                 C a N b H—C b (O)N c H 
                 N b   
                 −0.82688 
                 −0.82688 
                 0 
                 0 
                   
                 0.93084 
                 0.82562 
               
               
                 C a N b H—C b (O)N c H 
                 C b   
                 −0.82688 
                 −1.34946 
                 −0.82688 
                 0 
                 −154.61891 
                 0.91771 
                 0.76313 
               
               
                 (HN c )(HN b )C b ═O 
                 O b   
                 −1.34946 
                 0 
                 0 
                 0 
                   
                 1.00000 
                 0.84115 
               
               
                 (HN c )(HN b )C b ═O 
                 C b   
                 −1.34946 
                 −0.82688 
                 −0.92918 
                 0 
                 −154.72121 
                 0.91771 
                 0.75878 
               
               
                 N—H (N c H) 
                 N c   
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                   
                 0.93084 
                 0.81549 
               
               
                 N b (O)C b —N c HC c   
                 N c   
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                   
                 0.93084 
                 0.81549 
               
               
                 N b (O)C b —N c HC c   
                 C b   
                 −0.92918 
                 −1.34946 
                 −0.82688 
                 0 
                 −154.72121 
                 0.91771 
                 0.75878 
               
               
                 C b HN c —HC c C d   
                 N c   
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                   
                 0.93084 
                 0.81549 
               
               
                 C b HN c —HC c C d   
                 C c   
                 −0.92918 
                 −1.13379 
                 0 
                 0 
                 −153.67866 
                 0.91771 
                 0.80561 
               
               
                 C—H (C c H) 
                 C c   
                 −1.13380 
                 −0.92918 
                 0 
                 0 
                 −153.67867 
                 0.91771 
                 0.80561 
               
               
                 N c HC c ═C d C a (C e ) 
                 C c   
                 −1.13380 
                 −0.92918 
                 −0.72457 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 N c HC c ═C d C a (C e ) 
                 C d   
                 −1.13380 
                 0 
                 −0.72457 
                 0 
                 −153.47406 
                 0.91771 
                 0.81549 
               
               
                 C—H (CH 3 ) 
                 C e   
                 −0.72457 
                 0 
                 0 
                 0 
                 −152.34026 
                 0.91771 
                 0.87495 
               
               
                 (C a )C c C d —C e H 3   
                 C e   
                 −0.72457 
                 0 
                 0 
                 0 
                 −152.34026 
                 0.91771 
                 0.87495 
               
               
                 (C a )C c C d —C e H 3   
                 C d   
                 −0.72457 
                 −1.13379 
                 0 
                 0 
                 −153.47406 
                 0.91771 
                 0.81549 
               
               
                 (C e )C c C d —C a (O)N b   
                 C a   
                 0 
                 −1.34946 
                 −0.82688 
                 0 
                 −153.79203 
                 0.91771 
                 0.80024 
               
               
                 (C e )C c C d —C a (O)N b   
                 C d   
                 0 
                 −1.13379 
                 −0.72457 
                 0 
                 −153.47406 
                 0.91771 
                 0.81549 
               
               
                   
               
             
          
           
               
                   
                 E Coulomb (C2sp           
                 E(C2sp 3 ) 
                   
                   
                   
                   
                   
               
               
                   
                 (eV) 
                 (eV) 
                 θ′ 
                 θ 1   
                 θ 2   
                 d 1   
                 d 2   
               
               
                 Bond 
                 Final 
                 Final 
                 (°) 
                 (°) 
                 (°) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 N b (C d )C a ═O 
                 −16.17521 
                   
                 137.27 
                 42.73 
                 66.31 
                 0.52193 
                 0.61784 
               
               
                 N b (C d )C a ═O 
                 −17.00209 
                 −16.81123 
                 135.55 
                 44.45 
                 64.05 
                 0.56855 
                 0.57122 
               
               
                 N—H (N b H) 
                 −16.47951 
                   
                 118.03 
                 61.97 
                 63.59 
                 0.55339 
                 0.38795 
               
               
                 C d (O)C a —N b H(C b ) 
                 −16.47951 
                   
                 96.62 
                 83.38 
                 45.51 
                 1.22903 
                 0.09524 
               
               
                 C d (O)C a —N b H(C b ) 
                 −17.00209 
                 −16.81123 
                 94.42 
                 85.58 
                 43.95 
                 1.26264 
                 0.06164 
               
               
                 C a N b H—C b (O)N c H 
                 −16.47951 
                   
                 96.62 
                 83.38 
                 45.51 
                 1.22903 
                 0.09524 
               
               
                 C a N b H—C b (O)N c H 
                 −17.82897 
                 −17.63811 
                 90.94 
                 89.06 
                 41.58 
                 1.31179 
                 0.01249 
               
               
                 (HN c )(HN b )C b ═O 
                 −16.17521 
                   
                 137.27 
                 42.73 
                 66.31 
                 0.52193 
                 0.61784 
               
               
                 (HN c )(HN b )C b ═O 
                 −17.93127 
                 −17.74041 
                 133.67 
                 46.33 
                 61.70 
                 0.61582 
                 0.52395 
               
               
                 N—H (N c H) 
                 −16.68411 
                   
                 117.34 
                 62.66 
                 62.90 
                 0.56678 
                 0.37456 
               
               
                 N b (O)C b —N c HC c   
                 −16.68411 
                   
                 138.92 
                 41.08 
                 61.59 
                 0.68147 
                 0.61467 
               
               
                 N b (O)C b —N c HC c   
                 −17.93127 
                 −17.74041 
                 136.68 
                 43.32 
                 58.70 
                 0.74414 
                 0.55200 
               
               
                 C b HN c —HC c C d   
                 −16.68411 
                   
                 138.92 
                 41.08 
                 61.59 
                 0.68147 
                 0.61467 
               
               
                 C b HN c —HC c C d   
                 −16.88873 
                 −16.69786 
                 138.54 
                 41.46 
                 61.09 
                 0.69238 
                 0.60376 
               
               
                 C—H (C c H) 
                 −16.88873 
                 −16.69786 
                 83.35 
                 96.65 
                 43.94 
                 1.10452 
                 0.09331 
               
               
                 N c HC c ═C d C a (C e ) 
                 −17.61330 
                 −17.42244 
                 125.92 
                 54.08 
                 56.46 
                 0.81345 
                 0.45316 
               
               
                 N c HC c ═C d C a (C e ) 
                 −16.68412 
                 −16.49326 
                 128.10 
                 51.90 
                 58.77 
                 0.76344 
                 0.50317 
               
               
                 C—H (CH 3 ) 
                 −15.55033 
                 −15.35946 
                 78.85 
                 101.15 
                 42.40 
                 1.21777 
                 0.16921 
               
               
                 (C a )C c C d —C e H 3   
                 −15.55033 
                 −15.35946 
                 73.62 
                 106.38 
                 34.98 
                 1.67762 
                 0.24675 
               
               
                 (C a )C c C d —C e H 3   
                 −16.68412 
                 −16.49325 
                 65.99 
                 114.01 
                 30.58 
                 1.76270 
                 0.33183 
               
               
                 (C e )C c C d —C a (O)N b   
                 −17.00209 
                 −16.81123 
                 81.54 
                 98.46 
                 37.76 
                 1.49107 
                 0.11776 
               
               
                 (C e )C c C d —C a (O)N b   
                 −16.68412 
                 −16.49325 
                 92.72 
                 87.28 
                 45.17 
                 1.32975 
                 0.04357 
               
               
                   
               
               
                             indicates data missing or illegible when filed 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 24 
               
               
                   
               
               
                 The energy parameters (eV) of functional groups of thymine. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 C═O 
                 C—N 
                 NH (i) 
                 C═C 
                 CH 3   
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 n 1   
                 2 
                 1 
                 1 
                 2 
                 3 
               
               
                 n 2   
                 0 
                 0 
                 0 
                 0 
                 2 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.5 
                 0.5 
                 0.75 
                 0.5 
                 0.75 
               
               
                 C 2   
                 1 
                 1 
                 0.93613 
                 0.91771 
                 1 
               
               
                 c 1   
                 1 
                 1 
                 0.75 
                 1 
                 1 
               
               
                 c 2   
                 0.85395 
                 0.91140 
                 1 
                 0.91771 
                 0.91771 
               
               
                 c 3   
                 2 
                 0 
                 1 
                 0 
                 0 
               
               
                 c 4   
                 4 
                 2 
                 1 
                 4 
                 1 
               
               
                 c 5   
                 0 
                 0 
                 1 
                 0 
                 3 
               
               
                 C 1o   
                 0.5 
                 0.5 
                 0.75 
                 0.5 
                 0.75 
               
               
                 C 2o   
                 1 
                 1 
                 1 
                 0.91771 
                 1 
               
               
                 V e  (eV) 
                 −111.25473 
                 −36.88558 
                 −40.92593 
                 −102.08992 
                 −107.32728 
               
               
                 V p  (eV) 
                 23.87467 
                 10.27417 
                 14.21618 
                 21.48386 
                 38.92728 
               
               
                 T (eV) 
                 42.82081 
                 10.51650 
                 15.90963 
                 34.67062 
                 32.53914 
               
               
                 V m  (eV) 
                 −21.41040 
                 −5.25825 
                 −7.95482 
                 −17.33531 
                 −16.26957 
               
               
                 E(AO/HO) (eV) 
                 0 
                 −14.63489 
                 −14.53414 
                 0 
                 −15.56407 
               
               
                 ΔE H     2     MO  (AO/HO) (eV) 
                 −2.69893 
                 −4.35268 
                 −1.65376 
                 0 
                 0 
               
               
                 E T (AO/HO) (eV) 
                 2.69893 
                 −10.28221 
                 −12.88038 
                 0 
                 −15.56407 
               
               
                 E(n 3  AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 E T (H 2 MO) (eV) 
                 −63.27074 
                 −31.63537 
                 −31.63531 
                 −63.27075 
                 −67.69451 
               
               
                 E T (atom - atom, msp 3 .AO) (eV) 
                 −2.69893 
                 −1.65376 
                 0 
                 −2.26759 
                 0 
               
               
                 E T (MO) (eV) 
                 −65.96966 
                 −33.28912 
                 −31.63537 
                 −65.53833 
                 −67.69450 
               
               
                 ω(10 15  rad/s) 
                 59.4034 
                 12.5874 
                 44.9494 
                 43.0680 
                 24.9286 
               
               
                 E K  (eV) 
                 39.10034 
                 8.28526 
                 29.58649 
                 28.34813 
                 16.40846 
               
               
                 Ē D  (eV) 
                 −0.40804 
                 −0.18957 
                 −0.34043 
                 −0.34517 
                 −0.25352 
               
               
                 Ē Kvib  (eV) 
                 0.21077 [12] 
                 0.17358 [33] 
                 0.40696 [24] 
                 0.17897 [6] 
                 0.35532 
               
               
                   
                   
                   
                   
                   
                 Eq. (13.458) 
               
               
                 Ē osc  (eV) 
                 −0.30266 
                 −0.10278 
                 −0.13695 
                 −0.25568 
                 −0.22757 
               
               
                 E mag  (eV) 
                 0.11441 
                 0.14803 
                 0.14185 
                 0.14803 
                 0.14803 
               
               
                 E T (Group) (eV) 
                 −66.57498 
                 −33.39190 
                 −31.77232 
                 −66.04969 
                 −67.92207 
               
               
                 E initial (c 4 AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.53414 
                 −14.63489 
                 −14.63489 
               
               
                 E initial (c 5 AO/HO) (eV) 
                 0 
                 0 
                 −13.59844 
                 0 
                 −13.59844 
               
               
                 E D (Group) (eV) 
                 7.80660 
                 4.12212 
                 3.49788 
                 7.51014 
                 12.49186 
               
               
                   
               
               
                   
                 C—C (i) 
                 C—C (ii) 
                 C—N—C 
                 NH (ii) 
                 CH 
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 n 1   
                 1 
                 1 
                 2 
                 1 
                 1 
               
               
                 n 2   
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.5 
                 0.5 
                 0.5 
                 0.75 
                 0.75 
               
               
                 C 2   
                 1 
                 1 
                 0.85252 
                 0.93613 
                 1 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 0.75 
                 1 
               
               
                 c 2   
                 0.91771 
                 0.91771 
                 0.84665 
                 0.92171 
                 0.91771 
               
               
                 c 3   
                 1 
                 0 
                 0 
                 1 
                 1 
               
               
                 c 4   
                 2 
                 2 
                 4 
                 1 
                 1 
               
               
                 c 5   
                 0 
                 0 
                 0 
                 1 
                 1 
               
               
                 C 1o   
                 0.5 
                 0.5 
                 0.5 
                 0.75 
                 0.75 
               
               
                 C 2o   
                 1 
                 1 
                 0.85252 
                 1 
                 1 
               
               
                 V e  (eV) 
                 −30.19634 
                 −33.63376 
                 −106.58684 
                 −39.48897 
                 −39.09538 
               
               
                 V p  (eV) 
                 9.50874 
                 9.90728 
                 20.99432 
                 14.45367 
                 13.45505 
               
               
                 T (eV) 
                 7.37432 
                 8.91674 
                 37.21047 
                 15.86820 
                 12.74462 
               
               
                 V m  (eV) 
                 −3.68716 
                 −4.45837 
                 −18.60523 
                 −7.93410 
                 −6.37231 
               
               
                 E(AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 0 
                 −14.53414 
                 −14.63489 
               
               
                 ΔE H     2     MO (AO/HO) (eV) 
                 0 
                 −2.26759 
                 −3.71673 
                 0 
                 −2.26758 
               
               
                 E T (AO/HO) (eV) 
                 −14.63489 
                 −12.36730 
                 3.71673 
                 −14.53414 
                 −12.36731 
               
               
                 E(n 3  AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 E T (H 2 MO) (eV) 
                 −31.63534 
                 −31.63541 
                 −63.27056 
                 −31.63534 
                 −31.63533 
               
               
                 E T (atom-atom,msp 3  · AO) (eV) 
                 −1.44915 
                 0.00000 
                 −3.71673 
                 0 
                 0 
               
               
                 E T (MO) (eV) 
                 −33.08452 
                 −31.63537 
                 −66.98746 
                 −31.63537 
                 −31.63537 
               
               
                 ω(10 15  rad/s) 
                 9.97851 
                 19.8904 
                 15.7474 
                 48.7771 
                 28.9084 
               
               
                 E K  (eV) 
                 6.56803 
                 13.09221 
                 10.36521 
                 32.10594 
                 19.02803 
               
               
                 Ē D  (eV) 
                 −0.16774 
                 −0.22646 
                 −0.21333 
                 −0.35462 
                 −0.27301 
               
               
                 Ē Kvib  (eV) 
                 0.15895 [7] 
                 0.14667 [66] 
                 0.11159 [12] 
                 0.40696 [24] 
                 0.39427 [59] 
               
               
                 Ē osc  (eV) 
                 −0.08827 
                 −0.15312 
                 −0.15754 
                 −0.15115 
                 −0.07587 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                 E T (Group) (eV) 
                 −33.17279 
                 −31.64046 
                 −67.30254 
                 −31.78651 
                 −31.71124 
               
               
                 E initial (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.53414 
                 −14.63489 
               
               
                 E initial (c 5  AO/HO) (eV) 
                 0 
                 0 
                 0 
                 −13.59844 
                 −13.59844 
               
               
                 E D (Group) (eV) 
                 3.75498 
                 2.37068 
                 8.76298 
                 3.51208 
                 3.32988 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 25 
               
               
                   
               
               
                 The total gaseous bond energies of thymine calculated using the functional group composition 
               
               
                 and the energies of Table 24 compared to the experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                 C═O 
                 C—N 
                 NH (i) 
                 C═C 
                 CH 3   
                 C—C (i) 
                 C—C (ii) 
               
               
                 Formula 
                 Name 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 C 5 H 6 N 2 O 2   
                 Thymine 
                 2 
                 2 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 C—N—C 
                 NH (ii) 
                 CH 
                 Total Bond 
                 Total Bond 
               
               
                 Formula 
                 Name 
                 Group 
                 Group 
                 Group 
                 Energy (eV) 
                 Energy (eV) 
                 Relative Error 
               
               
                   
               
               
                 C 5 H 6 N 2 O 2   
                 Thymine 
                 1 
                 1 
                 1 
                 69.08792 
                 69.06438 
                 −0.00034 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 26 
               
               
                   
               
               
                 The bond angle parameters of thymine and experimental values [64]. In the calculation of θ v , the 
               
               
                 parameters from the preceding angle were used. E T  is E T  (atom-atom, msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                 2c′ 
                   
                 Atom 1 
                   
                 Atom 2 
                   
                   
               
               
                   
                 2c′ 
                 2c′ 
                 Terminal 
                   
                 Hybridization 
                   
                 Hybridization 
               
               
                 Atoms of 
                 Bond 1 
                 Bond 2 
                 Atoms 
                 E Coulombic   
                 Designation 
                 E Coulombic   
                 Designation 
                 c 2   
                 c 2   
               
               
                 Angle 
                 (a 0 ) 
                 (a 0 ) 
                 (a 0 ) 
                 Atom 1 
                 (Table 8) 
                 Atom 2 
                 (Table 8) 
                 Atom 1 
                 Atom 2 
               
               
                   
               
               
                 ∠N b C a C d   
                 2.64855 
                 2.74663 
                 4.5277 
                 −14.53414 
                 N 
                 −16.68412 
                 18 
                 0.91140 
                 0.81549 
               
               
                   
                   
                   
                   
                   
                   
                 C d   
                   
                 Eq. (15.135) 
               
               
                 ∠N b C a O 
                 2.64855 
                 2.27954 
                 4.2661 
                 −16.47951 
                 14 
                 −16.17521 
                 8 
                 0.82562 
                 0.84115 
               
               
                 ∠OC a C d   
               
               
                 ∠C b N b C a   
                 2.64855 
                 2.64855 
                 4.6904 
                 −17.40869 
                 30 
                 −16.58181 
                 16 
                 0.78155 
                 0.82053 
               
               
                 ∠N b C b N c   
                 2.64855 
                 2.59228 
                 4.4497 
                 −16.47951 
                 14 
                 −16.68411 
                 17 
                 0.82562 
                 0.81549 
               
               
                 ∠H b N b C a   
                 1.88268 
                 2.64855 
                 3.9158 
                 −14.53414 
                 N 
                 −14.82575 
                 1 
                 0.93613 
                 0.91771 
               
               
                   
                   
                   
                   
                   
                   
                 C a   
                   
                 Eq. (13.248) 
               
               
                 ∠C b N b H b   
               
               
                 ∠C b N c C c   
                 2.59228 
                 2.59228 
                 4.4944 
                 −17.93127 
                 38 
                 −16.88873 
                 20 
                 0.75878 
                 0.80561 
               
               
                 ∠N c C b O b   
                 2.59228 
                 2.27954 
                 4.2661 
                 −16.68411 
                 18 
                 −16.17521 
                 8 
                 0.81549 
                 0.84115 
               
               
                 ∠N b C b O b   
               
               
                 ∠N c C c C d   
                 2.59228 
                 2.53321 
                 4.5387 
                 −14.53414 
                 N 
                 −16.68412 
                 18 
                 0.84665 
                 0.81549 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Eq. (15.171) 
               
               
                 ∠H c N c C c   
                 1.88268 
                 2.59228 
                 3.8644 
                 −14.53414 
                 N 
                 −16.68412 
                 18 
                 0.84665 
                 0.81549 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Eq. (15.171) 
               
               
                 ∠H c N c C b   
               
               
                 ∠H c C c C d   
                 2.02241 
                 2.53321 
                 3.9833 
                 −15.95955 
                  6 
                 −15.95955 
                 6 
                 0.85252 
                 0.85252 
               
               
                 ∠H c C c N c   
               
               
                 ∠C a C d C c   
                 2.74663 
                 2.53321 
                 4.5387 
                 −17.00209 
                 22 
                 −17.61330 
                 32 
                 0.80024 
                 0.77247 
               
               
                 ∠C e C d C c   
                 2.86175 
                 2.53321 
                 4.7117 
                 −16.47951 
                 14 
                 −17.40869 
                 30 
                 0.82562 
                 0.78155 
               
               
                 ∠C e C d C a   
               
               
                 Methyl 
                 2.09711 
                 2.09711 
                 3.4252 
                 −15.75493 
                  4 
                 H 
                 H 
                 0.86359 
                 1 
               
               
                 ∠HC e H 
                   
                   
                   
                 C e   
               
               
                   
               
             
          
           
               
                   
                 Atoms of 
                   
                   
                   
                   
                 E T   
                 θ v   
                 θ 1   
                 θ 2   
                 Cal. θ 
                 Exp. θ 
               
               
                   
                 Angle 
                 C 1   
                 C 2   
                 c 1   
                 c 2 ′ 
                 (eV) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
               
               
                   
                   
               
               
                   
                 ∠N b C a C d   
                 1 
                 1 
                 1 
                 0.86345 
                 −1.44915 
                   
                   
                   
                 114.10 
                 115.7 
               
               
                   
                 ∠N b C a O 
                 1 
                 1 
                 1 
                 0.83339 
                 −1.44915 
                   
                   
                   
                 119.73 
                 119.5 
               
               
                   
                 ∠OC a C d   
                   
                   
                   
                   
                   
                   
                 114.10 
                 119.73 
                 126.17 
                 124.8 
               
               
                   
                 ∠C b N b C a   
                 1 
                 1 
                 1 
                 0.80104 
                 −1.85836 
                   
                   
                   
                 124.62 
                 126.1 
               
               
                   
                 ∠N b C b N c   
                 1 
                 1 
                 1 
                 0.82056 
                 −1.65376 
                   
                   
                   
                 116.21 
                 115.1 
               
               
                   
                 ∠H b N b C a   
                 0.75 
                 1 
                 0.75 
                 0.98033 
                 0 
                   
                   
                   
                 118.60 
               
               
                   
                 ∠C b N b H b   
                   
                   
                   
                   
                   
                   
                 124.62 
                 118.60 
                 116.78 
               
               
                   
                 ∠C b N c C c   
                 1 
                 1 
                 1 
                 0.78219 
                 −1.85836 
                   
                   
                   
                 120.20 
                 120.7 
               
               
                   
                 ∠N c C b O b   
                 1 
                 1 
                 1 
                 0.82832 
                 −1.44915 
                   
                   
                   
                 122.12 
                 123.7 
               
               
                   
                 ∠N b C b O b   
                   
                   
                   
                   
                   
                   
                 116.21 
                 122.12 
                 121.67 
                 121.2 
               
               
                   
                 ∠N c C c C d   
                 1 
                 1 
                 1 
                 0.83107 
                 −1.65376 
                   
                   
                   
                 124.63 
                 122.9 
               
               
                   
                 ∠H c N c C c   
                 0.75 
                 1 
                 0.75 
                 0.96320 
                 0 
                   
                   
                   
                 118.58 
               
               
                   
                 ∠H c N c C b   
                   
                   
                   
                   
                   
                   
                 120.20 
                 118.58 
                 121.23 
               
               
                   
                 ∠H c C c C d   
                 0.75 
                 1 
                 0.75 
                 1.00000 
                 0 
                   
                   
                   
                 121.54 
               
               
                   
                 ∠H c C c N c   
                   
                   
                   
                   
                   
                   
                 124.63 
                 121.54 
                 113.84 
               
               
                   
                 ∠C a C d C c   
                 1 
                 1 
                 1 
                 0.78636 
                 −1.85836 
                   
                   
                   
                 118.49 
                 118.5 
               
               
                   
                 ∠C e C d C c   
                 1 
                 1 
                 1 
                 0.80359 
                 −1.85836 
                   
                   
                   
                 121.58 
                 123.3 
               
               
                   
                 ∠C e C d C a   
                   
                   
                   
                   
                   
                   
                 118.49 
                 121.58 
                 119.93 
                 118.2 
               
               
                   
                 Methyl 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 109.50 
               
               
                   
                 ∠HC e H 
               
               
                   
                   
               
             
          
         
       
     
         [0215]    Guanine 
         [0216]    Guanine having the formula C 5 H 5 N 5 O is a purine with a carbonyl substitution at position C a , a primary amine moiety is at position C b  as shown in  FIG. 10 . The carbonyl functional group is equivalent to that of alkyl amides and the NH 2  and C b —N a  functional groups of the primary amine moiety are equivalent to the NH 2  and C a -N a  functional groups of adenine. Guanine further comprises an imidazole moiety wherein the CH, N d H, C d ═C c , C d —N e , N e ═C e , and C c —N d —C e  groups of the imidazole-type ring are equivalent to the corresponding groups of imidazole as given in the corresponding section. The six-membered ring also comprises the groups C a —N b —C b , N b H, N c ═C c , and C c —N d  that are equivalent to the corresponding imidazole and adenine functional groups. The C a -C d  bond comprises another functional group that is the C 60 -single-bond functional group except that E T (atom-atom, msp 3 .AO)═O in order to match the energies of the single and double-bonded moieties within the molecule. 
         [0217]    The symbols of the functional groups of guanine are given in Table 27. The geometrical (Eqs. (15.1-15.5) and (15.51)), intercept (Eqs. (15.80-15.87)), and energy (Eqs. (15.6-15.11) and (15.17-15.65)) parameters of guanine are given in Tables 28, 29, and 30, respectively. The total energy of guanine given in Table 31 was calculated as the sum over the integer multiple of each E D (Group) of Table 30 corresponding to functional-group composition of the molecule. The bond angle parameters of guanine determined using Eqs. (15.88-15.117) are given in Table 32. The color scale, charge-density of guanine comprising atoms with the outer shell bridged by one or more H 2 -type ellipsoidal MOs or joined with one or more hydrogen MOs is shown in  FIG. 11 . 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 27 
               
             
             
               
                   
               
               
                 The symbols of functional groups of guanine. 
               
             
          
           
               
                   
                 Functional Group 
                 Group Symbol 
               
               
                   
                   
               
               
                   
                 C a ═O (alkyl amide) 
                 C═O 
               
               
                   
                 C b —N a   
                 C—N (a) 
               
               
                   
                 NH 2  group 
                 NH 2   
               
               
                   
                 C c ═C d  double bond 
                 C═C 
               
               
                   
                 C a —C d   
                 C—C 
               
               
                   
                 N e ═C e  N c ═C b  double bond 
                 N═C 
               
               
                   
                 C d —N e  C c —N c   
                 C—N (b) 
               
               
                   
                 C c —N d —C e  C a —N b —C b   
                 C—N—C 
               
               
                   
                 N d H N b H group 
                 NH 
               
               
                   
                 C e H 
                 CH 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 28 
               
               
                   
               
               
                 The geometrical bond parameters of guanine and experimental values [1]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 C═O 
                 C—N (a) 
                 NH 2   
                 C═C 
                 C—C 
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 1.29907 
                 1.61032 
                 1.24428 
                 1.45103 
                 1.88599 
               
               
                 c′ (a 0 ) 
                 1.13977 
                 1.26898 
                 0.94134 
                 1.30463 
                 1.37331 
               
               
                 Bond Length 2c′ (Å) 
                 1.20628 
                 1.34303 
                 0.99627 
                 1.38076 
                 1.45345 
               
               
                 Exp. Bond Length 
                 1.220  
                 1.34 [64] 
                 0.998  
                 1.382  
                 1.42 [64] 
               
               
                 (Å) 
                 (acetamide) 
                 (guanine) 
                 (aniline) 
                 (pyrrole) 
                 (guanine) 
               
               
                   
                 1.225  
               
               
                   
                 (N-methylacetamide) 
               
               
                 b, c (a 0 ) 
                 0.62331 
                 0.99137 
                 0.81370 
                 0.63517 
                 1.29266 
               
               
                 e 
                 0.87737 
                 0.78803 
                 0.75653 
                 0.89910 
                 0.72817 
               
               
                   
               
             
          
           
               
                   
                 N═C 
                 C—N (b) 
                 C—N—C 
                 NH 
                 CH 
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 1.44926 
                 1.82450 
                 1.43222 
                 1.24428 
                 1.53380 
               
               
                 c′ (a 0 ) 
                 1.30383 
                 1.35074 
                 1.29614 
                 0.94134 
                 1.01120 
               
               
                 Bond Length 2c′ (Å) 
                 1.37991 
                 1.42956 
                 1.37178 
                  0.996270 
                 1.07021 
               
               
                 Exp. Bond Length 
                   
                   
                 1.370  
                 0.996  
                 1.076  
               
               
                 (Å) 
                   
                   
                 (pyrrole) 
                 (pyrrole) 
                 (pyrrole) 
               
               
                 b, c (a 0 ) 
                 0.63276 
                 1.22650 
                 0.60931 
                 0.81370 
                 1.15326 
               
               
                 e 
                 0.89965 
                 0.74033 
                 0.90499 
                 0.75653 
                 0.65928 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 29 
               
               
                   
               
               
                 The MO to HO intercept geometrical bond parameters of guanine. R 1  is an alkyl group and 
               
               
                 R, R′, R″ are H or alkyl groups. E T  is E T  (atom-atom, msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 Final Total 
                   
                   
               
               
                   
                   
                 E T   
                 E T   
                 E T   
                 E T   
                 Energy 
               
               
                   
                   
                 (eV) 
                 (eV) 
                 (eV) 
                 (eV) 
                 C2sp 3   
                 r initial   
                 r final   
               
               
                 Bond 
                 Atom 
                 Bond 1 
                 Bond 2 
                 Bond 3 
                 Bond 4 
                 (eV) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 N b (C d )C a ═O 
                 O 
                 −1.34946 
                 0 
                 0 
                 0 
                   
                 1.00000 
                 0.84115 
               
               
                 N b (C d )C a ═O 
                 C a   
                 −1.34946 
                 −0.92918 
                 0 
                 0 
                 −153.89433 
                 0.91771 
                 0.79546 
               
               
                 N—H (N b H) 
                 N b   
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                   
                 0.93084 
                 0.81549 
               
               
                 C d (O)C a —N b H(C b ) 
                 N b   
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                   
                 0.93084 
                 0.81549 
               
               
                 C d (O)C a —N b H(C b ) 
                 C a   
                 −1.34946 
                 −0.92918 
                 0 
                 0 
                 −153.89433 
                 0.91771 
                 0.79546 
               
               
                 C d (O)C a N b H—C b N c (N a H 2 ) 
                 N b   
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                   
                 0.93084 
                 0.81549 
               
               
                 C d (O)C a N b H—C b N c (N a H 2 ) 
                 C b   
                 −0.56690 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.04095 
                 0.91771 
                 0.78870 
               
               
                 N c (N b )C b N a H—H 
                 N a   
                 −0.56690 
                 0 
                 0 
                 0 
                   
                 0.93084 
                 0.88392 
               
               
                 HN b C b —N a H 2 (N c ) 
                 N a   
                 −0.56690 
                 0 
                 0 
                 0 
                   
                 0.93084 
                 0.88392 
               
               
                 HN b C b —N a H 2 (N c ) 
                 C b   
                 −0.56690 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.04095 
                 0.91771 
                 0.78870 
               
               
                 HN b C b ═N c C c (N a H 2 ) 
                 N c   
                 −0.92918 
                 −0.46459 
                 0 
                 0 
                   
                 0.93084 
                 0.83885 
               
               
                 HN b C b ═N c C c (N a H 2 ) 
                 C b   
                 −0.92918 
                 −0.92918 
                 −0.56690 
                 0 
                 −154.04095 
                 0.91771 
                 0.78870 
               
               
                 C b N c —C c C d (N d H) 
                 N c   
                 −0.46459 
                 −0.92918 
                 0 
                 0 
                   
                   
                 0.93084 
               
               
                 C b N c —C c C d (N d H) 
                 C c   
                 −0.46459 
                 −1.13380 
                 −0.92918 
                 0 
                 −154.14326 
                 0.91771 
                 0.78405 
               
               
                 N c (N d H)C c ═C d N e (C a ) 
                 C c   
                 −1.13380 
                 −0.92918 
                 −0.46459 
                 0 
                 −154.14326 
                 0.91771 
                 0.78405 
               
               
                 N c (N d H)C c ═C d N e (C a ) 
                 C d   
                 −1.13380 
                 −0.46459 
                 0 
                 0 
                 −153.21408 
                 0.91771 
                 0.82840 
               
               
                 N—H (N d H) 
                 N d   
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                   
                 0.93084 
                 0.81549 
               
               
                 (N c )C d C c —N d H(C e ) 
                 N d   
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                   
                 0.93084 
                 0.81549 
               
               
                 (N c )C d C c —N d H(C e ) 
                 C c   
                 −1.13379 
                 −0.92918 
                 −0.46459 
                 0 
                 −154.14326 
                 0.91771 
                 0.78405 
               
               
                 C—H (C e H) 
                 C e   
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                 −153.47405 
                 0.91771 
                 0.81549 
               
               
                 C c HN d H—C e H(N e ) 
                 N d   
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                   
                 0.93084 
                 0.81549 
               
               
                 C c HN d H—C e H(N e ) 
                 C e   
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                 −153.47405 
                 0.91771 
                 0.81549 
               
               
                 N d (H)C e ═N e C d   
                 N e   
                 −0.92918 
                 −0.46459 
                 0 
                 0 
                   
                 0.93084 
                 0.83885 
               
               
                 N d (H)C e ═N e C d   
                 C e   
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                 −153.47405 
                 0.91771 
                 0.81549 
               
               
                 C e N e —C d C a (C c ) 
                 N e   
                 −0.46459 
                 −0.92918 
                 0 
                 0 
                   
                 0.93084 
                 0.83885 
               
               
                 C e N e —C d C a (C c ) 
                 C d   
                 −0.46459 
                 −1.13380 
                 0 
                 0 
                 −153.21408 
                 0.91771 
                 0.82840 
               
               
                 (N e )C c C d —C a (O)N b   
                 C a   
                 0.00000 
                 −1.34946 
                 −0.92918 
                 0 
                 −153.89433 
                 0.91771 
                 0.79546 
               
               
                 (N e )C c C d —C a (O)N b   
                 C d   
                 0.00000 
                 −1.13379 
                 −0.46459 
                 0 
                 −153.21407 
                 0.91771 
                 0.82840 
               
               
                   
               
             
          
           
               
                   
                 E Coulomb   
                 E(C2sp 3 ) 
                   
                   
                   
                   
                   
               
               
                   
                 (C2sp 3 )(eV) 
                 (eV) 
                 θ′ 
                 θ 1   
                 θ 2   
                 d 1   
                 d 2   
               
               
                 Bond 
                 Final 
                 Final 
                 (°) 
                 (°) 
                 (°) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 N b (C d )C a ═O 
                 −16.17521 
                   
                 137.27 
                 42.73 
                 66.31 
                 0.52193 
                 0.61784 
               
               
                 N b (C d )C a ═O 
                 −17.10440 
                 −16.91353 
                 135.34 
                 44.66 
                 63.78 
                 0.57401 
                 0.56576 
               
               
                 N—H (N b H) 
                 −16.68411 
                   
                 117.34 
                 62.66 
                 62.90 
                 0.56678 
                 0.37456 
               
               
                 C d (O)C a —N b H(C b ) 
                 −16.68411 
                   
                 138.92 
                 41.08 
                 61.59 
                 0.68147 
                 0.61467 
               
               
                 C d (O)C a —N b H(C b ) 
                 −17.10440 
                 −16.91353 
                 138.15 
                 41.85 
                 60.58 
                 0.70361 
                 0.59253 
               
               
                 C d (O)C a N b H—C b N c (N a H 2 ) 
                 −16.68411 
                   
                 138.92 
                 41.08 
                 61.59 
                 0.68147 
                 0.61467 
               
               
                 C d (O)C a N b H—C b N c (N a H 2 ) 
                 −17.25101 
                 −17.06015 
                 137.89 
                 42.11 
                 60.23 
                 0.71108 
                 0.58506 
               
               
                 N c (N b )C b N a H—H 
                 −15.39265 
                   
                 121.74 
                 58.26 
                 67.49 
                 0.47634 
                 0.46500 
               
               
                 HN b C b —N a H 2 (N c ) 
                 −15.39265 
                   
                 113.13 
                 66.87 
                 55.08 
                 0.92180 
                 0.34719 
               
               
                 HN b C b —N a H 2 (N c ) 
                 −17.25101 
                 −17.06015 
                 106.68 
                 73.32 
                 49.65 
                 1.04263 
                 0.22636 
               
               
                 HN b C b ═N c C c (N a H 2 ) 
                 −16.21952 
                   
                 138.20 
                 41.80 
                 62.08 
                 0.67849 
                 0.62534 
               
               
                 HN b C b ═N c C c (N a H 2 ) 
                 −17.25101 
                 −17.06015 
                 136.24 
                 43.76 
                 59.56 
                 0.73424 
                 0.56959 
               
               
                 C b N c —C c C d (N d H) 
                 0.83885 
                 −16.21953 
                 91.32 
                 88.68 
                 43.14 
                 1.33135 
                 0.01939 
               
               
                 C b N c —C c C d (N d H) 
                 −17.35332 
                 −17.16246 
                 86.00 
                 94.00 
                 39.62 
                 1.40538 
                 0.05464 
               
               
                 N c (N d H)C c ═C d N e (C a ) 
                 −17.35332 
                 −17.16246 
                 135.87 
                 44.13 
                 59.25 
                 0.74183 
                 0.56280 
               
               
                 N c (N d H)C c ═C d N e (C a ) 
                 −16.42414 
                 −16.23327 
                 137.64 
                 42.36 
                 61.49 
                 0.69250 
                 0.61213 
               
               
                 N—H (N d H) 
                 −16.68411 
                   
                 117.34 
                 62.66 
                 62.90 
                 0.56678 
                 0.37456 
               
               
                 (N c )C d C c —N d H(C e ) 
                 −16.68411 
                   
                 138.92 
                 41.08 
                 61.59 
                 0.68147 
                 0.61467 
               
               
                 (N c )C d C c —N d H(C e ) 
                 −17.35332 
                 −17.16245 
                 137.70 
                 42.30 
                 59.99 
                 0.71622 
                 0.57992 
               
               
                 C—H (C e H) 
                 −16.68411 
                 −16.49325 
                 84.49 
                 95.51 
                 44.47 
                 1.08953 
                 0.07833 
               
               
                 C c HN d H—C e H(N e ) 
                 −16.68411 
                   
                 138.92 
                 41.08 
                 61.59 
                 0.68147 
                 0.61467 
               
               
                 C c HN d H—C e H(N e ) 
                 −16.68411 
                 −16.49325 
                 138.92 
                 41.08 
                 61.59 
                 0.68147 
                 0.61467 
               
               
                 N d (H)C e ═N e C d   
                 −16.21952 
                   
                 138.20 
                 41.80 
                 62.08 
                 0.67849 
                 0.62534 
               
               
                 N d (H)C e ═N e C d   
                 −16.68411 
                 −16.49325 
                 137.31 
                 42.69 
                 60.92 
                 0.70446 
                 0.59938 
               
               
                 C e N e —C d C a (C c ) 
                 −16.21953 
                   
                 91.32 
                 88.68 
                 43.14 
                 1.33135 
                 0.01939 
               
               
                 C e N e —C d C a (C c ) 
                 −16.42414 
                 −16.23327 
                 90.36 
                 89.64 
                 42.49 
                 1.34547 
                 0.00527 
               
               
                 (N e )C c C d —C a (O)N b   
                 −17.10440 
                 −16.91353 
                 81.01 
                 98.99 
                 37.43 
                 1.49764 
                 0.12433 
               
               
                 (N e )C c C d —C a (O)N b   
                 −16.42413 
                 −16.23327 
                 92.72 
                 87.28 
                 45.17 
                 1.32975 
                 0.04357 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 30 
               
               
                   
               
               
                 The energy parameters (eV) of functional groups of guanine. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 C═O 
                 C—N (a) 
                 NH 2   
                 C═C 
                 C—C 
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 n 1   
                 2 
                 1 
                 2 
                 2 
                 1 
               
               
                 n 2   
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 1 
                 0 
                 0 
               
               
                 C 1   
                 0.5 
                 0.5 
                 0.75 
                 0.5 
                 0.5 
               
               
                 C 2   
                 1 
                 1 
                 0.93613 
                 0.85252 
                 1 
               
               
                 c 1   
                 1 
                 1 
                 0.75 
                 1 
                 1 
               
               
                 c 2   
                 0.85395 
                 0.84665 
                 0.92171 
                 0.85252 
                 0.91771 
               
               
                 c 3   
                 2 
                 0 
                 0 
                 0 
                 0 
               
               
                 c 4   
                 4 
                 2 
                 1 
                 4 
                 2 
               
               
                 c 5   
                 0 
                 0 
                 2 
                 0 
                 0 
               
               
                 C 1o   
                 0.5 
                 0.5 
                 1.5 
                 0.5 
                 0.5 
               
               
                 C 2o   
                 1 
                 1 
                 1 
                 0.85252 
                 1 
               
               
                 V e  (eV) 
                 −111.25473 
                 −35.50149 
                 −78.97795 
                 −104.37986 
                 −33.63376 
               
               
                 V p  (eV) 
                 23.87467 
                 10.72181 
                 28.90735 
                 20.85777 
                 9.90728 
               
               
                 T (eV) 
                 42.82081 
                 11.02312 
                 31.73641 
                 35.96751 
                 8.91674 
               
               
                 V m  (eV) 
                 −21.41040 
                 −5.51156 
                 −15.86820 
                 −17.98376 
                 −4.45837 
               
               
                 E (AO/HO) (eV) 
                 0 
                 −14.63489 
                 −14.53414 
                 0 
                 −14.63489 
               
               
                 ΔE H   2 MO (AO/HO) (eV) 
                 −2.69893 
                 −2.26759 
                 0 
                 −2.26759 
                 −2.26759 
               
               
                 E T  (AO/HO) (eV) 
                 2.69893 
                 −12.36730 
                 −14.53414 
                 2.26759 
                 −12.36730 
               
               
                 E(n 3  AO/HO) (eV) 
                 0 
                 0 
                 −14.53414 
                 0 
                 0 
               
               
                 E T  (H 2 MO) (eV) 
                 −63.27074 
                 −31.63543 
                 −48.73654 
                 −63.27075 
                 −31.63541 
               
               
                 E T  (atom-atom, msp 3 .AO) (eV) 
                 −2.69893 
                 −1.13379 
                 0 
                 −2.26759 
                 0.00000 
               
               
                 E T  (MO) (eV) 
                 −65.96966 
                 −32.76916 
                 −48.73660 
                 −65.53833 
                 −31.63537 
               
               
                 ω (10 15  rad/s) 
                 59.4034 
                 14.3055 
                 68.9812 
                 15.4421 
                 19.8904 
               
               
                 E K  (eV) 
                 39.10034 
                 9.41610 
                 45.40465 
                 10.16428 
                 13.09221 
               
               
                 Ē D  (eV) 
                 −0.40804 
                 −0.19893 
                 −0.42172 
                 −0.20668 
                 −0.22646 
               
               
                 Ē Kvib  (eV) 
                 0.21077 [12] 
                 0.15498 [57] 
                 0.40929 [22] 
                 0.17897 [6]  
                 0.14667 [66] 
               
               
                 Ē osc  (eV) 
                 −0.30266 
                 −0.12144 
                 −0.21708 
                 −0.11720 
                 −0.15312 
               
               
                 E mag  (eV) 
                 0.11441 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                 E T  (Group) (eV) 
                 −66.57498 
                 −32.89060 
                 −49.17075 
                 −65.77272 
                 −31.64046 
               
               
                 E initial  (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.53414 
                 −14.63489 
                 −14.63489 
               
               
                 E initial  (c 5  AO/HO) (eV) 
                 0 
                 0 
                 −13.59844 
                 0 
                 0 
               
               
                 E D  (Group) (eV) 
                 7.80660 
                 3.62082 
                 7.43973 
                 7.23317 
                 2.37068 
               
               
                   
               
               
                   
                 N═C 
                 C—N (b) 
                 C—N—C 
                 NH 
                 CH 
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 n 1   
                 2 
                 1 
                 2 
                 1 
                 1 
               
               
                 n 2   
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.5 
                 0.5 
                 0.5 
                 0.75 
                 0.75 
               
               
                 C 2   
                 0.85252 
                 1 
                 0.85252 
                 0.93613 
                 1 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 0.75 
                 1 
               
               
                 c 2   
                 0.84665 
                 0.84665 
                 0.84665 
                 0.92171 
                 0.91771 
               
               
                 c 3   
                 0 
                 0 
                 0 
                 1 
                 1 
               
               
                 c 4   
                 4 
                 2 
                 4 
                 1 
                 1 
               
               
                 c 5   
                 0 
                 0 
                 0 
                 1 
                 1 
               
               
                 C 1o   
                 0.5 
                 0.5 
                 0.5 
                 0.75 
                 0.75 
               
               
                 C 2o   
                 0.85252 
                 1 
                 0.85252 
                 1 
                 1 
               
               
                 V e  (eV) 
                 −103.92756 
                 −32.44864 
                 −106.58684 
                 −39.48897 
                 −39.09538 
               
               
                 V p  (eV) 
                 20.87050 
                 10.07285 
                 20.99432 
                 14.45367 
                 13.45505 
               
               
                 T (eV) 
                 35.85539 
                 8.89248 
                 37.21047 
                 15.86820 
                 12.74462 
               
               
                 V m  (eV) 
                 −17.92770 
                 −4.44624 
                 −18.60523 
                 −7.93410 
                 −6.37231 
               
               
                 E (AO/HO) (eV) 
                 0 
                 −14.63489 
                 0 
                 −14.53414 
                 −14.63489 
               
               
                 ΔE H   2 MO (AO/HO) (eV) 
                 −1.85836 
                 −0.92918 
                 −3.71673 
                 0 
                 −2.26758 
               
               
                 E T  (AO/HO) (eV) 
                 1.85836 
                 −13.70571 
                 3.71673 
                 −14.53414 
                 −12.36731 
               
               
                 E (n 3  AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 E T  (H 2 MO) (eV) 
                 −63.27100 
                 −31.63527 
                 −63.27056 
                 −31.63534 
                 −31.63533 
               
               
                 E T  (atom-atom, msp 3 .AO) (eV) 
                 −1.85836 
                 −0.92918 
                 −3.71673 
                 0 
                 0 
               
               
                 E T  (MO) (eV) 
                 −65.12910 
                 −32.56455 
                 −66.98746 
                 −31.63537 
                 −31.63537 
               
               
                 ω (10 15  rad/s) 
                 15.4704 
                 21.5213 
                 15.7474 
                 48.7771 
                 28.9084 
               
               
                 E K  (eV) 
                 10.18290 
                 14.16571 
                 10.36521 
                 32.10594 
                 19.02803 
               
               
                 Ē D  (eV) 
                 −0.20558 
                 −0.24248 
                 −0.21333 
                 −0.35462 
                 −0.27301 
               
               
                 Ē Kvib  (eV) 
                 0.20768 [61] 
                 0.12944 [23] 
                 0.11159 [12] 
                 0.40696 [24] 
                 0.39427 [59] 
               
               
                 Ē osc  (eV) 
                 −0.10174 
                 −0.17775 
                 −0.15754 
                 −0.15115 
                 −0.07587 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                 E T  (Group) (eV) 
                 −65.33259 
                 −32.74230 
                 −67.30254 
                 −31.78651 
                 −31.71124 
               
               
                 E initial  (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.53414 
                 −14.63489 
               
               
                 E initial  (c 5  AO/HO) (eV) 
                 0 
                 0 
                 0 
                 −13.59844 
                 −13.59844 
               
               
                 E D  (Group) (eV) 
                 6.79303 
                 3.47253 
                 8.76298 
                 3.51208 
                 3.32988 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 31 
               
               
                   
               
               
                 The total gaseous bond energies of guanine calculated using the functional group 
               
               
                 composition and the energies of Table 30 compared to the experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                 C═O 
                 C—N (a) 
                 NH 2   
                 C═C 
                 C—C 
                 N═C 
                 C—N (b) 
               
               
                 Formula 
                 Name 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 C 5 H 5 N 5 O 
                 Guanine 
                 1 
                 1 
                 1 
                 1 
                 1 
                 2 
                 2 
               
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 C—N—C 
                 NH 
                 CH 
                 Total Bond 
                 Total Bond 
               
               
                 Formula 
                 Name 
                 Group 
                 Group 
                 Group 
                 Energy (eV) 
                 Energy (eV) 
                 Relative Error 
               
               
                   
               
               
                 C 5 H 5 N 5 O 
                 Guanine 
                 2 
                 2 
                 1 
                 76.88212 
                 77.41849 a   
                 0.00693 
               
               
                   
               
               
                   a Crystal. 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 32 
               
               
                   
               
               
                 The bond angle parameters of guanine and experimental values [64]. In the calculation of θ v , the 
               
               
                 parameters from the preceding angle were used. E T  is E T  (atom-atom, msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                 2c′ 
                   
                 Atom 1 
                   
                 Atom 2 
                   
               
               
                   
                 2c′ 
                 2c′ 
                 Terminal 
                   
                 Hybridization 
                   
                 Hybridization 
               
               
                 Atoms of 
                 Bond 1 
                 Bond 2 
                 Atoms 
                 E Coulombic   
                 Designation 
                 E Coulombic   
                 Designation 
                 c 2   
               
               
                 Angle 
                 (a 0 ) 
                 (a 0 ) 
                 (a 0 ) 
                 Atom 1 
                 (Table 8) 
                 Atom 2 
                 (Table 8) 
                 Atom 1 
               
               
                   
               
               
                 ∠N b C a C d   
                 2.59228 
                 2.74663 
                 4.3359 
                 −14.53414 
                 N 
                 −16.42413 
                 13 
                 0.84665 
               
               
                   
                   
                   
                   
                   
                   
                 C d   
                   
                 Eq. (15.171) 
               
               
                 ∠N b C a O 
                 2.59228 
                 2.27954 
                 4.2426 
                 −16.68411 
                 18 
                 −16.17521 
                 8 
                 0.81549 
               
               
                 ∠OC a C d   
               
               
                 ∠C b N b C a   
                 2.59228 
                 2.59228 
                 4.5826 
                 −17.25101 
                 28 
                 −17.10440 
                 25 
                 0.78870 
               
               
                 ∠N b C b N c   
                 2.59228 
                 2.60766 
                 4.5166 
                 −15.75493 
                  4 
                 −15.75493 
                 4 
                 0.86359 
               
               
                 ∠H b N b C a   
                 1.88268 
                 2.64855 
                 3.9158 
                 −14.53414 
                 N 
                 −14.82575 
                 1 
                 0.93613 
               
               
                   
                   
                   
                   
                   
                   
                 C a   
                   
                 Eq. (13.248) 
               
               
                 ∠C b N b H b   
               
               
                 ∠N b C b N a   
                 2.59228 
                 2.53797 
                 4.3818 
                 −16.68411 
                 18 
                 −15.39265 
                 2 
                 0.81549 
               
               
                 ∠N a C b N c   
                 2.53797 
                 2.60766 
                 4.4721 
                 −15.39265 
                  2 
                 −16.21952 
                 9 
                 0.88392 
               
               
                 ∠HN a C b   
                 1.88268 
                 2.53797 
                 3.8987 
                 −14.53414 
                 N 
                 −16.32183 
                 11 
                 0.93613 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Eq. (13.248) 
               
               
                 ∠HN a H 
                 1.88268 
                 1.88268 
                 3.1559 
                 −14.53414 
                 N 
                 H 
                 H 
                 0.93613 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Eq. (13.248) 
               
               
                 ∠C b N c C c   
                 2.60766 
                 2.70148 
                 4.4721 
                 −17.25101 
                 28 
                 −17.35332 
                 29 
                 0.78870 
               
               
                 ∠N c C c N d   
                 2.70148 
                 2.59228 
                 4.7117 
                 −14.53414 
                 N 
                 −14.53414 
                 N 
                 0.84665 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Eq. (15.171) 
               
               
                 ∠N c C c C d   
                 2.70148 
                 2.60925 
                 4.7539 
                 −14.53414 
                 N 
                 −15.95955 
                 6 
                 0.84665 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Eq. (15.171) 
               
               
                 ∠C a C d C c   
                 2.74663 
                 2.60925 
                 4.6476 
                 −17.10440 
                 25 
                 −16.88873 
                 20 
                 0.79546 
               
               
                 ∠C c N d C e   
                 2.59228 
                 2.59228 
                 4.2071 
                 −17.95963 
                 39 
                 −17.95963 
                 39 
                 0.75758 
               
               
                 ∠N d C c C d   
                 2.59228 
                 2.60925 
                 4.1473 
                 −14.53414 
                 N 
                 −17.35332 
                 29 
                 0.84665 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Eq. (15.171) 
               
               
                 ∠N e C e N d   
                 2.60766 
                 2.60287 
                 4.3359 
                 −16.21952 
                  9 
                 −16.03838 
                 7 
                 0.83885 
               
               
                 ∠C e N d H 
                 2.59228 
                 1.88268 
                 4.0166 
                 −14.53414 
                 N 
                 −15.95954 
                 6 
                 0.84665 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Eq. (15.171) 
               
               
                 ∠C c N d H 
               
               
                 ∠HC e N e   
                 2.02241 
                 2.60766 
                 4.1312 
                 −16.68411 
                 18 
                 −14.53414 
                 N 
                 0.81549 
               
               
                 ∠N d C e H 
               
               
                 ∠C d N e C e   
                 2.70148 
                 2.60766 
                 4.2661 
                 −17.92022 
                 37 
                 −17.92022 
                 37 
                 0.75924 
               
               
                 ∠N e C d C c   
                 2.70148 
                 2.60925 
                 4.2895 
                 −14.53414 
                 N 
                 −16.42414 
                 13 
                 0.84665 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Eq. (15.171) 
               
               
                 ∠C a C d N e   
                 2.74663 
                 2.70148 
                 4.9396 
                 −17.10440 
                 25 
                 −14.53414 
                 N 
                 0.79546 
               
               
                   
               
             
          
           
               
                 Atoms of 
                 c 2   
                   
                   
                   
                   
                 E T   
                 θ v   
                 θ 1   
                 θ 2   
                 Cal. θ 
                 Exp. θ 
               
               
                 Angle 
                 Atom 2 
                 C 1   
                 C 2   
                 c 1   
                 c 2 ′ 
                 (eV) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
               
               
                   
               
               
                 ∠N b C a C d   
                 0.82840 
                 1 
                 1 
                 1 
                 0.83753 
                 −1.44915 
                   
                   
                   
                 108.57 
                 110.8 
               
               
                 ∠N b C a O 
                 0.84115 
                 1 
                 1 
                 1 
                 0.82832 
                 −1.44915 
                   
                   
                   
                 120.98 
                 120.4 
               
               
                 ∠OC a C d   
                   
                   
                   
                   
                   
                   
                   
                 108.57 
                 120.98 
                 130.44 
                 128.8 
               
               
                 ∠C b N b C a   
                 0.79546 
                 1 
                 1 
                 1 
                 0.79208 
                 −1.85836 
                   
                   
                   
                 124.23 
                 125.6 
               
               
                 ∠N b C b N c   
                 0.86359 
                 1 
                 1 
                 1 
                 0.86359 
                 −1.44915 
                   
                   
                   
                 120.59 
                 123.3 
               
               
                 ∠H b N b C a   
                 0.91771 
                 0.75 
                 1 
                 0.75 
                 0.98033 
                 0 
                   
                   
                   
                 118.60 
               
               
                 ∠C b N b H b   
                   
                   
                   
                   
                   
                   
                   
                 124.23 
                 118.60 
                 117.17 
               
               
                 ∠N b C b N a   
                 0.88392 
                 1 
                 1 
                 1 
                 0.84971 
                 −1.44915 
                   
                   
                   
                 117.32 
                 115.8 
               
               
                 ∠N a C b N c   
                 0.83885 
                 1 
                 1 
                 1 
                 0.86138 
                 −1.44915 
                   
                   
                   
                 120.71 
                 120.9 
               
               
                 ∠HN a C b   
                 0.83360 
                 0.75 
                 1 
                 0.75 
                 0.98458 
                 0 
                   
                   
                   
                 123.07 
                 118 [65] 
               
               
                 ∠HN a H 
                 1     
                 1 
                 1 
                 0.75 
                 1.06823 
                 0 
                   
                   
                   
                 113.89 
                 113.9 [1]   
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (aniline) 
               
               
                 ∠C b N c C c   
                 0.78405 
                 1 
                 1 
                 1 
                 0.78637 
                 −1.85836 
                   
                   
                   
                 114.77 
                 112.6 
               
               
                 ∠N c C c N d   
                 0.84665 
                 1 
                 1 
                 1 
                 0.84665 
                 −1.65376 
                   
                   
                   
                 125.75 
                 125.8 
               
               
                   
                 Eq. (15.171) 
               
               
                 ∠N c C c C d   
                 0.85252 
                 1 
                 1 
                 1 
                 0.84958 
                 −1.65376 
                   
                   
                   
                 127.05 
                 128.3 
               
               
                 ∠C a C d C c   
                 0.80561 
                 1 
                 1 
                 1 
                 0.80054 
                 −1.85836 
                   
                   
                   
                 120.38 
                 119.4 
               
               
                 ∠C c N d C e   
                 0.75758 
                 1 
                 1 
                 1 
                 0.75758 
                 −1.85836 
                   
                   
                   
                 108.48 
                 108.2 
               
               
                 ∠N d C c C d   
                 0.78405 
                 1 
                 1 
                 1 
                 0.81535 
                 −1.44915 
                   
                   
                   
                 105.75 
                 105.9 
               
               
                 ∠N e C e N d   
                 0.84833 
                 1 
                 1 
                 1 
                 0.84359 
                 −1.44915 
                   
                   
                   
                 112.64 
                 110.0 
               
               
                 ∠C e N d H 
                 0.85252 
                 0.75 
                 1 
                 0.75 
                 1.00693 
                 0 
                   
                   
                   
                 126.96 
                 127 [65] 
               
               
                 ∠C c N d H 
                   
                   
                   
                   
                   
                   
                   
                 108.48 
                 126.96 
                 124.56 
                 127   
               
               
                 ∠HC e N e   
                 0.84665 
                 0.75 
                 1 
                 0.75 
                 1.03820 
                 0 
                   
                   
                   
                 125.85 
                 126 [65] 
               
               
                   
                 Eq. (15.171) 
               
               
                 ∠N d C e H 
                   
                   
                   
                   
                   
                   
                   
                 112.64 
                 125.85 
                 121.52 
                 119 [65] 
               
               
                 ∠C d N e C e   
                 0.75924 
                 1 
                 1 
                 1 
                 0.75924 
                 −1.85836 
                   
                   
                   
                 106.93 
                  108.0° 
               
               
                 ∠N e C d C c   
                 0.82840 
                 1 
                 1 
                 1 
                 0.83753 
                 −1.44915 
                   
                   
                   
                 107.73 
                 107.9 
               
               
                 ∠C a C d N e   
                 0.84665 
                 1 
                 1 
                 1 
                 0.82105 
                 −1.85836 
                   
                   
                   
                 130.10 
                 133.6 
               
               
                   
                 Eq. (15.171) 
               
               
                   
               
             
          
         
       
     
         [0218]    Cytosine 
         [0219]    Cytosine having the formula C 4 H 5 N 3 O is a pyrimidine with a carbonyl substitution at position C b , and a primary amine moiety is at position C a  as shown in  FIG. 12 . The carbonyl and adjacent C b —N b  functional groups are equivalent to the corresponding groups of alkyl amides. The NH 2  and C a —N a  functional groups of the primary amine moiety are equivalent to the NH 2  and C a —N a  functional groups of adenine. The vinyl moiety, HC c ═C d H, comprises C═C and CH functional groups that are equivalent to the corresponding alkene groups. Cytosine further comprises N b ═C a , N c H, and C b —N c —C c  groups that are equivalent to the corresponding groups of imidazole as given in the corresponding section. The C a —C d  bond comprises another functional group that is equivalent to the C a —C d  group of guanine and thymine except that E T (atom-atom,msp 3 .AO) is equivalent to the contribution of a C2sp 3  HO of an alkane, −0.92918 eV (Eq. (14.513)), in order to match the energies of the single and double-bonded moieties within the molecule. 
         [0220]    The symbols of the functional groups of cytosine are given in Table 33. The geometrical (Eqs. (15.1-15.5) and (15.51)), intercept (Eqs. (15.80-15.87)), and energy (Eqs. (15.6-15.11) and (15.17-15.65)) parameters of cytosine are given in Tables 34, 35, and 36, respectively. The total energy of cytosine given in Table 37 was calculated as the sum over the integer multiple of each E D (Group) of Table 36 corresponding to functional-group composition of the molecule. The bond angle parameters of cytosine determined using Eqs. (15.88-15.117) are given in Table 38. The color scale, charge-density of cytosine comprising atoms with the outer shell bridged by one or more H 2 -type ellipsoidal MOs or joined with one or more hydrogen MOs is shown in  FIG. 13 . 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 33 
               
             
             
               
                   
               
               
                 The symbols of functional groups of cytosine. 
               
             
          
           
               
                   
                 Functional Group 
                 Group Symbol 
               
               
                   
                   
               
               
                   
                 C a —N a   
                 C—N (a) 
               
               
                   
                 NH 2  group 
                 NH 2   
               
               
                   
                 N b ═C a  double bond 
                 N═C 
               
               
                   
                 C b ═O (alkyl amide) 
                 C═O 
               
               
                   
                 C b —N b  amide 
                 C—N (b) 
               
               
                   
                 C c ═C d  double bond 
                 C═C 
               
               
                   
                 C c H C d H 
                 CH 
               
               
                   
                 C a —C d   
                 C—C 
               
               
                   
                 C b —N c —C c   
                 C—N—C 
               
               
                   
                 N c H group 
                 NH 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 34 
               
               
                   
               
               
                 The geometrical bond parameters of cytosine and experimental values [1]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 C—N (a) 
                 NH 2   
                 N═C 
                 C═O 
                 C—N (b) 
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 1.61032 
                 1.24428 
                 1.44926 
                 1.29907 
                 1.75370 
               
               
                 c′ (a 0 ) 
                 1.26898 
                 0.94134 
                 1.30383 
                 1.13977 
                 1.32427 
               
               
                 Bond Length 2c′ (Å) 
                 1.34303 
                 0.99627 
                 1.37991 
                 1.20628 
                 1.40155 
               
               
                 Exp. Bond Length 
                 1.34 [64] 
                 0.998  
                   
                 1.220  
                 1.380  
               
               
                 (Å) 
                 (adenine) 
                 (aniline) 
                   
                 (acetamide) 
                 (acetamide) 
               
               
                   
                   
                   
                   
                 1.225  
               
               
                   
                   
                   
                   
                 (N-methylacetamide) 
               
               
                 b, c (a 0 ) 
                 0.99137 
                 0.81370 
                 0.63276 
                 0.62331 
                 1.14968 
               
               
                 e 
                 0.78803 
                 0.75653 
                 0.89965 
                 0.87737 
                 0.75513 
               
               
                   
               
             
          
           
               
                   
                 C═C 
                 CH 
                 C—C 
                 C—N—C 
                 NH 
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 1.47228 
                 1.53380 
                 1.88599 
                 1.43222 
                 1.24428 
               
               
                 c′ (a 0 ) 
                 1.26661 
                 1.01120 
                 1.37331 
                 1.29614 
                 0.94134 
               
               
                 Bond Length 2c′ (Å) 
                 1.34052 
                 1.07021 
                 1.45345 
                 1.37178 
                  0.996270 
               
               
                 Exp. Bond Length 
                 1.34 [64] 
                 1.076  
                 1.43 [64] 
                 1.370  
                 0.996  
               
               
                 (Å) 
                 (cytosine) 
                 (pyrrole) 
                 (cytosine) 
                 (pyrrole) 
                 (pyrrole) 
               
               
                   
                 1.342  
               
               
                   
                 (2-methylpropene) 
               
               
                   
                 1.346  
               
               
                   
                 (2-butene) 
               
               
                   
                 1.349  
               
               
                   
                 (1,3-butadiene) 
               
               
                 b, c (a 0 ) 
                 0.75055 
                 1.15326 
                 1.29266 
                 0.60931 
                 0.81370 
               
               
                 e 
                 0.86030 
                 0.65928 
                 0.72817 
                 0.90499 
                 0.75653 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 35 
               
               
                   
               
               
                 The MO to HO intercept geometrical bond parameters of cytosine. 
               
               
                 R 1  is an alkyl group and R, R′, R″ are H or alkyl 
               
               
                 groups. E T  is E T  (atom-atom, msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 Final Total 
                   
                   
               
               
                   
                   
                 E T   
                 E T   
                 E T   
                 E T   
                 Energy 
               
               
                   
                   
                 (eV) 
                 (eV) 
                 (eV) 
                 (eV) 
                 C2sp 3   
                 r initial   
                 r final   
               
               
                 Bond 
                 Atom 
                 Bond 1 
                 Bond 2 
                 Bond 3 
                 Bond 4 
                 (eV) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 C d (N b )C a N a H—H 
                 N a   
                 −0.56690 
                 0 
                 0 
                 0 
                   
                 0.93084 
                 0.88392 
               
               
                 C d (N b )C a —N a H 2   
                 N a   
                 −0.56690 
                 0 
                 0 
                 0 
                   
                 0.93084 
                 0.88392 
               
               
                 C d (N b )C a —N a H 2   
                 C a   
                 −0.56690 
                 −0.92918 
                 −0.46459 
                 0 
                 −153.57636 
                 0.91771 
                 0.81052 
               
               
                 C d (N a )C a ═N b C b   
                 N b   
                 −0.92918 
                 −0.82688 
                 0 
                 0 
                   
                 0.93084 
                 0.82053 
               
               
                 C d (N a )C a ═N b C b   
                 C a   
                 −0.92918 
                 −0.56690 
                 −0.46459 
                 0 
                 −153.57636 
                 0.91771 
                 0.81052 
               
               
                 C a N b —C b (O)N c   
                 N b   
                 −0.82688 
                 −0.92918 
                 0 
                 0 
                   
                 0.93084 
                 0.82053 
               
               
                 C a N b —C b (O)N c   
                 C b   
                 −0.82688 
                 −1.34946 
                 −0.92918 
                 0 
                 −154.72121 
                 0.91771 
                 0.75878 
               
               
                 N b (N c )C b ═O 
                 O a   
                 −1.34946 
                 0 
                 0 
                 0 
                   
                 1.00000 
                 0.84115 
               
               
                 N b (N c )C b ═O 
                 C b   
                 −1.34946 
                 −0.82688 
                 −0.92918 
                 0 
                 −154.72121 
                 0.91771 
                 0.75878 
               
               
                 N—H (N c H) 
                 N c   
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                   
                 0.93084 
                 0.81549 
               
               
                 C—H (C c H) 
                 C c   
                 −1.13380 
                 −0.92918 
                 0 
                 0 
                 −153.67867 
                 0.91771 
                 0.80561 
               
               
                 C—H (C d H) 
                 C d   
                 −1.13380 
                 −0.46459 
                 0 
                 0 
                 −153.21408 
                 0.91771 
                 0.82840 
               
               
                 N b (O)C b —N c HC c   
                 N c   
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                   
                 0.93084 
                 0.81549 
               
               
                 N b (O)C b —N c HC c   
                 C b   
                 −0.92918 
                 −1.34946 
                 −0.82688 
                 0 
                 −154.72121 
                 0.91771 
                 0.75878 
               
               
                 C b HN c —C c HC d   
                 N c   
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                   
                 0.93084 
                 0.81549 
               
               
                 C b HN c —C c HC d   
                 C d   
                 −0.92918 
                 −1.13379 
                 0 
                 0 
                 −153.67866 
                 0.91771 
                 0.80561 
               
               
                 N c HC c ═C d HC a   
                 C c   
                 −1.13380 
                 −0.92918 
                 0.00000 
                 0 
                 −153.67867 
                 0.91771 
                 0.80561 
               
               
                 N c HC c ═C d HC a   
                 C d   
                 −1.13380 
                 −0.46459 
                 0.00000 
                 0 
                 −153.21408 
                 0.91771 
                 0.82840 
               
               
                 HC c C d —C a (N a )N b   
                 C a   
                 −0.46459 
                 −0.56690 
                 −0.92918 
                 0 
                 −153.57636 
                 0.91771 
                 0.81052 
               
               
                 HC c C d —C a (N a )N b   
                 C d   
                 −0.46459 
                 −1.13379 
                 0 
                 0 
                 −153.21407 
                 0.91771 
                 0.82840 
               
               
                   
               
             
          
           
               
                   
                   
                 E (C2sp 3 ) 
                   
                   
                   
                   
                   
               
               
                   
                 E Coulomb  (C2sp 3 )(eV) 
                 (eV) 
                 θ′ 
                 θ 1   
                 θ 2   
                 d 1   
                 d 2   
               
               
                 Bond 
                 Final 
                 Final 
                 (°) 
                 (°) 
                 (°) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 C d (N b )C a N a H—H 
                 −15.39265 
                   
                 121.74 
                 58.26 
                 67.49 
                 0.47634 
                 0.46500 
               
               
                 C d (N b )C a —N a H 2   
                 −15.39265 
                   
                 113.13 
                 66.87 
                 55.08 
                 0.92180 
                 0.34719 
               
               
                 C d (N b )C a —N a H 2   
                 −16.78642 
                 −16.59556 
                 108.27 
                 71.73 
                 50.93 
                 1.01493 
                 0.25406 
               
               
                 C d (N a )C a ═N b C b   
                 −16.58181 
                   
                 137.50 
                 42.50 
                 61.17 
                 0.69886 
                 0.60497 
               
               
                 C d (N a )C a ═N b C b   
                 −16.78642 
                 −16.59556 
                 137.11 
                 42.89 
                 60.67 
                 0.70998 
                 0.59385 
               
               
                 C a N b —C b (O)N c   
                 −16.58181 
                   
                 96.19 
                 83.81 
                 45.20 
                 1.23578 
                 0.08850 
               
               
                 C a N b —C b (O)N c   
                 −17.93127 
                 −17.74041 
                 90.51 
                 89.49 
                 41.30 
                 1.31755 
                 0.00672 
               
               
                 N b (N c )C b ═O 
                 −16.17521 
                   
                 137.27 
                 42.73 
                 66.31 
                 0.52193 
                 0.61784 
               
               
                 N b (N c )C b ═O 
                 −17.93127 
                 −17.74041 
                 133.67 
                 46.33 
                 61.70 
                 0.61582 
                 0.52395 
               
               
                 N—H (N c H) 
                 −16.68411 
                   
                 117.34 
                 62.66 
                 62.90 
                 0.56678 
                 0.37456 
               
               
                 C—H (C c H) 
                 −16.88873 
                 −16.69786 
                 83.35 
                 96.65 
                 43.94 
                 1.10452 
                 0.09331 
               
               
                 C—H (C d H) 
                 −16.42414 
                 −16.23327 
                 85.93 
                 94.07 
                 45.77 
                 1.06995 
                 0.05875 
               
               
                 N b (O)C b —N c HC c   
                 −16.68411 
                   
                 138.92 
                 41.08 
                 61.59 
                 0.68147 
                 0.61467 
               
               
                 N b (O)C b —N c HC c   
                 −17.93127 
                 −17.74041 
                 136.68 
                 43.32 
                 58.70 
                 0.74414 
                 0.55200 
               
               
                 C b HN c —C c HC d   
                 −16.68411 
                   
                 138.92 
                 41.08 
                 61.59 
                 0.68147 
                 0.61467 
               
               
                 C b HN c —C c HC d   
                 −16.88873 
                 −16.69786 
                 138.54 
                 41.46 
                 61.09 
                 0.69238 
                 0.60376 
               
               
                 N c HC c ═C d HC a   
                 −16.88873 
                 −16.69786 
                 127.61 
                 52.39 
                 58.24 
                 0.77492 
                 0.49168 
               
               
                 N c HC c ═C d HC a   
                 −16.42414 
                 −16.23327 
                 128.72 
                 51.28 
                 59.45 
                 0.74844 
                 0.51817 
               
               
                 HC c C d —C a (N a )N b   
                 −16.78642 
                 −16.59556 
                 82.65 
                 97.35 
                 38.45 
                 1.47695 
                 0.10364 
               
               
                 HC c C d —C a (N a )N b   
                 −16.42414 
                 −16.23327 
                 84.52 
                 95.48 
                 39.64 
                 1.45240 
                 0.07908 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 36 
               
               
                   
               
               
                 The energy parameters (eV) of functional groups of cytosine. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 C—N (a) 
                 NH 2   
                 N═C 
                 C═O 
                 C—N (b) 
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 n 1   
                 1 
                 2 
                 2 
                 2 
                 1 
               
               
                 n 2   
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 1 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.5 
                 0.75 
                 0.5 
                 0.5 
                 0.5 
               
               
                 C 2   
                 1 
                 0.93613 
                 0.85252 
                 1 
                 1 
               
               
                 c 1   
                 1 
                 0.75 
                 1 
                 1 
                 1 
               
               
                 c 2   
                 0.84665 
                 0.92171 
                 0.84665 
                 0.85395 
                 0.91140 
               
               
                 c 3   
                 0 
                 0 
                 0 
                 2 
                 0 
               
               
                 c 4   
                 2 
                 1 
                 4 
                 4 
                 2 
               
               
                 c 5   
                 0 
                 2 
                 0 
                 0 
                 0 
               
               
                 C 1o   
                 0.5 
                 1.5 
                 0.5 
                 0.5 
                 0.5 
               
               
                 C 2o   
                 1 
                 1 
                 0.85252 
                 1 
                 1 
               
               
                 V e  (eV) 
                 −35.50149 
                 −78.97795 
                 −103.92756 
                 −111.25473 
                 −36.88558 
               
               
                 V p  (eV) 
                 10.72181 
                 28.90735 
                 20.87050 
                 23.87467 
                 10.27417 
               
               
                 T (eV) 
                 11.02312 
                 31.73641 
                 35.85539 
                 42.82081 
                 10.51650 
               
               
                 V m  (eV) 
                 −5.51156 
                 −15.86820 
                 −17.92770 
                 −21.41040 
                 −5.25825 
               
               
                 E (AO/HO) (eV) 
                 −14.63489 
                 −14.53414 
                 0 
                 0 
                 −14.63489 
               
               
                 ΔE H   2   MO  (AO/HO) (eV) 
                 −2.26759 
                 0 
                 −1.85836 
                 −2.69893 
                 −4.35268 
               
               
                 E T  (AO/HO) (eV) 
                 −12.36730 
                 −14.53414 
                 1.85836 
                 2.69893 
                 −10.28221 
               
               
                 E (n 3  AO/HO) (eV) 
                 0 
                 −14.53414 
                 0 
                 0 
                 0 
               
               
                 E T  (H 2 MO) (eV) 
                 −31.63543 
                 −48.73654 
                 −63.27100 
                 −63.27074 
                 −31.63537 
               
               
                 E T  (atom-atom, msp 3 .AO) (eV) 
                 −1.13379 
                 0 
                 −1.85836 
                 −2.69893 
                 −1.65376 
               
               
                 E T  (Mo) (eV) 
                 −32.76916 
                 −48.73660 
                 −65.12910 
                 −65.96966 
                 −33.28912 
               
               
                 ω (10 15  rad/s) 
                 14.3055 
                 68.9812 
                 15.4704 
                 59.4034 
                 12.5874 
               
               
                 E K  (eV) 
                 9.41610 
                 45.40465 
                 10.18290 
                 39.10034 
                 8.28526 
               
               
                 Ē D  (eV) 
                 −0.19893 
                 −0.42172 
                 −0.20558 
                 −0.40804 
                 −0.18957 
               
               
                 Ē Kvib  (eV) 
                 0.15498 [57] 
                 0.40929 [22] 
                 0.20768 [61] 
                 0.21077 [12] 
                 0.17358 [33] 
               
               
                 Ē osc  (eV) 
                 −0.12144 
                 −0.21708 
                 −0.10174 
                 −0.30266 
                 −0.10278 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.11441 
                 0.14803 
               
               
                 E T  (Group) (eV) 
                 −32.89060 
                 −49.17075 
                 −65.33259 
                 −66.57498 
                 −33.39190 
               
               
                 E initial  (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.53414 
                 −14.63489 
                 −14.63489 
                 −14.63489 
               
               
                 E initial  (c 5  AO/HO) (eV) 
                 0 
                 −13.59844 
                 0 
                 0 
                 0 
               
               
                 E D  (Group) (eV) 
                 3.62082 
                 7.43973 
                 6.79303 
                 7.80660 
                 4.12212 
               
               
                   
               
               
                   
                 C═C 
                 CH 
                 C—C 
                 C—N—C 
                 NH 
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 n 1   
                 2 
                 1 
                 1 
                 2 
                 1 
               
               
                 n 2   
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.5 
                 0.75 
                 0.5 
                 0.5 
                 0.75 
               
               
                 C 2   
                 0.91771 
                 1 
                 1 
                 0.85252 
                 0.93613 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 0.75 
               
               
                 c 2   
                 0.91771 
                 0.91771 
                 0.91771 
                 0.84665 
                 0.92171 
               
               
                 c 3   
                 0 
                 1 
                 0 
                 0 
                 1 
               
               
                 c 4   
                 4 
                 1 
                 2 
                 4 
                 1 
               
               
                 c 5   
                 0 
                 1 
                 0 
                 0 
                 1 
               
               
                 C 1o   
                 0.5 
                 0.75 
                 0.5 
                 0.5 
                 0.75 
               
               
                 C 2o   
                 0.91771 
                 1 
                 1 
                 0.85252 
                 1 
               
               
                 V e  (eV) 
                 −102.08992 
                 −39.09538 
                 −33.63376 
                 −106.58684 
                 −39.48897 
               
               
                 V p  (eV) 
                 21.48386 
                 13.45505 
                 9.90728 
                 20.99432 
                 14.45367 
               
               
                 T (eV) 
                 34.67062 
                 12.74462 
                 8.91674 
                 37.21047 
                 15.86820 
               
               
                 V m  (eV) 
                 −17.33531 
                 −6.37231 
                 −4.45837 
                 −18.60523 
                 −7.93410 
               
               
                 E (AO/HO) (eV) 
                 0 
                 −14.63489 
                 −14.63489 
                 0 
                 −14.53414 
               
               
                 ΔE H     2     MO  (AO/HO) (eV) 
                 0 
                 −2.26758 
                 −2.26759 
                 −3.71673 
                 0 
               
               
                 E T  (AO/HO) (eV) 
                 0 
                 −12.36731 
                 −12.36730 
                 3.71673 
                 −14.53414 
               
               
                 E (n 3  AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 E T  (H 2 MO) (eV) 
                 −63.27075 
                 −31.63533 
                 −31.63541 
                 −63.27056 
                 −31.63534 
               
               
                 E T  (atom-atom, msp 3 .AO) (eV) 
                 −2.26759 
                 0 
                 −0.92918 
                 −3.71673 
                 0 
               
               
                 E T  (MO) (eV) 
                 −65.53833 
                 −31.63537 
                 −32.56455 
                 −66.98746 
                 −31.63537 
               
               
                 ω (10 15  rad/s) 
                 43.0680 
                 28.9084 
                 19.8904 
                 15.7474 
                 48.7771 
               
               
                 E K  (eV) 
                 28.34813 
                 19.02803 
                 13.09221 
                 10.36521 
                 32.10594 
               
               
                 Ē D  (eV) 
                 −0.34517 
                 −0.27301 
                 −0.23311 
                 −0.21333 
                 −0.35462 
               
               
                 Ē Kvib  (eV) 
                 0.17897 [6] 
                 0.39427 [59] 
                 0.14667 [66] 
                 0.11159 [12] 
                 0.40696 [24] 
               
               
                 Ē osc  (eV) 
                 −0.25568 
                 −0.07587 
                 −0.15977 
                 −0.15754 
                 −0.15115 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                 E T  (Group) (eV) 
                 −66.04969 
                 −31.71124 
                 −32.57629 
                 −67.30254 
                 −31.78651 
               
               
                 E initial  (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.53414 
               
               
                 E initial  (c 5  AO/HO) (eV) 
                 0 
                 −13.59844 
                 0 
                 0 
                 −13.59844 
               
               
                 E D  (Group) (eV) 
                 7.51014 
                 3.32988 
                 3.30651 
                 8.76298 
                 3.51208 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 37 
               
               
                   
               
               
                 The total gaseous bond energies of cytosine calculated using the functional 
               
               
                 group composition and the energies of Table 36 compared to the 
               
               
                 experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                 C—N (a) 
                 NH 2   
                 N═C 
                 C═O 
                 C—N (b) 
                 C═C 
                 CH 
               
               
                 Formula 
                 Name 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 C 4 H 5 N 3 O 
                 Cytosine 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 2 
               
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 C—C 
                 C—N—C 
                 NH 
                 Total Bond 
                 Total Bond 
               
               
                 Formula 
                 Name 
                 Group 
                 Group 
                 Group 
                 Energy (eV) 
                 Energy (eV) 
                 Relative Error 
               
               
                   
               
               
                 C 4 H 5 N 3 O 
                 Cytosine 
                 1 
                 1 
                 1 
                 59.53378 
                 60.58056 
                 0.01728 
               
               
                   
               
               
                   a Crystal. 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 38 
               
               
                   
               
               
                 The bond angle parameters of cytosine and experimental values [64]. In the calculation of θ v , the parameters from the 
               
               
                 preceding angle were used. E T  is E T  (atom-atom, msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                 Atom 1 
                   
                 Atom 2 
                   
               
               
                   
                 2c′ 
                 2c′ 
                 2c′ 
                   
                 Hybridization 
                   
                 Hybridization 
               
               
                 Atoms of 
                 Bond 1 
                 Bond 2 
                 Terminal 
                 E Coulombic   
                 Designation 
                 E Coulombic   
                 Designation 
                 c 2   
               
               
                 Angle 
                 (a 0 ) 
                 (a 0 ) 
                 Atoms (a 0 ) 
                 Atom 1 
                 (Table 8) 
                 Atom 2 
                 (Table 8) 
                 Atom 1 
               
               
                   
               
               
                 ∠HNH 
                 1.88268 
                 1.88268 
                 3.1559 
                 −14.53414 
                 N 
                 H 
                 H 
                 0.93613 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Eq. (13.248) 
               
               
                 ∠C a NH 
                 2.53797 
                 1.88268 
                 3.8123 
                 −16.78642 
                 19 
                 −14.53414 
                 N 
                 0.81052 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Eq. (15.71) 
               
               
                 ∠N b C a C d   
                 2.60766 
                 2.74663 
                 4.6476 
                 −14.53414 
                 N 
                 −16.42414 
                 13 
                 0.84665 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Eq. (15.171) 
               
               
                 ∠N b C a N a   
                 2.60766 
                 2.53797 
                 4.4272 
                 −15.39265 
                  2 
                 −16.58181 
                 16 
                 0.88392 
               
               
                 ∠C d C a N a   
               
               
                 ∠C b N b C a   
                 2.64855 
                 2.60766 
                 4.4944 
                 −17.93127 
                 38 
                 −16.78642 
                 19 
                 0.75878 
               
               
                 ∠N b C b N c   
                 2.64855 
                 2.59228 
                 4.4721 
                 −16.58181 
                 16 
                 −16.68411 
                 17 
                 0.82053 
               
               
                 ∠N c C b O 
                 2.59228 
                 2.27954 
                 4.2426 
                 −16.68411 
                 17 
                 −16.17521 
                  8 
                 0.81549 
               
               
                 ∠N b C b O 
               
               
                 ∠C b N c C c   
                 2.59228 
                 2.59228 
                 4.4944 
                 −17.93127 
                 38 
                 −16.88873 
                 20 
                 0.75878 
               
               
                 ∠N c C c C d   
                 2.59228 
                 2.53321 
                 4.4272 
                 −14.53414 
                 N 
                 −15.95955 
                  6 
                 0.84665 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Eq. (15.171) 
               
               
                 ∠H c N c C c   
                 1.88268 
                 2.59228 
                 3.8644 
                 −14.53414 
                 N 
                 −16.68411 
                 17 
                 0.84665 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Eq. (15.171) 
               
               
                 ∠H c N c C b   
               
               
                 ∠C a C d C c   
                 2.74663 
                 2.53321 
                 4.5166 
                 −16.78642 
                 19 
                 −17.81791 
                 36 
                 0.81052 
               
               
                 ∠H c C c C d   
                 2.02241 
                 2.53321 
                 3.9833 
                 −15.95955 
                  6 
                 −15.95955 
                  6 
                 0.85252 
               
               
                 ∠H c C c N c   
               
               
                 ∠H d C d C c   
                 2.02241 
                 2.53321 
                 3.9833 
                 −15.95955 
                  6 
                 −15.95955 
                  6 
                 0.85252 
               
               
                 ∠H d C d C a   
               
               
                   
               
             
          
           
               
                 Atoms of 
                 c 2   
                   
                   
                   
                   
                 E T   
                 θ v   
                 θ 1   
                 θ 2   
                 Cal. θ 
                 Exp. θ 
               
               
                 Angle 
                 Atom 2 
                 C 1   
                 C 2   
                 c 1   
                 c 2 ′ 
                 (eV) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
               
               
                   
               
               
                 ∠HNH 
                 1     
                 1 
                 1 
                 0.75 
                 1.06823 
                 0 
                   
                   
                   
                 113.89 
                 113.9 [1] 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (aniline) 
               
               
                 ∠C a NH 
                 0.77638 
                 0.75 
                 1 
                 0.75 
                 0.95787 
                 0 
                   
                   
                   
                 118.42 
                 118 [65] 
               
               
                   
                 Eq. (15.173) 
               
               
                 ∠N b C a C d   
                 0.82840 
                 1 
                 1 
                 1 
                 0.83753 
                 −1.65376 
                   
                   
                   
                 120.43 
                 121.4 
               
               
                 ∠N b C a N a   
                 0.82053 
                 1 
                 1 
                 1 
                 0.85222 
                 −1.44915 
                   
                   
                   
                 118.71 
                 117.5 
               
               
                 ∠C d C a N a   
                   
                   
                   
                   
                   
                   
                   
                 120.43 
                 118.71 
                 120.85 
                 121.1 
               
               
                 ∠C b N b C a   
                 0.81052 
                 1 
                 1 
                 1 
                 0.78465 
                 −1.85836 
                   
                   
                   
                 117.53 
                 120.3 
               
               
                 ∠N b C b N c   
                 0.81549 
                 1 
                 1 
                 1 
                 0.81801 
                 −1.65376 
                   
                   
                   
                 117.15 
                 118.9 
               
               
                 ∠N c C b O 
                 0.84115 
                 1 
                 1 
                 1 
                 0.82832 
                 −1.44915 
                   
                   
                   
                 120.98 
                 119.8 
               
               
                 ∠N b C b O 
                   
                   
                   
                   
                   
                   
                   
                 117.15 
                 120.98 
                 121.87 
                 121.3 
               
               
                 ∠C b N c C c   
                 0.80561 
                 1 
                 1 
                 1 
                 0.78219 
                 −1.85836 
                   
                   
                   
                 120.20 
                 121.7 
               
               
                 ∠N c C c C d   
                 0.85252 
                 1 
                 1 
                 1 
                 0.84958 
                 −1.44915 
                   
                   
                   
                 119.48 
                 121.4 
               
               
                 ∠H c N c C c   
                 0.81549 
                 0.75 
                 1 
                 0.75 
                 0.96320 
                 0 
                   
                   
                   
                 118.58 
               
               
                 ∠H c N c C b   
                   
                   
                   
                   
                   
                   
                   
                 120.20 
                 118.58 
                 121.23 
               
               
                 ∠C a C d C c   
                 0.76360 
                 1 
                 1 
                 1 
                 0.78706 
                 −1.85836 
                   
                   
                   
                 117.56 
                 116.4 
               
               
                 ∠H c C c C d   
                 0.85252 
                 0.75 
                 1 
                 0.75 
                 1.00000 
                 0 
                   
                   
                   
                 121.54 
               
               
                 ∠H c C c N c   
                   
                   
                   
                   
                   
                   
                   
                 119.48 
                 121.54 
                 118.99 
               
               
                 ∠H d C d C c   
                 0.85252 
                 0.75 
                 1 
                 0.75 
                 1.00000 
                 0 
                   
                   
                   
                 121.54 
               
               
                 ∠H d C d C a   
                   
                   
                   
                   
                   
                   
                   
                 117.56 
                 121.54 
                 120.90 
               
               
                   
               
             
          
         
       
     
         [0221]    Alkyl Phosphines (C n H 2n+1  ) 3 P, n=1,2,3,4,5 . . . ∞) 
         [0222]    The alkyl phosphines, (C n H 2n+1 ) 3 P, comprise a P—C functional group. The alkyl portion of the alkyl phosphine may comprise at least two terminal methyl groups (CH 3 ) at each end of each chain, and may comprise methylene (CH 2 ), and methylyne (CH) functional groups as well as C bound by carbon-carbon single bonds. The methyl and methylene functional groups are equivalent to those of straight-chain alkanes. Six types of C—C bonds can be identified. The n-alkane C—C bond is the same as that of straight-chain alkanes. In addition, the C—C bonds within isopropyl ((CH 3 ) 2 CH) and t-butyl ((CH 3 ) 3 C) groups and the isopropyl to isopropyl, isopropyl to t-butyl, and t-butyl to t-butyl C—C bonds comprise functional groups. The branched-chain-alkane groups in alkyl phosphines are equivalent to those in branched-chain alkanes. The P—C group may further join the P3sp 3  HO to an aryl HO. 
         [0223]    As in the case of carbon, the bonding in the phosphorous atom involves sp 3  hybridized orbitals formed, in this case, from the 3p and 3s electrons of the outer shells with five P3sp 3  HOs rather than four C2sp 3  HOs. The P—C bond forms between P3sp 3  and C2sp 3  HOs to yield phosphines. The semimajor axis a of the P—C functional group is solved using Eq. (15.51). Using the semimajor axis and the relationships between the prolate spheroidal axes, the geometric and energy parameters of the MO are calculated using Eqs. (15.1-15.117) in the same manner as the organic functional groups given in Organic Molecular Functional Groups and Molecules section. 
         [0224]    The energy of phosphorous is less than the Coulombic energy between the electron and proton of H given by Eq. (1.231). A minimum energy is achieved while matching the potential, kinetic, and orbital energy relationships given in the Hydroxyl Radical (OH) section with hybridization of the phosphorous atom such that in Eqs. (15.51) and (15.61), the sum of the energies of the H 2 -type ellipsoidal MOs is matched to that of the P3sp 3  shell as in the case of the corresponding carbon and silicon molecules. 
         [0225]    The P electron configuration is [Ne]3s 2 3p 3  corresponding to the ground state  4 S 3/2 , and the 3sp 3  hybridized orbital arrangement after Eq. (13.422) is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       ↑ 
                       ↓ 
                     
                     
                       0 
                       , 
                       0 
                     
                   
                    
                   
                     
                       
                         ↑ 
                         
                           1 
                           , 
                           
                             - 
                             1 
                           
                         
                       
                        
                       
                         ↑ 
                         
                           1 
                           , 
                           0 
                         
                       
                     
                     
                       3 
                        
                       
                         sp 
                         3 
                       
                        
                       
                           
                       
                        
                       state 
                     
                   
                    
                   
                     ↑ 
                     
                       1 
                       , 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   15.174 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where the quantum numbers (l, m l ) are below each electron. The total energy of the state is given by the sum over the five electrons. The sum E T (P,3sp 3 ) of experimental energies [38] of P, P + , P 2+ , P 3+ , and P 4+  is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             T 
                           
                            
                           
                             ( 
                             
                               P 
                               , 
                               
                                 3 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             65.0251 
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             51.4439 
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             30.2027 
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             19.7695 
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           10.48669 
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           176.92789 
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15.175 
                   ) 
                 
               
             
           
         
       
     
         [0226]    By considering that the central field decreases by an integer for each successive electron of the shell, the radius r 3sp     3    of the P3sp 3  shell may be calculated from the Coulombic energy using Eq. (15.13): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           
                             3 
                              
                             
                               sp 
                               3 
                             
                           
                         
                         = 
                           
                          
                         
                           
                             ∑ 
                             
                               n 
                               = 
                               10 
                             
                             14 
                           
                            
                           
                             
                               
                                 ( 
                                 
                                   Z 
                                   - 
                                   n 
                                 
                                 ) 
                               
                                
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               
                                 
                                   πɛ 
                                   0 
                                 
                                  
                                 
                                   ( 
                                   
                                     e 
                                      
                                     
                                         
                                     
                                      
                                     176.92789 
                                      
                                     
                                         
                                     
                                      
                                     eV 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             15 
                              
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             π 
                              
                             
                                 
                             
                              
                             
                               
                                 ɛ 
                                 0 
                               
                                
                               
                                 ( 
                                 
                                   e 
                                    
                                   
                                       
                                   
                                    
                                   176.92789 
                                    
                                   
                                       
                                   
                                    
                                   eV 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           1.15350 
                            
                           
                             a 
                             0 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15.176 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where Z=15 for phosphorous. Using Eq. (15.14), the Coulombic energy E Coulomb (P,3sp 3 ) of
 
the outer electron of the P3sp 3  shell is
 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             Coulomb 
                           
                            
                           
                             ( 
                             
                               P 
                               , 
                               
                                 3 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             
                               r 
                               
                                 3 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             1.15350 
                              
                             
                               a 
                               0 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             11.79519 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15.177 
                   ) 
                 
               
             
           
         
       
     
         [0227]    During hybridization, the spin-paired 3s electrons are promoted to P3sp 3  shell as paired electrons at the radius r 3sp     3    of the P3sp 3  shell. The energy for the promotion is the difference in the magnetic energy given by Eq. (15.15) at the initial radius of the 3s electrons and the final radius of the P3sp 3  electrons. From Eq. (10.255) with Z=15, the radius R 12  of P3s shell is 
         [0000]      r 12 =1.09443a 0    (15.178) 
         [0000]    Using Eqs. (15.15) and (15.178), the unpairing energy is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           E 
                            
                           
                             ( 
                             magnetic 
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               2 
                                
                               
                                 πμ 
                                 0 
                               
                                
                               
                                  
                                 2 
                               
                                
                               
                                 ℏ 
                                 2 
                               
                             
                             
                               m 
                               e 
                               2 
                             
                           
                            
                           
                             ( 
                             
                               
                                 1 
                                 
                                   
                                     ( 
                                     
                                       r 
                                       12 
                                     
                                     ) 
                                   
                                   3 
                                 
                               
                               - 
                               
                                 1 
                                 
                                   
                                     ( 
                                     
                                       r 
                                       
                                         3 
                                          
                                         
                                           sp 
                                           3 
                                         
                                       
                                     
                                     ) 
                                   
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           8 
                            
                           
                             πμ 
                             o 
                           
                            
                           
                             
                               μ 
                               B 
                               2 
                             
                              
                             
                               ( 
                               
                                 
                                   1 
                                   
                                     
                                       ( 
                                       
                                         1.09443 
                                          
                                         
                                           a 
                                           0 
                                         
                                       
                                       ) 
                                     
                                     3 
                                   
                                 
                                 - 
                                 
                                   1 
                                   
                                     
                                       ( 
                                       
                                         1.15350 
                                          
                                         
                                           a 
                                           0 
                                         
                                       
                                       ) 
                                     
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           0.01273 
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15.179 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Using Eqs. (15.177) and (15.179), the energy E(P,3sp 3 ) of the outer electron of the P3sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           E 
                            
                           
                             ( 
                             
                               P 
                               , 
                               
                                 3 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               - 
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 r 
                                 
                                   3 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                             
                           
                           + 
                           
                             
                               
                                 2 
                                  
                                 
                                   πμ 
                                   0 
                                 
                                  
                                 
                                    
                                   2 
                                 
                                  
                                 
                                   ℏ 
                                   2 
                                 
                               
                               
                                 m 
                                 e 
                                 2 
                               
                             
                              
                             
                               ( 
                               
                                 
                                   1 
                                   
                                     
                                       ( 
                                       
                                         r 
                                         12 
                                       
                                       ) 
                                     
                                     3 
                                   
                                 
                                 - 
                                 
                                   1 
                                   
                                     
                                       ( 
                                       
                                         r 
                                         
                                           3 
                                            
                                           
                                             sp 
                                             3 
                                           
                                         
                                       
                                       ) 
                                     
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               11.79519 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             0.01273 
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             11.78246 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15.180 
                   ) 
                 
               
             
           
         
       
     
         [0228]    For the P—C functional group, hybridization of the 2s and 2p AOs of each C and the 3s and 3p AOs of each P to form single 2sp 3  and 3sp 3  shells, respectively, forms an energy minimum, and the sharing of electrons between the C2sp 3  and P3sp 3  HOs to form a MO permits each participating orbital to decrease in radius and energy. In branched-chain alkyl phosphines, the energy of phosphorous is less than the Coulombic energy between the electron and proton of H given by Eq. (1.231). Thus, c 2  in Eq. (15.61) is one, and the energy matching condition is determined by the C 2  parameter. Then, the C2sp 3  HO has an energy of E(C,2sp 3 )=−14.63489 eV (Eq. (15.25)), and the P3sp 3  HO has an energy of E(P,3sp 3 )=−11.78246 eV (Eq. (15.180)). To meet the equipotential condition of the union of the P—C H 2 -type-ellipsoidal-MO with these orbitals, the hybridization factor C 2  of Eq. (15.61) for the P—C-bond MO given by Eqs. (15.77), (15.79), and (13.430) is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             C 
                             2 
                           
                            
                           
                             ( 
                             
                               C 
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                                
                               
                                   
                               
                                
                               to 
                                
                               
                                   
                               
                                
                               P 
                                
                               
                                   
                               
                                
                               3 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               E 
                                
                               
                                 ( 
                                 
                                   P 
                                   , 
                                   
                                     3 
                                      
                                     
                                       sp 
                                       3 
                                     
                                   
                                 
                                 ) 
                               
                             
                             
                               E 
                                
                               
                                 ( 
                                 
                                   C 
                                   , 
                                   
                                     2 
                                      
                                     
                                       sp 
                                       3 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                            
                           
                             
                               c 
                               2 
                             
                              
                             
                               ( 
                               
                                 C 
                                  
                                 
                                     
                                 
                                  
                                 2 
                                  
                                 
                                   sp 
                                   3 
                                 
                                  
                                 HO 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               
                                 - 
                                 11.78246 
                               
                                
                               
                                   
                               
                                
                               eV 
                             
                             
                               
                                 - 
                                 14.63489 
                               
                                
                               
                                   
                               
                                
                               eV 
                             
                           
                            
                           
                             ( 
                             0.91771 
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         0.73885 
                       
                     
                   
                 
               
               
                 
                   ( 
                   15.181 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The energy of the P—C-bond MO is the sum of the component energies of the H 2 -type ellipsoidal MO given in Eq. (15.51) with E(AO/HO)=E(P,3sp 3 ) given by Eq. (15.180), and E T (atom-atom,msp 3 .AO) is one half −0.72457 eV given by Eq. (14.151) in order to match the energies of the carbon and phosphorous HOs. 
         [0229]    The symbols of the functional groups of branched-chain alkyl phosphines are given in Table 39. The geometrical (Eqs. (15.1-15.5) and (15.51)), intercept (Eqs. (15.80-15.87)), and energy (Eqs. (15.6-15.11) and (15.17-15.65)) parameters of alkyl phosphines are given in Tables 40, 41, and 42, respectively. The total energy of each alkyl phosphine given in Table 43 was calculated as the sum over the integer multiple of each E D (Group) of Table 42 corresponding to functional-group composition of the molecule. The bond angle parameters of alkyl phosphines determined using Eqs. (15.88-15.117) are given in Table 44. The color scale, charge-density of exemplary alkyl phosphine, triphenylphosphine, comprising atoms with the outer shell bridged by one or more H 2 -type ellipsoidal MOs or joined with one or more hydrogen MOs is shown in  FIG. 14 . 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 39 
               
             
             
               
                   
               
               
                 The symbols of functional groups of alkyl phosphines. 
               
             
          
           
               
                   
                 Functional Group 
                 Group Symbol 
               
               
                   
                   
               
               
                   
                 P—C 
                 P—C 
               
               
                   
                 CH 3  group 
                 C—H (CH 3 ) 
               
               
                   
                 CH 2  group 
                 C—H (CH 2 ) 
               
               
                   
                 CH 
                 C—H (i) 
               
               
                   
                 CC bond (n-C) 
                 C—C (a) 
               
               
                   
                 CC bond (iso-C) 
                 C—C (b) 
               
               
                   
                 CC bond (tert-C) 
                 C—C (c) 
               
               
                   
                 CC (iso to iso-C) 
                 C—C (d) 
               
               
                   
                 CC (t to t-C) 
                 C—C (e) 
               
               
                   
                 CC (t to iso-C) 
                 C—C (f) 
               
               
                   
                 CC (aromatic bond) 
                 C 3e ═C 
               
               
                   
                 CH (aromatic) 
                 CH (ii) 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 40 
               
               
                   
               
               
                 The geometrical bond parameters of alkyl phosphines and experimental values [1]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 P—C 
                 C—H(CH 3 ) 
                 C—H(CH 2 ) 
                 C—H (i) 
                 C—C (a) 
                 C—C (b) 
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 2.29513 
                 1.64920 
                 1.67122 
                 1.67465 
                 2.12499 
                 2.12499 
               
               
                 c′ (a 0 ) 
                 1.76249 
                 1.04856 
                 1.05553 
                 1.05661 
                 1.45744 
                 1.45744 
               
               
                 Bond Length 2c′ (Å) 
                 1.86534 
                 1.10974 
                 1.11713 
                 1.11827 
                 1.54280 
                 1.54280 
               
               
                 Exp. Bond Length 
                 1.847 
                 1.107 
                 1.107 
                 1.122 
                 1.532 
                 1.532 
               
               
                 (Å) 
                 ((CH 3 ) 2 PCH 3 ) 
                 (C—H 
                 (C—H 
                 (isobutane) 
                 (propane) 
                 (propane) 
               
               
                   
                 1.858 
                 propane) 
                 propane) 
                   
                 1.531 
                 1.531 
               
               
                   
                 (H 2 PCH 3 ) 
                 1.117 
                 1.117 
                   
                 (butane) 
                 (butane) 
               
               
                   
                   
                 (C—H 
                 (C—H 
               
               
                   
                   
                 butane) 
                 butane) 
               
               
                 b, c (a 0 ) 
                 1.47012 
                 1.27295 
                 1.29569 
                 1.29924 
                 1.54616 
                 1.54616 
               
               
                 e 
                 0.76793 
                 0.63580 
                 0.63159 
                 0.63095 
                 0.68600 
                 0.68600 
               
               
                 a (a 0 ) 
                 2.29513 
                 1.64920 
                 1.67122 
                 1.67465 
                 2.12499 
                 2.12499 
               
               
                 c′ (a 0 ) 
                 1.76249 
                 1.04856 
                 1.05553 
                 1.05661 
                 1.45744 
                 1.45744 
               
               
                 Bond Length 2c′ (Å) 
                 1.86534 
                 1.10974 
                 1.11713 
                 1.11827 
                 1.54280 
                 1.54280 
               
               
                 Exp. Bond Length 
                 1.847 
                 1.107 
                 1.107 
                 1.122 
                 1.532 
                 1.532 
               
               
                 (Å) 
                 ((CH 3 ) 2 PCH 3 ) 
                 (C—H 
                 (C—H 
                 (isobutane) 
                 (propane) 
                 (propane) 
               
               
                   
                 1.858 
                 propane) 
                 propane) 
                   
                 1.531 
                 1.531 
               
               
                   
                 (H 2 PCH 3 ) 
                 1.117 
                 1.117 
                   
                 (butane) 
                 (butane) 
               
               
                   
                   
                 (C—H 
                 (C—H 
               
               
                   
                   
                 butane) 
                 butane) 
               
               
                 b, c (a 0 ) 
                 1.47012 
                 1.27295 
                 1.29569 
                 1.29924 
                 1.54616 
                 1.54616 
               
               
                 e 
                 0.76793 
                 0.63580 
                 0.63159 
                 0.63095 
                 0.68600 
                 0.68600 
               
               
                   
               
             
          
           
               
                   
                 C—C (c) 
                 C—C (d) 
                 C—C (e) 
                 C—C (f) 
                 C 3e ═C 
                 CH (ii) 
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 2.10725 
                 2.12499 
                 2.10725 
                 2.10725 
                 1.47348 
                 1.60061 
               
               
                 c′ (a 0 ) 
                 1.45164 
                 1.45744 
                 1.45164 
                 1.45164 
                 1.31468 
                 1.03299 
               
               
                 Bond Length 2c′ (Å) 
                 1.53635 
                 1.54280 
                 1.53635 
                 1.53635 
                 1.39140 
                 1.09327 
               
               
                 Exp. Bond Length 
                 1.532 
                 1.532 
                 1.532 
                 1.532 
                 1.399 
                 1.101 
               
               
                 (Å) 
                 (propane) 
                 (propane) 
                 (propane) 
                 (propane) 
                 (benzene) 
                 (benzene) 
               
               
                   
                 1.531 
                 1.531 
                 1.531 
                 1.531 
               
               
                   
                 (butane) 
                 (butane) 
                 (butane) 
                 (butane) 
               
               
                 b, c (a 0 ) 
                 1.52750 
                 1.54616 
                 1.52750 
                 1.52750 
                 0.66540 
                 1.22265 
               
               
                 e 
                 0.68888 
                 0.68600 
                 0.68888 
                 0.68888 
                 0.89223 
                 0.64537 
               
               
                 a (a 0 ) 
                 2.10725 
                 2.12499 
                 2.10725 
                 2.10725 
                 1.47348 
                 1.60061 
               
               
                 c′ (a 0 ) 
                 1.45164 
                 1.45744 
                 1.45164 
                 1.45164 
                 1.31468 
                 1.03299 
               
               
                 Bond Length 2c′ (Å) 
                 1.53635 
                 1.54280 
                 1.53635 
                 1.53635 
                 1.39140 
                 1.09327 
               
               
                 Exp. Bond Length 
                 1.532 
                 1.532 
                 1.532 
                 1.532 
                 1.399 
                 1.101 
               
               
                 (Å) 
                 (propane) 
                 (propane) 
                 (propane) 
                 (propane) 
                 (benzene) 
                 (benzene) 
               
               
                   
                 1.531 
                 1.531 
                 1.531 
                 1.531 
               
               
                   
                 (butane) 
                 (butane) 
                 (butane) 
                 (butane) 
               
               
                 b, c (a 0 ) 
                 1.52750 
                 1.54616 
                 1.52750 
                 1.52750 
                 0.66540 
                 1.22265 
               
               
                 e 
                 0.68888 
                 0.68600 
                 0.68888 
                 0.68888 
                 0.89223 
                 0.64537 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 41 
               
               
                   
               
               
                 The MO to HO intercept geometrical bond parameters of alkyl phosphines. R 1  is an alkyl group and R, R′, R″ are H or 
               
               
                 alkyl groups. E T  is E T  (atom-atom, msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 Final Total 
                   
                   
               
               
                   
                   
                 E T   
                 E T   
                 E T   
                 E T   
                 Energy 
               
               
                   
                   
                 (eV) 
                 (eV) 
                 (eV) 
                 (eV) 
                 C2sp 3   
                 r initial   
                 r final   
               
               
                 Bond 
                 Atom 
                 Bond 1 
                 Bond 2 
                 Bond 3 
                 Bond 4 
                 (eV) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 C—H (CH 3 ) 
                 C 
                 −0.36229 
                 0 
                 0 
                 0 
                 −151.97798 
                 0.91771 
                 0.89582 
               
               
                 (CH 3 ) 2 P—CH 3   
                 C 
                 −0.18114 
                 0 
                 0 
                 0 
                   
                 0.91771 
                 0.90664 
               
               
                 (CH 3 ) 2 P—CH 3   
                 P 
                 −0.18114 
                 −0.18114 
                 −0.18114 
                 0 
                   
                 1.15350 
                 0.88527 
               
               
                 C—H (CH 3 ) 
                 C 
                 −0.92918 
                 0 
                 0 
                 0 
                 −152.54487 
                 0.91771 
                 0.86359 
               
               
                 C—H (CH 2 ) 
                 C 
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                 −153.47406 
                 0.91771 
                 0.81549 
               
               
                 C—H (CH) 
                 C 
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 C a   
                 −0.92918 
                 0 
                 0 
                 0 
                 −152.54487 
                 0.91771 
                 0.86359 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                 −153.47406 
                 0.91771 
                 0.81549 
               
               
                 R—H 2 C a C b (H 2 C c —R′)HCH 2 —(C—C (b)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 R—H 2 C a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (c)) 
                 C b   
                 −0.92918 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.71860 
                 0.91771 
                 0.75889 
               
               
                 isoC a C b (H 2 C c —R′)HCH 2 —(C—C (d)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 tertC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (e)) 
                 C b   
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.51399 
                 0.91771 
                 0.76765 
               
               
                 tertC a C b (H 2 C c —R′)HCH 2 —(C—C (f)) 
                 C b   
                 −0.72457 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.19863 
                 0.91771 
                 0.78155 
               
               
                 isoC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (f)) 
                 C b   
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.51399 
                 0.91771 
                 0.76765 
               
               
                   
               
             
          
           
               
                   
                   
                 E Coulomb   
                 E (C2sp 3 ) 
                   
                   
                   
                   
                   
               
               
                   
                   
                 (eV) 
                 (eV) 
                 θ′ 
                 θ 1   
                 θ 2   
                 d 1   
                 d 2   
               
               
                   
                 Bond 
                 Final 
                 Final 
                 (°) 
                 (°) 
                 (°) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
                   
               
               
                   
                 C—H (CH 3 ) 
                 −15.18804 
                 −14.99717 
                 81.24 
                 98.76 
                 44.07 
                 1.18494 
                 0.13638 
               
               
                   
                 (CH 3 ) 2 P—CH 3   
                 −15.00689 
                 −14.81603 
                 87.12 
                 92.88 
                 38.02 
                 1.80811 
                 0.04562 
               
               
                   
                 (CH 3 ) 2 P—CH 3   
                 −15.36918 
                   
                 85.24 
                 94.76 
                 36.88 
                 1.83594 
                 0.07345 
               
               
                   
                 C—H (CH 3 ) 
                 −15.75493 
                 −15.56407 
                 77.49 
                 102.51 
                 41.48 
                 1.23564 
                 0.18708 
               
               
                   
                 C—H (CH 2 ) 
                 −16.68412 
                 −16.49325 
                 68.47 
                 111.53 
                 35.84 
                 1.35486 
                 0.29933 
               
               
                   
                 C—H (CH) 
                 −17.61330 
                 −17.42244 
                 61.10 
                 118.90 
                 31.37 
                 1.42988 
                 0.37326 
               
               
                   
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 −15.75493 
                 −15.56407 
                 63.82 
                 116.18 
                 30.08 
                 1.83879 
                 0.38106 
               
               
                   
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 −16.68412 
                 −16.49325 
                 56.41 
                 123.59 
                 26.06 
                 1.90890 
                 0.45117 
               
               
                   
                 R—H 2 C a C b (H 2 C c —R′)HCH 2 —(C—C (b)) 
                 −17.61330 
                 −17.42244 
                 48.30 
                 131.70 
                 21.90 
                 1.97162 
                 0.51388 
               
               
                   
                 R—H 2 C a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (c)) 
                 −17.92866 
                 −17.73779 
                 48.21 
                 131.79 
                 21.74 
                 1.95734 
                 0.50570 
               
               
                   
                 isoC a C b (H 2 C c —R′)HCH 2 —(C—C (d)) 
                 −17.61330 
                 −17.42244 
                 48.30 
                 131.70 
                 21.90 
                 1.97162 
                 0.51388 
               
               
                   
                 tertC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (e)) 
                 −17.92866 
                 −17.73779 
                 50.04 
                 129.96 
                 22.66 
                 1.94462 
                 0.49298 
               
               
                   
                 tertC a C b (H 2 C c —R′)HCH 2 —(C—C (f)) 
                 −17.40869 
                 −17.21783 
                 52.78 
                 127.22 
                 24.04 
                 1.92443 
                 0.47279 
               
               
                   
                 isoC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (f)) 
                 −17.92866 
                 −17.73779 
                 50.04 
                 129.96 
                 22.66 
                 1.94462 
                 0.49298 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 42 
               
               
                   
               
               
                 The energy parameters (eV) of functional groups of alkyl phosphines. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                 P—C 
                 CH 3   
                 CH 2   
                 CH (i) 
                 C—C (a) 
               
               
                   
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
                   
               
               
                   
                 f 1   
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                   
                 n 1   
                 1 
                 3 
                 2 
                 1 
                 1 
               
               
                   
                 n 2   
                 0 
                 2 
                 1 
                 0 
                 0 
               
               
                   
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                   
                 C 1   
                 0.5 
                 0.75 
                 0.75 
                 0.75 
                 0.5 
               
               
                   
                 C 2   
                 0.73885 
                 1 
                 1 
                 1 
                 1 
               
               
                   
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                   
                 c 2   
                 1 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
               
               
                   
                 c 3   
                 0 
                 0 
                 1 
                 1 
                 0 
               
               
                   
                 c 4   
                 2 
                 1 
                 1 
                 1 
                 2 
               
               
                   
                 c 5   
                 0 
                 3 
                 2 
                 1 
                 0 
               
               
                   
                 C 1o   
                 0.5 
                 0.75 
                 0.75 
                 0.75 
                 0.5 
               
               
                   
                 C 2o   
                 0.73885 
                 1 
                 1 
                 1 
                 1 
               
               
                   
                 V e  (eV) 
                 −31.34959 
                 −107.32728 
                 −70.41425 
                 −35.12015 
                 −28.79214 
               
               
                   
                 V p  (eV) 
                 7.71965 
                 38.92728 
                 25.78002 
                 12.87680 
                 9.33352 
               
               
                   
                 T (eV) 
                 6.82959 
                 32.53914 
                 21.06675 
                 10.48582 
                 6.77464 
               
               
                   
                 V m  (eV) 
                 −3.41479 
                 −16.26957 
                 −10.53337 
                 −5.24291 
                 −3.38732 
               
               
                   
                 E (AO/HO) (eV) 
                 −11.78246 
                 −15.56407 
                 −15.56407 
                 −14.63489 
                 −15.56407 
               
               
                   
                 ΔE H     2     MO  (AO/HO) (eV) 
                 −0.36229 
                 0 
                 0 
                 0 
                 0 
               
               
                   
                 E T  (AO/HO) (eV) 
                 −11.42017 
                 −15.56407 
                 −15.56407 
                 −14.63489 
                 −15.56407 
               
               
                   
                 E T  (H 2 MO) (eV) 
                 −31.63532 
                 −67.69451 
                 −49.66493 
                 −31.63533 
                 −31.63537 
               
               
                   
                 E T  (atom-atom, msp 3 .AO) (eV) 
                 −0.36229 
                 0 
                 0 
                 0 
                 −1.85836 
               
               
                   
                 E T  (Mo) (eV) 
                 −31.99766 
                 −67.69450 
                 −49.66493 
                 −31.63537 
                 −33.49373 
               
               
                   
                 ω (10 15  rad/s) 
                 7.22663 
                 24.9286 
                 24.2751 
                 24.1759 
                 9.43699 
               
               
                   
                 E K  (eV) 
                 4.75669 
                 16.40846 
                 15.97831 
                 15.91299 
                 6.21159 
               
               
                   
                 Ē D  (eV) 
                 −0.13806 
                 −0.25352 
                 −0.25017 
                 −0.24966 
                 −0.16515 
               
               
                   
                 Ē Kvib  (eV) 
                 0.17606 [67] 
                 0.35532 
                 0.35532 
                 0.35532 
                 0.12312 [2] 
               
               
                   
                   
                   
                 (Eq. (13.458)) 
                 (Eq. (13.458)) 
                 (Eq. (13.458)) 
               
               
                   
                 Ē osc  (eV) 
                 −0.05003 
                 −0.22757 
                 −0.14502 
                 −0.07200 
                 −0.10359 
               
               
                   
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                   
                 E T  (Group) (eV) 
                 −32.04769 
                 −67.92207 
                 −49.80996 
                 −31.70737 
                 −33.59732 
               
               
                   
                 E initial  (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
               
               
                   
                 E initial  (c 5  AO/HO) (eV) 
                 0 
                 −13.59844 
                 −13.59844 
                 −13.59844 
                 0 
               
               
                   
                 E D  (Group) (eV) 
                 2.77791 
                 12.49186 
                 7.83016 
                 3.32601 
                 4.32754 
               
               
                   
                   
               
             
          
           
               
                   
                 C—C (b) 
                 C—C (c) 
                 C—C (d) 
                 C—C (e) 
                 C—C (f) 
                 C 3e ═C 
                 CH (ii) 
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 f 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 0.75 
                 1 
               
               
                 n 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 2 
                 1 
               
               
                 n 2   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.75 
               
               
                 C 2   
                 1 
                 1 
                 1 
                 1 
                 1 
                 0.85252 
                 1 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 2   
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.85252 
                 0.91771 
               
               
                 c 3   
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
               
               
                 c 4   
                 2 
                 2 
                 2 
                 2 
                 2 
                 3 
                 1 
               
               
                 c 5   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
               
               
                 C 1o   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.75 
               
               
                 C 2o   
                 1 
                 1 
                 1 
                 1 
                 1 
                 0.85252 
                 1 
               
               
                 V e  (eV) 
                 −28.79214 
                 −29.10112 
                 −28.79214 
                 −29.10112 
                 −29.10112 
                 −101.12679 
                 −37.10024 
               
               
                 V p  (eV) 
                 9.33352 
                 9.37273 
                 9.33352 
                 9.37273 
                 9.37273 
                 20.69825 
                 13.17125 
               
               
                 T (eV) 
                 6.77464 
                 6.90500 
                 6.77464 
                 6.90500 
                 6.90500 
                 34.31559 
                 11.58941 
               
               
                 V m  (eV) 
                 −3.38732 
                 −3.45250 
                 −3.38732 
                 −3.45250 
                 −3.45250 
                 −17.15779 
                 −5.79470 
               
               
                 E (AO/HO) (eV) 
                 −15.56407 
                 −15.35946 
                 −15.56407 
                 −15.35946 
                 −15.35946 
                 0 
                 −14.63489 
               
               
                 ΔE H     2     MO  (AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 −1.13379 
               
               
                 E T  (AO/HO) (eV) 
                 −15.56407 
                 −15.35946 
                 −15.56407 
                 −15.35946 
                 −15.35946 
                 0 
                 −13.50110 
               
               
                 E T  (H 2 MO) (eV) 
                 −31.63537 
                 −31.63535 
                 −31.63537 
                 −31.63535 
                 −31.63535 
                 −63.27075 
                 −31.63539 
               
               
                 E T  (atom-atom, msp 3 .AO) (eV) 
                 −1.85836 
                 −1.44915 
                 −1.85836 
                 −1.44915 
                 −1.44915 
                 −2.26759 
                 −0.56690 
               
               
                 E T  (MO) (eV) 
                 −33.49373 
                 −33.08452 
                 −33.49373 
                 −33.08452 
                 −33.08452 
                 −65.53833 
                 −32.20226 
               
               
                 ω (10 15  rad/s) 
                 9.43699 
                 15.4846 
                 9.43699 
                 9.55643 
                 9.55643 
                 49.7272 
                 26.4826 
               
               
                 E K  (eV) 
                 6.21159 
                 10.19220 
                 6.21159 
                 6.29021 
                 6.29021 
                 32.73133 
                 17.43132 
               
               
                 Ē D  (eV) 
                 −0.16515 
                 −0.20896 
                 −0.16515 
                 −0.16416 
                 −0.16416 
                 −0.35806 
                 −0.26130 
               
               
                 Ē Kvib  (eV) 
                 0.17978 [4] 
                 0.09944 [5] 
                 0.12312 [2] 
                 0.12312 [2] 
                 0.12312 [2] 
                 0.19649 [49] 
                 0.35532 
               
               
                   
                   
                   
                   
                   
                   
                   
                 Eq. (13.458) 
               
               
                 Ē osc  (eV) 
                 −0.07526 
                 −0.15924 
                 −0.10359 
                 −0.10260 
                 −0.10260 
                 −0.25982 
                 −0.08364 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                 E T  (Group) (eV) 
                 −33.49373 
                 −33.24376 
                 −33.59732 
                 −33.18712 
                 −33.18712 
                 −49.54347 
                 −32.28590 
               
               
                 E initial  (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
               
               
                 E initial  (c 5  AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 −13.59844 
               
               
                 E D  (Group) (eV) 
                 4.29921 
                 3.97398 
                 4.17951 
                 3.62128 
                 3.91734 
                 5.63881 
                 3.90454 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 43 
               
               
                   
               
               
                 The total bond energies of alkyl phosphines calculated using the functional group 
               
               
                 composition and the energies of Table 42 compared to the experimental values [68]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Formula 
                 Name 
                 P—C 
                 CH 3   
                 CH 2   
                 CH (i) 
                 C—C (a) 
                 C—C (b) 
                 C—C (c) 
                 C—C (d) 
               
               
                   
               
               
                 C 3 H 9 P 
                 Trimethylphosphine 
                 3 
                 3 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 6 H 15 P 
                 Triethylphosphine 
                 3 
                 3 
                 3 
                 0 
                 3 
                 0 
                 0 
                 0 
               
               
                 C 18 H 15 P 
                 Triphenylphosphine 
                 3 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                   
                   
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 C—C (e) 
                 C—C (f) 
                 C3e═C 
                 CH (ii) 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 C 3 H 9 P 
                 Trimethylphosphine 
                 0 
                 0 
                 0 
                 0 
                 45.80930 
                 46.87333 
                 0.02270 
               
               
                 C 6 H 15 P 
                 Triethylphosphine 
                 0 
                 0 
                 0 
                 0 
                 82.28240 
                 82.24869 
                 −0.00041 
               
               
                 C 18 H 15 P 
                 Triphenylphosphine 
                 0 
                 0 
                 18 
                 15 
                 168.40033 
                 167.46591 
                 −0.00558 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 44 
               
               
                   
               
               
                 The bond angle parameters of alkyl phosphines and experimental values [1]. 
               
               
                 In the calculation of θ v , the parameters from the preceding angle 
               
               
                 were used. E T  is E T  (atom-atom, msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                 Atom 1 
                   
                 Atom 2 
                   
               
               
                   
                   
                   
                 2c′ 
                 E Coulombic   
                 Hybridization 
                   
                 Hybridization 
               
               
                 Atoms of 
                 2c′ 
                 2c′ 
                 Terminal 
                 or E 
                 Designation 
                 E Coulombic   
                 Designation 
                 c 2   
               
               
                 Angle 
                 Bond 1 (a 0 ) 
                 Bond 2 (a 0 ) 
                 Atoms (a 0 ) 
                 Atom 1 
                 (Table 7) 
                 Atom 2 
                 (Table 7) 
                 Atom 1 
               
               
                   
               
               
                 Methyl 
                 2.09711 
                 2.09711 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
               
               
                 ∠HC a H 
               
               
                 ∠H a C a P 
               
               
                 ∠C a PC b   
                 3.52498 
                 3.52498 
                 5.3479 
                 −15.93607 
                 9 
                 −15.93607 
                 9 
                 0.85377 
               
               
                 Methylene 
                 2.11106 
                 2.11106 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
               
               
                 ∠C a C b H 
               
               
                 Methyl 
                 2.09711 
                 2.09711 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
               
               
                 ∠C a C b H 
               
               
                 ∠C b C a C c   
                 2.91547 
                 2.91547 
                 4.7958 
                 −16.68412 
                 26 
                 −16.68412 
                 26  
                 0.81549 
               
               
                 iso C a   
                   
                   
                   
                 C b   
                   
                 C c   
               
               
                 ∠C b C a H 
                 2.91547 
                 2.11323 
                 4.1633 
                 −15.55033 
                 5 
                 −14.82575 
                 1 
                 0.87495 
               
               
                 iso C a   
                   
                   
                   
                 C a   
                   
                 C b   
               
               
                 ∠C a C b H 
                 2.91547 
                 2.09711 
                 4.1633 
                 −15.55033 
                 5 
                 −14.82575 
                 1 
                 0.87495 
               
               
                 iso C a   
                   
                   
                   
                 C b   
                   
                 C a   
               
               
                 ∠C b C a C b   
                 2.90327 
                 2.90327 
                 4.7958 
                 −16.68412 
                 26 
                 −16.68412 
                 26  
                 0.81549 
               
               
                 tert C a   
                   
                   
                   
                 C b   
                   
                 C b   
               
               
                 ∠C b C a C d   
               
               
                   
               
             
          
           
               
                 Atoms of 
                 c 2   
                   
                   
                   
                   
                 E T   
                 θ v   
                 θ 1   
                 θ 2   
                 Cal. θ 
                 Exp. θ 
               
               
                 Angle 
                 Atom 2 
                 C 1   
                 C 2   
                 c 1   
                 c 2 ′ 
                 (eV) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
               
               
                   
               
               
                 Methyl 
                 1 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 109.50 
               
               
                 ∠HC a H 
               
               
                 ∠H a C a P 
                   
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
                 110.7 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (trimethyl 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 phosphine) 
               
               
                 ∠C a PC b   
                 0.85377 
                 1 
                 1 
                 1 
                 0.85377 
                 −1.85836 
                   
                   
                   
                 98.68 
                  98.6 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (trimethyl 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 phosphine) 
               
               
                 Methylene 
                 1 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 108.44 
                 107   
               
               
                 ∠HC a H 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (propane) 
               
               
                 ∠C a C b C c   
                   
                   
                   
                   
                   
                   
                 69.51 
                   
                   
                 110.49 
                 112   
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (propane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 113.8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (butane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 110.8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C a C b H 
                   
                   
                   
                   
                   
                   
                 69.51 
                   
                   
                 110.49 
                 111.0 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (butane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 111.4 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 Methyl 
                 1 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 109.50 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
                   
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                 ∠C a C b H 
                   
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                 ∠C b C a C c   
                 0.81549 
                 1 
                 1 
                 1 
                 0.81549 
                 −1.85836 
                   
                   
                   
                 110.67 
                 110.8 
               
               
                 iso C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C b C a H 
                 0.91771 
                 0.75 
                 1 
                 0.75 
                 1.04887 
                 0 
                   
                   
                   
                 110.76 
               
               
                 iso C a   
               
               
                 ∠C a C b H 
                 0.91771 
                 0.75 
                 1 
                 0.75 
                 1.04887 
                 0 
                   
                   
                   
                 111.27 
                 111.4 
               
               
                 iso C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C b C a C b   
                 0.81549 
                 1 
                 1 
                 1 
                 0.81549 
                 −1.85836 
                   
                   
                   
                 111.37 
                 110.8 
               
               
                 tert C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C b C a C d   
                   
                   
                   
                   
                   
                   
                 72.50 
                   
                   
                 107.50 
               
               
                   
               
             
          
         
       
     
         [0230]    Alkyl Phosphites (C n H 2n+1 O) 3 P, n=1,2,3,4,5 . . . ∞) 
         [0231]    The alkyl phosphites, (C n H 2n+1 O) 3 P, comprise P—O and C—O functional groups. The alkyl portion of the alkyl phosphite may comprise at least two terminal methyl groups (CH 3 ) at each end of each chain, and may comprise methylene (CH 2 ), and methylyne (CH) functional groups as well as C bound by carbon-carbon single bonds. The methyl and methylene functional groups are equivalent to those of straight-chain alkanes. Six types of C—C bonds can be identified. The n-alkane C—C bond is the same as that of straight-chain alkanes. In addition, the C—C bonds within isopropyl ((CH 3 ) 2 CH) and t-butyl ((CH 3 ) 3 C) groups and the isopropyl to isopropyl, isopropyl to t-butyl, and t-butyl to t-butyl C—C bonds comprise functional groups. The branched-chain-alkane groups in alkyl phosphites are equivalent to those in branched-chain alkanes. 
         [0232]    The ether portion comprises two types of C—O functional groups, one for methyl or t-butyl groups corresponding to the C, and the other for general alkyl groups that are equivalent to those in the Ethers section. The P—O bond forms between the P3sp 3  HO and an O2p AO to yield phosphites. The semimajor axis a of the P—O functional group is solved using Eq. (15.51). Using the semimajor axis and the relationships between the prolate spheroidal axes, the geometric and energy parameters of the MO are calculated using Eqs. (15.1-15.117) in the same manner as the organic functional groups given in Organic Molecular Functional Groups and Molecules section. 
         [0233]    For the P—O functional group, hybridization the 3s and 3p AOs of each to form a single 3sp 3  shell forms an energy minimum, and the sharing of electrons between the O2p AOs and P3sp 3  HOs to form a MO permits each participating orbital to decrease in radius and energy. The O AO has an energy of E(O)=—13.61805 eV, and the P3sp 3  HO has an energy of E(P,3sp 3 )=−11.78246 eV (Eq. (15.180)). In branched-chain alkyl phosphites, the energy matching condition is determined by the c 2  and C 2  parameters of Eq. (15.51) given by Eqs. (15.77), (15.79), and (13.430): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             c 
                             2 
                           
                            
                           
                               
                           
                            
                           and 
                            
                           
                               
                           
                            
                           
                             
                               C 
                               2 
                             
                              
                             
                               ( 
                               
                                 O 
                                  
                                 
                                     
                                 
                                  
                                 2 
                                  
                                 p 
                                  
                                 
                                     
                                 
                                  
                                 AO 
                                  
                                 
                                     
                                 
                                  
                                 to 
                                  
                                 
                                     
                                 
                                  
                                 P 
                                  
                                 
                                     
                                 
                                  
                                 3 
                                  
                                 
                                   sp 
                                   3 
                                 
                                  
                                 HO 
                               
                               ) 
                             
                           
                         
                         = 
                           
                          
                         
                           
                             
                               E 
                                
                               
                                 ( 
                                 
                                   P 
                                   , 
                                   
                                     3 
                                      
                                     
                                       sp 
                                       3 
                                     
                                   
                                 
                                 ) 
                               
                             
                             
                               E 
                                
                               
                                 ( 
                                 
                                   O 
                                   , 
                                   
                                     2 
                                      
                                     p 
                                   
                                 
                                 ) 
                               
                             
                           
                            
                           
                             
                               c 
                               2 
                             
                              
                             
                               ( 
                               
                                 C 
                                  
                                 
                                     
                                 
                                  
                                 2 
                                  
                                 
                                   sp 
                                   3 
                                 
                                  
                                 HO 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               
                                 - 
                                 11.78246 
                               
                                
                               
                                   
                               
                                
                               eV 
                             
                             
                               
                                 - 
                                 13.61805 
                               
                                
                               
                                   
                               
                                
                               eV 
                             
                           
                            
                           
                             ( 
                             0.91771 
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         0.79401 
                       
                     
                   
                 
               
               
                 
                   ( 
                   15.182 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The energy of the P—O-bond MO is the sum of the component energies of the H 2 -type ellipsoidal MO given in Eq. (15.51) with E (AO/HO) being E (P,3sp 3 ) given by Eq. (23.180), and E T (atom-atom,msp 3 .AO) is equivalent to that of single bond, −1.44914 eV, given by twice Eq. (14.151) in order to match the energies of the oxygen AO with the phosphorous and carbon HOs. 
         [0234]    The symbols of the functional groups of branched-chain alkyl phosphites are given in Table 45. The geometrical (Eqs. (15.1-15.5) and (15.51)), intercept (Eqs. (15.80-15.87)), and energy (Eqs. (15.6-15.11) and (15.17-15.65)) parameters of alkyl phosphites are given in Tables 46, 47, and 48, respectively. The total energy of each alkyl phosphite given in Table 49 was calculated as the sum over the integer multiple of each E D (Group) of Table 48 corresponding to functional-group composition of the molecule. The bond angle parameters of alkyl phosphites determined using Eqs. (15.88-15.117) are given in Table 50. The color scale, charge-density of exemplary alkyl phosphite, tri-isopropyl phosphite, comprising atoms with the outer shell bridged by one or more H 2 -type ellipsoidal MOs or joined with one or more hydrogen MOs is shown in  FIG. 15 . 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 45 
               
             
             
               
                   
               
               
                 The symbols of functional groups of alkyl phosphites. 
               
             
          
           
               
                   
                 Functional Group 
                 Group Symbol 
               
               
                   
                   
               
               
                   
                 P—O 
                 P—O 
               
               
                   
                 C—O (CH 3 —O- and (CH 3 ) 3 C—O—) 
                 C—O (i) 
               
               
                   
                 C—O (alkyl) 
                 C—O (ii) 
               
               
                   
                 CH 2  group 
                 C—H (CH 2 ) 
               
               
                   
                 CH 
                 C—H 
               
               
                   
                 CC bond (n-C) 
                 C—C (a) 
               
               
                   
                 CC bond (iso-C) 
                 C—C (b) 
               
               
                   
                 CC bond (tert-C) 
                 C—C (c) 
               
               
                   
                 CC (iso to iso-C) 
                 C—C (d) 
               
               
                   
                 CC (t to t-C) 
                 C—C (e) 
               
               
                   
                 CC (t to iso-C) 
                 C—C (f) 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 46 
               
               
                   
               
               
                 The geometrical bond parameters of alkyl phosphites and experimental values [1]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 P—O 
                 C—O (i) 
                 C—O (ii) 
                 C—H(CH 3 ) 
                 C—H(CH 2 ) 
                 C—H 
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 1.84714 
                 1.80717 
                 1.79473 
                 1.64920 
                 1.67122 
                 1.67465 
               
               
                 c′ (a 0 ) 
                 1.52523 
                 1.34431 
                 1.33968 
                 1.04856 
                 1.05553 
                 1.05661 
               
               
                 Bond Length 2c′ (Å) 
                 1.61423 
                 1.42276 
                 1.41785 
                 1.10974 
                 1.11713 
                 1.11827 
               
               
                 Exp. Bond Length 
                 1.631 [69] 
                 1.416 
                 1.418 
                 1.107 
                 1.107 
                 1.122 
               
               
                 (Å) 
                 (MHP) 
                 (dimethyl 
                 (ethyl methyl 
                 (C—H 
                 (C—H 
                 (isobutane) 
               
               
                   
                 1.60 [64] 
                 ether) 
                 ether (avg.)) 
                 propane) 
                 propane) 
               
               
                   
                 (DNA) 
                   
                   
                 1.117 
                 1.117 
               
               
                   
                   
                   
                   
                 (C—H 
                 (C—H 
               
               
                   
                   
                   
                   
                 butane) 
                 butane) 
               
               
                 b, c (a 0 ) 
                 1.04192 
                 1.20776 
                 1.19429 
                 1.27295 
                 1.29569 
                 1.29924 
               
               
                 e 
                 0.82573 
                 0.74388 
                 0.74645 
                 0.63580 
                 0.63159 
                 0.63095 
               
               
                   
               
               
                   
                 C—C (a) 
                 C—C (b) 
                 C—C (c) 
                 C—C (d) 
                 C—C (e) 
                 C—C (f) 
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 2.12499 
                 2.12499 
                 2.10725 
                 2.12499 
                 2.10725 
                 2.10725 
               
               
                 c′ (a 0 ) 
                 1.45744 
                 1.45744 
                 1.45164 
                 1.45744 
                 1.45164 
                 1.45164 
               
               
                 Bond Length 2c′ (Å) 
                 1.54280 
                 1.54280 
                 1.53635 
                 1.54280 
                 1.53635 
                 1.53635 
               
               
                 Exp. Bond Length 
                 1.532 
                 1.532 
                 1.532 
                 1.532 
                 1.532 
                 1.532 
               
               
                 (Å) 
                 (propane) 
                 (propane) 
                 (propane) 
                 (propane) 
                 (propane) 
                 (propane) 
               
               
                   
                 1.531 
                 1.531 
                 1.531 
                 1.531 
                 1.531 
                 1.531 
               
               
                   
                 (butane) 
                 (butane) 
                 (butane) 
                 (butane) 
                 (butane) 
                 (butane) 
               
               
                 b, c (a 0 ) 
                 1.54616 
                 1.54616 
                 1.52750 
                 1.54616 
                 1.52750 
                 1.52750 
               
               
                 e 
                 0.68600 
                 0.68600 
                 0.68888 
                 0.68600 
                 0.68888 
                 0.68888 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 47 
               
               
                   
               
               
                 The MO to HO intercept geometrical bond parameters of alkyl phosphites. 
               
               
                 R, R′, R″ are H or alkyl groups. E T  is E T  (atom-atom, msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 Final Total 
                   
                   
               
               
                   
                   
                 E T   
                 E T   
                 E T   
                 E T   
                 Energy 
               
               
                   
                   
                 (eV) 
                 (eV) 
                 (eV) 
                 (eV) 
                 C2sp 3   
                 r initial   
                 r final   
               
               
                 Bond 
                 Atom 
                 Bond 1 
                 Bond 2 
                 Bond 3 
                 Bond 4 
                 (eV) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 (CH 3 O) 2 P—OCH 3   
                 O 
                 −0.72457 
                 −0.72457 
                 0 
                 0 
                   
                 1.00000 
                 0.83600 
               
               
                 (CH 3 O) 2 P—OC(CH 3 ) 3   
               
               
                 (C—O (i)) 
               
               
                 (CH 3 O) 2 P—OCH 3   
                 P 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 0 
                   
                 1.15350 
                 0.80037 
               
               
                 (CH 3 O) 2 P—OC(CH 3 ) 3   
               
               
                 (CH 3 O) 2 P—OCH 2 R 
               
               
                 (C—O (i)) and (C—O (ii)) 
               
               
                 (CH 3 O) 2 P—OCH 2 R 
                 O 
                 −0.72457 
                 −0.82688 
                 0 
                 0 
                   
                 1.00000 
                 0.83078 
               
               
                 (C—O (ii)) 
               
               
                 C—H (OC a H 3 ) 
                 C a   
                 −0.72457 
                 0 
                 0 
                 0 
                 −152.34026 
                 0.91771 
                 0.87495 
               
               
                 (CH 3 O) 2 PO—C a H 3   
                 C a   
                 −0.72457 
                 0 
                 0 
                 0 
                 −152.34026 
                 0.91771 
                 0.87495 
               
               
                 (CH 3 O) 2 PO—C a (CH 3 ) 3   
                 C a   
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.51399 
                 0.91771 
                 0.76765 
               
               
                 (C—O (i)) 
               
               
                 (H 3 CO) 2 PO—C a H 3   
                 O 
                 −0.72457 
                 −0.72457 
                 0 
                 0 
                   
                 1.00000 
                 0.83600 
               
               
                 (CH 3 ) 3 C a —OP(OC b H 3 ) 2   
               
               
                 (C—O (i)) 
               
               
                 —H 2 C a —OP(OCH 3 ) 2   
                 C a   
                 −0.82688 
                 −0.92918 
                 0 
                 0 
                 −153.37175 
                 0.91771 
                 0.82053 
               
               
                 (C—O (ii)) 
               
               
                 (CH 3 O) 2 PO—C a H(CH 3 ) 2   
                 C a   
                 −0.82688 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.30093 
                 0.91771 
                 0.77699 
               
               
                 (C—O (ii)) 
               
               
                 —H 2 C a —OP(OCH 3 ) 2   
                 O 
                 −0.72457 
                 −0.82688 
                 0 
                 0 
                   
                 1.00000 
                 0.83078 
               
               
                 (H 3 C) 2 HC a —OP(OCH 3 ) 2   
               
               
                 (C—O (ii)) 
               
               
                 C—H (CH 3 ) 
                 C 
                 −0.92918 
                 0 
                 0 
                 0 
                 −152.54487 
                 0.91771 
                 0.86359 
               
               
                 C—H (CH 2 ) 
                 C 
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                 −153.47406 
                 0.91771 
                 0.81549 
               
               
                 C—H (CH) 
                 C 
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 C a   
                 −0.92918 
                 0 
                 0 
                 0 
                 −152.54487 
                 0.91771 
                 0.86359 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                 −153.47406 
                 0.91771 
                 0.81549 
               
               
                 R—H 2 C a C b (H 2 C c —R′)HCH 2 —(C—C (b)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 R—H 2 C a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (c)) 
                 C b   
                 −0.92918 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.71860 
                 0.91771 
                 0.75889 
               
               
                 isoC a C b (H 2 C c —R′)HCH 2 —(C—C (d)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 tertC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (e)) 
                 C b   
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.51399 
                 0.91771 
                 0.76765 
               
               
                 tertC a C b (H 2 C c —R′)HCH 2 —(C—C (f)) 
                 C b   
                 −0.72457 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.19863 
                 0.91771 
                 0.78155 
               
               
                 isoC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (f)) 
                 C b   
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.51399 
                 0.91771 
                 0.76765 
               
               
                   
               
             
          
           
               
                   
                   
                 E (C2sp 3 ) 
                   
                   
                   
                   
                   
               
               
                   
                 E Coulomb  (eV) 
                 (eV) 
                 θ′ 
                 θ 1   
                 θ 2   
                 d 1   
                 d 2   
               
               
                 Bond 
                 Final 
                 Final 
                 (°) 
                 (°) 
                 (°) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 (CH 3 O) 2 P—OCH 3   
                 −16.27489 
                   
                 111.08 
                 68.92 
                 48.48 
                 1.22455 
                 0.30068 
               
               
                 (CH 3 O) 2 P—OC(CH 3 ) 3   
               
               
                 (C—O (i)) 
               
               
                 (CH 3 O) 2 P—OCH 3   
                 −16.99947 
                   
                 108.77 
                 71.23 
                 46.66 
                 1.26770 
                 0.25753 
               
               
                 (CH 3 O) 2 P—OC(CH 3 ) 3   
               
               
                 (CH 3 O) 2 P—OCH 2 R 
               
               
                 (C—O (i)) and (C—O (ii)) 
               
               
                 (CH 3 O) 2 P—OCH 2 R 
                 −16.37720 
                   
                 110.75 
                 69.25 
                 48.21 
                 1.23087 
                 0.29436 
               
               
                 (C—O (ii)) 
               
               
                 C—H (OC a H 3 ) 
                 −15.55033 
                 −15.35946 
                 78.85 
                 101.15 
                 42.40 
                 1.21777 
                 0.16921 
               
               
                 (CH 3 O) 2 PO—C a H 3   
                 −15.55033 
                 −15.35946 
                 95.98 
                 84.02 
                 46.10 
                 1.25319 
                 0.09112 
               
               
                 (CH 3 O) 2 PO—C a (CH 3 ) 3   
                 −17.72405 
                   
                 86.03 
                 93.97 
                 39.35 
                 1.39744 
                 0.05313 
               
               
                 (C—O (i)) 
               
               
                 (H 3 CO) 2 PO—C a H 3   
                 −16.27490 
                   
                 92.66 
                 87.34 
                 43.74 
                 1.30555 
                 0.03876 
               
               
                 (CH 3 ) 3 C a —OP(OC b H 3 ) 2   
               
               
                 (C—O (i)) 
               
               
                 —H 2 C a —OP(OCH 3 ) 2   
                 −16.58181 
                 −16.39095 
                 92.41 
                 87.59 
                 43.35 
                 1.30512 
                 0.03456 
               
               
                 (C—O (ii)) 
               
               
                 (CH 3 O) 2 PO—C a H(CH 3 ) 2   
                 −17.51099 
                 −17.32013 
                 88.25 
                 91.75 
                 40.56 
                 1.36345 
                 0.02377 
               
               
                 (C—O (ii)) 
               
               
                 —H 2 C a —OP(OCH 3 ) 2   
                 −16.37720 
                   
                 93.33 
                 86.67 
                 43.98 
                 1.29138 
                 0.04829 
               
               
                 (H 3 C) 2 HC a —OP(OCH 3 ) 2   
               
               
                 (C—O (ii)) 
               
               
                 C—H (CH 3 ) 
                 −15.75493 
                 −15.56407 
                 77.49 
                 102.51 
                 41.48 
                 1.23564 
                 0.18708 
               
               
                 C—H (CH 2 ) 
                 −16.68412 
                 −16.49325 
                 68.47 
                 111.53 
                 35.84 
                 1.35486 
                 0.29933 
               
               
                 C—H (CH) 
                 −17.61330 
                 −17.42244 
                 61.10 
                 118.90 
                 31.37 
                 1.42988 
                 0.37326 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 −15.75493 
                 −15.56407 
                 63.82 
                 116.18 
                 30.08 
                 1.83879 
                 0.38106 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 −16.68412 
                 −16.49325 
                 56.41 
                 123.59 
                 26.06 
                 1.90890 
                 0.45117 
               
               
                 R—H 2 C a C b (H 2 C c —R′)HCH 2 —(C—C (b)) 
                 −17.61330 
                 −17.42244 
                 48.30 
                 131.70 
                 21.90 
                 1.97162 
                 0.51388 
               
               
                 R—H 2 C a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (c)) 
                 −17.92866 
                 −17.73779 
                 48.21 
                 131.79 
                 21.74 
                 1.95734 
                 0.50570 
               
               
                 isoC a C b (H 2 C c —R′)HCH 2 —(C—C (d)) 
                 −17.61330 
                 −17.42244 
                 48.30 
                 131.70 
                 21.90 
                 1.97162 
                 0.51388 
               
               
                 tertC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (e)) 
                 −17.92866 
                 −17.73779 
                 50.04 
                 129.96 
                 22.66 
                 1.94462 
                 0.49298 
               
               
                 tertC a C b (H 2 C c —R′)HCH 2 —(C—C (f)) 
                 −17.40869 
                 −17.21783 
                 52.78 
                 127.22 
                 24.04 
                 1.92443 
                 0.47279 
               
               
                 isoC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (f)) 
                 −17.92866 
                 −17.73779 
                 50.04 
                 129.96 
                 22.66 
                 1.94462 
                 0.49298 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 48 
               
               
                   
               
               
                 The energy parameters (eV) of functional groups of alkyl phosphites. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 P—O 
                 C—O (i) 
                 C—O (ii) 
                 CH 3   
                 CH 2   
                 CH (i) 
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 n 1   
                 1 
                 1 
                 1 
                 3 
                 2 
                 1 
               
               
                 n 2   
                 0 
                 0 
                 0 
                 2 
                 1 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.5 
                 0.5 
                 0.5 
                 0.75 
                 0.75 
                 0.75 
               
               
                 C 2   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 2   
                 0.79401 
                 0.85395 
                 0.85395 
                 0.91771 
                 0.91771 
                 0.91771 
               
               
                 c 3   
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
               
               
                 c 4   
                 2 
                 2 
                 2 
                 1 
                 1 
                 1 
               
               
                 c 5   
                 0 
                 0 
                 0 
                 3 
                 2 
                 1 
               
               
                 C 1o   
                 0.5 
                 0.5 
                 0.5 
                 0.75 
                 0.75 
                 0.75 
               
               
                 C 2o   
                 0.79401 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 V e  (eV) 
                 −33.27738 
                 −33.15757 
                 −33.47304 
                 −107.32728 
                 −70.41425 
                 −35.12015 
               
               
                 V p  (eV) 
                 8.92049 
                 10.12103 
                 10.15605 
                 38.92728 
                 25.78002 
                 12.87680 
               
               
                 T (eV) 
                 9.00781 
                 9.17389 
                 9.32537 
                 32.53914 
                 21.06675 
                 10.48582 
               
               
                 V m  (eV) 
                 −4.50391 
                 −4.58695 
                 −4.66268 
                 −16.26957 
                 −10.53337 
                 −5.24291 
               
               
                 E (AO/HO) (eV) 
                 −11.78246 
                 −14.63489 
                 −14.63489 
                 −15.56407 
                 −15.56407 
                 −14.63489 
               
               
                 ΔE  H     2     MO  (AO/HO) (eV) 
                 0 
                 −1.44915 
                 −1.65376 
                 0 
                 0 
                 0 
               
               
                 E T  (AO/HO) (eV) 
                 −11.78246 
                 −13.18574 
                 −12.98113 
                 −15.56407 
                 −15.56407 
                 −14.63489 
               
               
                 E T  (H 2 MO) (eV) 
                 −31.63544 
                 −31.63533 
                 −31.63544 
                 −67.69451 
                 −49.66493 
                 −31.63533 
               
               
                 E T  (atom-atom, msp 3 .AO) (eV) 
                 −1.44914 
                 −1.44915 
                 −1.65376 
                 0 
                 0 
                 0 
               
               
                 E T  (MO) (eV) 
                 −33.08451 
                 −33.08452 
                 −33.28912 
                 −67.69450 
                 −49.66493 
                 −31.63537 
               
               
                 ω (10 15  rad/s) 
                 10.3761 
                 12.0329 
                 12.1583 
                 24.9286 
                 24.2751 
                 24.1759 
               
               
                 E K  (eV) 
                 6.82973 
                 7.92028 
                 8.00277 
                 16.40846 
                 15.97831 
                 15.91299 
               
               
                 Ē D  (eV) 
                 −0.17105 
                 −0.18420 
                 −0.18631 
                 −0.25352 
                 −0.25017 
                 −0.24966 
               
               
                 Ē Kvib  (eV) 
                 0.10477 
                 0.13663 
                 0.16118 
                 0.35532 
                 0.35532 
                 0.35532 
               
               
                   
                 [70] 
                 [21] 
                 [4] 
                 (Eq. 
                 (Eq. 
                 (Eq. 
               
               
                   
                   
                   
                   
                 (13.458)) 
                 (13.458)) 
                 (13.458)) 
               
               
                 Ē osc  (eV) 
                 −0.11867 
                 −0.11589 
                 −0.10572 
                 −0.22757 
                 −0.14502 
                 −0.07200 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                 E T  (Group) (eV) 
                 −33.20318 
                 −33.20040 
                 −33.39484 
                 −67.92207 
                 −49.80996 
                 −31.70737 
               
               
                 E initial  (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
               
               
                 E initial  (c 5  AO/HO) (eV) 
                 0 
                 0 
                 0 
                 −13.59844 
                 −13.59844 
                 −13.59844 
               
               
                 E D  (Group) (eV) 
                 3.93340 
                 3.93062 
                 4.12506 
                 12.49186 
                 7.83016 
                 3.32601 
               
               
                   
               
               
                   
                 C—C (a) 
                 C—C (b) 
                 C—C (c) 
                 C—C (d) 
                 C—C (e) 
                 C—C (f) 
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 n 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 n 2   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
               
               
                 C 2   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 2   
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
               
               
                 c 3   
                 0 
                 0 
                 0 
                 1 
                 1 
                 0 
               
               
                 c 4   
                 2 
                 2 
                 2 
                 2 
                 2 
                 2 
               
               
                 c 5   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1o   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
               
               
                 C 2o   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 V e  (eV) 
                 −28.79214 
                 −28.79214 
                 −29.10112 
                 −28.79214 
                 −29.10112 
                 −29.10112 
               
               
                 V p  (eV) 
                 9.33352 
                 9.33352 
                 9.37273 
                 9.33352 
                 9.37273 
                 9.37273 
               
               
                 T (eV) 
                 6.77464 
                 6.77464 
                 6.90500 
                 6.77464 
                 6.90500 
                 6.90500 
               
               
                 V m  (eV) 
                 −3.38732 
                 −3.38732 
                 −3.45250 
                 −3.38732 
                 −3.45250 
                 −3.45250 
               
               
                 E (AO/HO) (eV) 
                 −15.56407 
                 −15.56407 
                 −15.35946 
                 −15.56407 
                 −15.35946 
                 −15.35946 
               
               
                 ΔE H     2     MO  (AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 E T  (AO/HO) (eV) 
                 −15.56407 
                 −15.56407 
                 −15.35946 
                 −15.56407 
                 −15.35946 
                 −15.35946 
               
               
                 E T  (H 2 MO) (eV) 
                 −31.63537 
                 −31.63537 
                 −31.63535 
                 −31.63537 
                 −31.63535 
                 −31.63535 
               
               
                 E T  (atom-atom, msp 3 .AO) (eV) 
                 −1.85836 
                 −1.85836 
                 −1.44915 
                 −1.85836 
                 −1.44915 
                 −1.44915 
               
               
                 E T  (MO) (eV) 
                 −33.49373 
                 −33.49373 
                 −33.08452 
                 −33.49373 
                 −33.08452 
                 −33.08452 
               
               
                 ω (10 15  rad/s) 
                 9.43699 
                 9.43699 
                 15.4846 
                 9.43699 
                 9.55643 
                 9.55643 
               
               
                 E K  (eV) 
                 6.21159 
                 6.21159 
                 10.19220 
                 6.21159 
                 6.29021 
                 6.29021 
               
               
                 Ē D  (eV) 
                 −0.16515 
                 −0.16515 
                 −0.20896 
                 −0.16515 
                 −0.16416 
                 −0.16416 
               
               
                 Ē Kvib  (eV) 
                 0.12312 
                 0.17978 
                 0.09944 
                 0.12312 
                 0.12312 
                 0.12312 
               
               
                   
                 [2] 
                 [4] 
                 [5] 
                 [2] 
                 [2] 
                 [2] 
               
               
                 Ē osc  (eV) 
                 −0.10359 
                 −0.07526 
                 −0.15924 
                 −0.10359 
                 −0.10260 
                 −0.10260 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                 E T  (Group) (eV) 
                 −33.59732 
                 −33.49373 
                 −33.24376 
                 −33.59732 
                 −33.18712 
                 −33.18712 
               
               
                 E initial  (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
               
               
                 E initial  (c 5  AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 E D  (Group) (eV) 
                 4.32754 
                 4.29921 
                 3.97398 
                 4.17951 
                 3.62128 
                 3.91734 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 49 
               
               
                   
               
               
                 The total bond energies of alkyl phosphites calculated using the functional group composition 
               
               
                 and the energies of Table 48 compared to the experimental values [68]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                 C—O 
                   
                   
                   
                 C—C 
                 C—C 
               
               
                 Formula 
                 Name 
                 P—O 
                 C—O (i) 
                 (ii) 
                 CH 3   
                 CH 2   
                 CH (i) 
                 (a) 
                 (b) 
               
               
                   
               
               
                 C 3 H 9 O 3 P 
                 Trimethyl phosphite 
                 3 
                 3 
                 0 
                 3 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 6 H 15 O 3 P 
                 Triethyl phosphite 
                 3 
                 0 
                 3 
                 3 
                 3 
                 0 
                 3 
                 0 
               
               
                 C 9 H 21 O 3 P 
                 Tri-isopropyl phosphite 
                 3 
                 0 
                 3 
                 6 
                 0 
                 3 
                 0 
                 6 
               
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 Calculated 
                 Experimental 
                   
                   
               
               
                   
                   
                 C—C 
                 C—C 
                 C—C 
                 C—C 
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 (c) 
                 (d) 
                 (e) 
                 (f) 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 C 3 H 9 O 3 P 
                 Trimethyl phosphite 
                 0 
                 0 
                 0 
                 0 
                 61.06764 
                 60.94329 
                 −0.00204 
               
               
                 C 6 H 15 O 3 P 
                 Triethyl phosphite 
                 0 
                 0 
                 0 
                 0 
                 98.12406 
                 97.97947 
                 −0.00148 
               
               
                 C 9 H 21 O 3 P 
                 Tri-isopropyl phosphite 
                 0 
                 0 
                 0 
                 0 
                 134.89983 
                 135.00698 
                 0.00079 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 50 
               
               
                   
               
               
                 The bond angle parameters of alkyl phosphites and experimental values [1]. In the calculation of θ v , 
               
               
                 the parameters from the preceding angle were used. E T  is E T  (atom-atom,msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                 2c′ 
                   
                 Atom 1 
                   
                 Atom 2 
                   
               
               
                   
                 2c′ 
                 2c′ 
                 Terminal 
                 E Coulombic   
                 Hybridization 
                   
                 Hybridization 
               
               
                 Atoms of 
                 Bond 1 
                 Bond 2 
                 Atoms 
                 or E 
                 Designation 
                 E Coulombic   
                 Designation 
                 c 2   
               
               
                 Angle 
                 (a 0 ) 
                 (a 0 ) 
                 (a 0 ) 
                 Atom 1 
                 (Table 7) 
                 Atom 2 
                 (Table 7) 
                 Atom 1 
               
               
                   
               
               
                 ∠OPO 
                 3.05046 
                 3.05046 
                 4.5826 
                 −16.27489 
                 16 
                 −16.27489 
                 16 
                 0.83600 
               
               
                 ∠POC 
                 3.05046 
                 2.68862 
                 4.9768 
                 −11.78246 
                 Psp 3   
                 −15.75493 
                 7 
                 0.73885 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Eq. 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 (23.181) 
               
               
                 ∠C b C a O 
                 2.91547 
                 2.67935 
                 4.5607 
                 −16.68412 
                 26 
                 −13.61806 
                 O 
                 0.81549 
               
               
                 Methylene 
                 2.11106 
                 2.11106 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
               
               
                 ∠C a C b H 
               
               
                 Methyl 
                 2.09711 
                 2.09711 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
               
               
                 ∠C a C b H 
               
               
                 ∠C b C a C c   
                 2.91547 
                 2.91547 
                 4.7958 
                 −16.68412 
                 26 
                 −16.68412 
                 26 
                 0.81549 
               
               
                 iso C a   
                   
                   
                   
                 C b   
                   
                 C c   
               
               
                 ∠C b C a H 
                 2.91547 
                 2.11323 
                 4.1633 
                 −15.55033 
                 5 
                 −14.82575 
                 1 
                 0.87495 
               
               
                 iso C a   
                   
                   
                   
                 C a   
                   
                 C b   
               
               
                 ∠C a C b H 
                 2.91547 
                 2.09711 
                 4.1633 
                 −15.55033 
                 5 
                 −14.82575 
                 1 
                 0.87495 
               
               
                 iso C a   
                   
                   
                   
                 C b   
                   
                 C a   
               
               
                 ∠C b C a C b   
                 2.90327 
                 2.90327 
                 4.7958 
                 −16.68412 
                 26 
                 −16.68412 
                 26 
                 0.81549 
               
               
                 tert C a   
                   
                   
                   
                 C b   
                   
                 C b   
               
               
                 ∠C b C a C d   
               
               
                   
               
             
          
           
               
                 Atoms of 
                 c 2   
                   
                   
                   
                   
                 E T   
                 θ v   
                 θ 1   
                 θ 2   
                 Cal. θ 
                 Exp. θ 
               
               
                 Angle 
                 Atom 2 
                 C 1   
                 C 2   
                 c 1   
                 c 2 ′ 
                 (eV) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
               
               
                   
               
               
                 ∠OPO 
                 0.83600 
                 1 
                 1 
                 1 
                 0.83600 
                 −1.65376 
                   
                   
                   
                 97.38 
                  96 [71] 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (triethyl 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 phosphite) 
               
               
                 ∠POC 
                 0.86359 
                 1 
                 0.73885 
                 1 
                 0.80122 
                 −0.72457 
                   
                   
                   
                 120.13 
                 120 [71] 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (triethyl 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 phosphite) 
               
               
                 ∠C b C a O 
                 0.85395 
                 1 
                 1 
                 1 
                 0.83472 
                 −1.65376 
                   
                   
                   
                 109.13 
                 109.4 
               
               
                   
                 (Eq. 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (ethyl methyl 
               
               
                   
                 (15.133)) 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 ether) 
               
               
                 Methylene 
                 1 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 108.44 
                 107 
               
               
                 ∠HC a H 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (propane) 
               
               
                 ∠C a C b C c   
                   
                   
                   
                   
                   
                   
                 69.51 
                   
                   
                 110.49 
                 112 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (propane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 113.8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (butane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 110.8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C a C b H 
                   
                   
                   
                   
                   
                   
                 69.51 
                   
                   
                 110.49 
                 111.0 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (butane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 111.4 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 Methyl 
                 1 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 109.50 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
                   
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                 ∠C a C b H 
                   
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                 ∠C b C a C c   
                 0.81549 
                 1 
                 1 
                 1 
                 0.81549 
                 −1.85836 
                   
                   
                   
                 110.67 
                 110.8 
               
               
                 iso C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C b C a H 
                 0.91771 
                 0.75 
                 1 
                 0.75 
                 1.04887 
                 0 
                   
                   
                   
                 110.76 
               
               
                 iso C a   
               
               
                 ∠C a C b H 
                 0.91771 
                 0.75 
                 1 
                 0.75 
                 1.04887 
                 0 
                   
                   
                   
                 111.27 
                 111.4 
               
               
                 iso C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C b C a C b   
                 0.81549 
                 1 
                 1 
                 1 
                 0.81549 
                 −1.85836 
                   
                   
                   
                 111.37 
                 110.8 
               
               
                 tert C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C b C a C d   
                   
                   
                   
                   
                   
                   
                 72.50 
                   
                   
                 107.50 
               
               
                   
               
             
          
         
       
     
         [0235]    Alkyl Phosphine Oxides (C n H 2n+1 ) 3 P═O, n=1,2,3,4,5 . . . ∞) 
         [0236]    The alkyl phosphine oxides, (C n H 2n+1 ) 3 P═O, comprise P—C and P═O functional groups. The alkyl portion of the alkyl phosphine oxide may comprise at least two terminal methyl groups (CH 3 ) at each end of each chain, and may comprise methylene (CH 2 ), and methylyne (CH) functional groups as well as C bound by carbon-carbon single bonds. The methyl and methylene functional groups are equivalent to those of straight-chain alkanes. Six types of C—C bonds can be identified. The n-alkane C—C bond is the same as that of straight-chain alkanes. In addition, the C—C bonds within isopropyl ((CH 3 ) 2 CH) and t-butyl ((CH 3 ) 3 C) groups and the isopropyl to isopropyl, isopropyl to t-butyl, and t-butyl to t-butyl C—C bonds comprise functional groups. The branched-chain-alkane groups in alkyl phosphine oxides are equivalent to those in branched-chain alkanes. 
         [0237]    The P—C functional group is equivalent to that of alkyl phosphines. The P═O bond forms between the P3sp 3  HO and an O2p AO to yield phosphine oxides. The semimajor axis a of the P═O functional group is solved using Eq. (15.51). Using the semimajor axis and the relationships between the prolate spheroidal axes, the geometric and energy parameters of the MO are calculated using Eqs. (15.1-15.117) in the same manner as the organic functional groups given in Organic Molecular Functional Groups and Molecules section. 
         [0000]    For the P═O functional group, hybridization the 3s and 3p AOs of each P to form a single 3sp 3  shells forms an energy minimum, and the sharing of electrons between the O2p AOs and P3sp 3  HOs to form a MO permits each participating orbital to decrease in radius and energy. In branched-chain alkyl phosphine oxides, the energy of phosphorous is less than the Coulombic energy between the electron and proton of H given by Eq. (1.231). The energy matching condition is determined by the c 2  parameter given by Eq. (15.182). The energy of the P═O— bond MO is the sum of the component energies of the H 2 -type ellipsoidal MO given in Eq. (15.51) with E(AO/HO) being twice E(P,3sp 3 ) given by Eq. (15.180) corresponding to the double bond, and E T (atom-atom, msp 3 .AO) is equivalent to that of an alkene double bond, −2.26758 eV, given by Eq. (14.247) in order to match the energies of the carbon and phosphorous HOs and the oxygen AO. 
         [0238]    The symbols of the functional groups of branched-chain alkyl phosphine oxides are given in Table 51. The geometrical (Eqs. (15.1-15.5) and (15.51)), intercept (Eqs. (15.80-15.87)), and energy (Eqs. (15.6-15.11) and (15.17-15.65)) parameters of alkyl phosphine oxides are given in Tables 52, 53, and 54, respectively. The total energy of each alkyl phosphine oxide given in Table 55 was calculated as the sum over the integer multiple of each E D (Group) of Table 54 corresponding to functional-group composition of the molecule. The bond angle parameters of alkyl phosphine oxides determined using Eqs. (15.88-15.117) are given in Table 56. The color scale, charge-density of exemplary alkyl phosphine oxide, trimethylphosphine oxide, comprising atoms with the outer shell bridged by one or more H 2 -type ellipsoidal MOs or joined with one or more hydrogen MOs is shown in  FIG. 16 . 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 51 
               
             
             
               
                   
               
               
                 The symbols of functional groups of alkyl phosphine oxides. 
               
             
          
           
               
                   
                 Functional Group 
                 Group Symbol 
               
               
                   
                   
               
               
                   
                 P═O 
                 P═O 
               
               
                   
                 P—C 
                 P—C 
               
               
                   
                 CH 3  group 
                 C—H (CH 3 ) 
               
               
                   
                 CH 2  group 
                 C—H (CH 2 ) 
               
               
                   
                 CH 
                 C—H (i) 
               
               
                   
                 CC bond (n-C) 
                 C—C (a) 
               
               
                   
                 CC bond (iso-C) 
                 C—C (b) 
               
               
                   
                 CC bond (tert-C) 
                 C—C (c) 
               
               
                   
                 CC (iso to iso-C) 
                 C—C (d) 
               
               
                   
                 CC (t to t-C) 
                 C—C (e) 
               
               
                   
                 CC (t to iso-C) 
                 C—C (f) 
               
               
                   
                 CC (aromatic bond) 
                 C 3e ═C 
               
               
                   
                 CH (aromatic) 
                 CH (ii) 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 52 
               
               
                   
               
               
                 The geometrical bond parameters of alkyl phosphine oxides and experimental values [1]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 P═O 
                 P—C 
                 C—H (CH 3 ) 
                 C—H (CH 2 ) 
                 C—H (i) 
                 C—C (a) 
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 1.91663 
                 2.29513 
                 1.64920 
                 1.67122 
                 1.67465 
                 2.12499 
               
               
                 c′ (a 0 ) 
                 1.38442 
                 1.76249 
                 1.04856 
                 1.05553 
                 1.05661 
                 1.45744 
               
               
                 Bond Length 
                 1.46521E−10 
                 1.86534 
                 1.10974 
                 1.11713 
                 1.11827 
                 1.54280 
               
               
                 2c′ (Å) 
               
               
                 Exp. Bond 
                 1.48 [64] 
                 1.847 
                 1.107 
                 1.107 
                 1.122 
                 1.532 
               
               
                 Length 
                 (DNA) 
                 ((CH3) 2 PCH 3 ) 
                 (C—H propane) 
                 (C—H propane) 
                 (isobutane) 
                 (propane) 
               
               
                 (Å) 
                 1.4759 
                 1.858 
                 1.117 
                 1.117 
                   
                 1.531 
               
               
                   
                 (PO) 
                 (H 2 PCH 3 ) 
                 (C—H butane) 
                 (C—H butane) 
                   
                 (butane) 
               
               
                 b, c (a 0 ) 
                 1.32546 
                 1.47012 
                 1.27295 
                 1.29569 
                 1.29924 
                 1.54616 
               
               
                 e 
                 0.72232 
                 0.76793 
                 0.63580 
                 0.63159 
                 0.63095 
                 0.68600 
               
               
                   
               
             
          
           
               
                   
                 C—C (b) 
                 C—C (c) 
                 C—C (d) 
                 C—C (e) 
                 C—C (f) 
                 C 3e ═C 
                 CH (ii) 
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 2.12499 
                 2.10725 
                 2.12499 
                 2.10725 
                 2.10725 
                 1.47348 
                 1.60061 
               
               
                 c′ (a 0 ) 
                 1.45744 
                 1.45164 
                 1.45744 
                 1.45164 
                 1.45164 
                 1.31468 
                 1.03299 
               
               
                 Bond Length 
                 1.54280 
                 1.53635 
                 1.54280 
                 1.53635 
                 1.53635 
                 1.39140 
                 1.09327 
               
               
                 2c′ (Å) 
               
               
                 Exp. Bond 
                 1.532 
                 1.532 
                 1.532 
                 1.532 
                 1.532 
                 1.399 
                 1.101 
               
               
                 Length 
                 (propane) 
                 (propane) 
                 (propane) 
                 (propane) 
                 (propane) 
                 (benzene) 
                 (benzene) 
               
               
                 (Å) 
                 1.531 
                 1.531 
                 1.531 
                 1.531 
                 1.531 
               
               
                   
                 (butane) 
                 (butane) 
                 (butane) 
                 (butane) 
                 (butane) 
               
               
                 b, c (a 0 ) 
                 1.54616 
                 1.52750 
                 1.54616 
                 1.52750 
                 1.52750 
                 0.66540 
                 1.22265 
               
               
                 e 
                 0.68600 
                 0.68888 
                 0.68600 
                 0.68888 
                 0.68888 
                 0.89223 
                 0.64537 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 53 
               
               
                   
               
               
                 The MO to HO intercept geometrical bond parameters of alkyl phosphine oxides. R, R′, R″ are H or alkyl groups. E T  is 
               
               
                 E T  (atom-atom, msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                 E T   
                 E T   
                 E T   
                 E T   
                 Final Total Energy 
                   
                   
               
               
                   
                   
                 (eV) 
                 (eV) 
                 (eV) 
                 (eV) 
                 C2sp 3   
                 r initial   
                 r final   
               
               
                 Bond 
                 Atom 
                 Bond 1 
                 Bond 2 
                 Bond 3 
                 Bond 4 
                 (eV) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 (CH 3 ) 3 P═O 
                 O 
                 −1.13379 
                 0 
                 0 
                 0 
                   
                 1.00000 
                 0.85252 
               
               
                 (CH 3 ) 3 P═O 
                 P 
                 −1.13379 
                 −0.18114 
                 −0.18114 
                 −0.18114 
                   
                 1.15350 
                 0.82445 
               
               
                 (CH 3 ) 2 (O)P—CH 3   
                 C 
                 −0.18114 
                 0 
                 0 
                 0 
                   
                 0.91771 
                 0.90664 
               
               
                 (CH 3 ) 2 (O)P—CH 3   
                 P 
                 −0.18114 
                 −0.18114 
                 −0.18114 
                 −1.13379 
                   
                 1.15350 
                 0.82445 
               
               
                 C—H(CH 3 ) 
                 C 
                 −0.92918 
                 0 
                 0 
                 0 
                 −152.54487 
                 0.91771 
                 0.86359 
               
               
                 C—H(CH 2 ) 
                 C 
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                 −153.47406 
                 0.91771 
                 0.81549 
               
               
                 C—H(CH) 
                 C 
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 C a   
                 −0.92918 
                 0 
                 0 
                 0 
                 −152.54487 
                 0.91771 
                 0.86359 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                 −153.47406 
                 0.91771 
                 0.81549 
               
               
                 R—H 2 C a C b (H 2 C c —R′)HCH 2 —(C—C (b)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 R—H 2 C a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (c)) 
                 C b   
                 −0.92918 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.71860 
                 0.91771 
                 0.75889 
               
               
                 isoC a C b (H 2 C c —R′)HCH 2 —(C—C (d)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 tertC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (e)) 
                 C b   
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.51399 
                 0.91771 
                 0.76765 
               
               
                 tertC a C b (H 2 C c —R′)HCH 2 —(C—C (f)) 
                 C b   
                 −0.72457 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.19863 
                 0.91771 
                 0.78155 
               
               
                 isoC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (f)) 
                 C b   
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.51399 
                 0.91771 
                 0.76765 
               
               
                   
               
             
          
           
               
                   
                 E Coulomb  (eV) 
                 E (C2sp 3 ) (eV) 
                 θ′ 
                 θ 1   
                 θ 2   
                 d 1   
                 d 2   
               
               
                 Bond 
                 Final 
                 Final 
                 (°) 
                 (°) 
                 (°) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 (CH 3 ) 3 P═O 
                 −15.95954 
                   
                 84.02 
                 95.98 
                 39.77 
                 1.47318 
                 0.08876 
               
               
                 (CH 3 ) 3 P═O 
                 −16.50297 
                   
                 81.09 
                 98.91 
                 37.92 
                 1.51205 
                 0.12762 
               
               
                 (CH 3 ) 2 (O)P—CH 3   
                 −15.00689 
                 −14.81603 
                 87.12 
                 92.88 
                 38.02 
                 1.80811 
                 0.04562 
               
               
                 (CH 3 ) 2 (O)P—CH 3   
                 −16.50297 
                   
                 79.33 
                 100.67 
                 33.44 
                 1.91514 
                 0.15265 
               
               
                 C—H(CH 3 ) 
                 −15.75493 
                 −15.56407 
                 77.49 
                 102.51 
                 41.48 
                 1.23564 
                 0.18708 
               
               
                 C—H(CH 2 ) 
                 −16.68412 
                 −16.49325 
                 68.47 
                 111.53 
                 35.84 
                 1.35486 
                 0.29933 
               
               
                 C—H(CH) 
                 −17.61330 
                 −17.42244 
                 61.10 
                 118.90 
                 31.37 
                 1.42988 
                 0.37326 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 −15.75493 
                 −15.56407 
                 63.82 
                 116.18 
                 30.08 
                 1.83879 
                 0.38106 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 −16.68412 
                 −16.49325 
                 56.41 
                 123.59 
                 26.06 
                 1.90890 
                 0.45117 
               
               
                 R—H 2 C a C b (H 2 C c —R′)HCH 2 —(C—C (b)) 
                 −17.61330 
                 −17.42244 
                 48.30 
                 131.70 
                 21.90 
                 1.97162 
                 0.51388 
               
               
                 R—H 2 C a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (c)) 
                 −17.92866 
                 −17.73779 
                 48.21 
                 131.79 
                 21.74 
                 1.95734 
                 0.50570 
               
               
                 isoC a C b (H 2 C c —R′)HCH 2 —(C—C (d)) 
                 −17.61330 
                 −17.42244 
                 48.30 
                 131.70 
                 21.90 
                 1.97162 
                 0.51388 
               
               
                 tertC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (e)) 
                 −17.92866 
                 −17.73779 
                 50.04 
                 129.96 
                 22.66 
                 1.94462 
                 0.49298 
               
               
                 tertC a C b (H 2 C c —R′)HCH 2 —(C—C (f)) 
                 −17.40869 
                 −17.21783 
                 52.78 
                 127.22 
                 24.04 
                 1.92443 
                 0.47279 
               
               
                 isoC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (f)) 
                 −17.92866 
                 −17.73779 
                 50.04 
                 129.96 
                 22.66 
                 1.94462 
                 0.49298 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 54 
               
               
                   
               
               
                 The energy parameters (eV) of functional groups of alkyl phosphine oxides. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 P═O 
                 P—C 
                 CH 3   
                 CH 2   
                 CH (i) 
                 C—C (a) 
                 C—C (b) 
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 f 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 n 1   
                 2 
                 1 
                 3 
                 2 
                 1 
                 1 
                 1 
               
               
                 n 2   
                 0 
                 0 
                 2 
                 1 
                 0 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.5 
                 0.5 
                 0.75 
                 0.75 
                 0.75 
                 0.5 
                 0.5 
               
               
                 C 2   
                 1 
                 0.73885 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 2   
                 0.79401 
                 1 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
               
               
                 c 3   
                 0 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
               
               
                 c 4   
                 4 
                 2 
                 1 
                 1 
                 1 
                 2 
                 2 
               
               
                 c 5   
                 0 
                 0 
                 3 
                 2 
                 1 
                 0 
                 0 
               
               
                 C 1o   
                 0.5 
                 0.5 
                 0.75 
                 0.75 
                 0.75 
                 0.5 
                 0.5 
               
               
                 C 2o   
                 1 
                 0.73885 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 V e  (eV) 
                 −56.96374 
                 −31.34959 
                 −107.32728 
                 −70.41425 
                 −35.12015 
                 −28.79214 
                 −28.79214 
               
               
                 V p  (eV) 
                 9.82777 
                 7.71965 
                 38.92728 
                 25.78002 
                 12.87680 
                 9.33352 
                 9.33352 
               
               
                 T (eV) 
                 14.86039 
                 6.82959 
                 32.53914 
                 21.06675 
                 10.48582 
                 6.77464 
                 6.77464 
               
               
                 V m  (eV) 
                 −7.43020 
                 −3.41479 
                 −16.26957 
                 −10.53337 
                 −5.24291 
                 −3.38732 
                 −3.38732 
               
               
                 E (AO/HO) (eV) 
                 −23.56492 
                 −11.78246 
                 −15.56407 
                 −15.56407 
                 −14.63489 
                 −15.56407 
                 −15.56407 
               
               
                 ΔE H     2     MO  (AO/HO) (eV) 
                 0 
                 −0.36229 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 E T  (AO/HO) (eV) 
                 −23.56492 
                 −11.42017 
                 −15.56407 
                 −15.56407 
                 −14.63489 
                 −15.56407 
                 −15.56407 
               
               
                 E T  (H 2 MO) (eV) 
                 −63.27069 
                 −31.63532 
                 −67.69451 
                 −49.66493 
                 −31.63533 
                 −31.63537 
                 −31.63537 
               
               
                 E T  (atom-atom, msp 3 .AO) (eV) 
                 −2.26758 
                 −0.36229 
                 0 
                 0 
                 0 
                 −1.85836 
                 −1.85836 
               
               
                 E T  (MO) (eV) 
                 −65.53832 
                 −31.99766 
                 −67.69450 
                 −49.66493 
                 −31.63537 
                 −33.49373 
                 −33.49373 
               
               
                 ω (10 15  rad/s) 
                 11.0170 
                 7.22663 
                 24.9286 
                 24.2751 
                 24.1759 
                 9.43699 
                 9.43699 
               
               
                 E K  (eV) 
                 7.25157 
                 4.75669 
                 16.40846 
                 15.97831 
                 15.91299 
                 6.21159 
                 6.21159 
               
               
                 Ē D  (eV) 
                 −0.17458 
                 −0.13806 
                 −0.25352 
                 −0.25017 
                 −0.24966 
                 −0.16515 
                 −0.16515 
               
               
                 Ē Kvib  (eV) 
                 0.15292 
                 0.17606 
                 0.35532 
                 0.35532 
                 0.35532 
                 0.12312 
                 0.17978 
               
               
                   
                 [24] 
                 [67] 
                 (Eq. 
                 (Eq. 
                 (Eq. 
                 [2] 
                 [4] 
               
               
                   
                   
                   
                 (13.458)) 
                 (13.458)) 
                 (13.458)) 
               
               
                 Ē osc  (eV) 
                 −0.09812 
                 −0.05003 
                 −0.22757 
                 −0.14502 
                 −0.07200 
                 −0.10359 
                 −0.07526 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                 E T  (Group) (eV) 
                 −65.73455 
                 −32.04769 
                 −67.92207 
                 −49.80996 
                 −31.70737 
                 −33.59732 
                 −33.49373 
               
               
                 E initial  (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
               
               
                 E initial  (c 5  AO/HO) (eV) 
                 0 
                 0 
                 −13.59844 
                 −13.59844 
                 −13.59844 
                 0 
                 0 
               
               
                 E D  (Group) (eV) 
                 7.19500 
                 2.77791 
                 12.49186 
                 7.83016 
                 3.32601 
                 4.32754 
                 4.29921 
               
               
                   
               
             
          
           
               
                   
                 C—C (c) 
                 C—C (d) 
                 C—C (e) 
                 C—C (f) 
                 C 3e ═C 
                 CH (ii) 
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 f 1   
                 1 
                 1 
                 1 
                 1 
                 0.75 
                 1 
               
               
                 n 1   
                 1 
                 1 
                 1 
                 1 
                 2 
                 1 
               
               
                 n 2   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.75 
               
               
                 C 2   
                 1 
                 1 
                 1 
                 1 
                 0.85252 
                 1 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 2   
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.85252 
                 0.91771 
               
               
                 c 3   
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
               
               
                 c 4   
                 2 
                 2 
                 2 
                 2 
                 3 
                 1 
               
               
                 c 5   
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
               
               
                 C 1o   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.75 
               
               
                 C 2o   
                 1 
                 1 
                 1 
                 1 
                 0.85252 
                 1 
               
               
                 V e  (eV) 
                 −29.10112 
                 −28.79214 
                 −29.10112 
                 −29.10112 
                 −101.12679 
                 −37.10024 
               
               
                 V p  (eV) 
                 9.37273 
                 9.33352 
                 9.37273 
                 9.37273 
                 20.69825 
                 13.17125 
               
               
                 T (eV) 
                 6.90500 
                 6.77464 
                 6.90500 
                 6.90500 
                 34.31559 
                 11.58941 
               
               
                 V m  (eV) 
                 −3.45250 
                 −3.38732 
                 −3.45250 
                 −3.45250 
                 −17.15779 
                 −5.79470 
               
               
                 E (AO/HO) (eV) 
                 −15.35946 
                 −15.56407 
                 −15.35946 
                 −15.35946 
                 0 
                 −14.63489 
               
               
                 ΔE H     2     MO  (AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 −1.13379 
               
               
                 E T  (AO/HO) (eV) 
                 −15.35946 
                 −15.56407 
                 −15.35946 
                 −15.35946 
                 0 
                 −13.50110 
               
               
                 E T  (H 2 MO) (eV) 
                 −31.63535 
                 −31.63537 
                 −31.63535 
                 −31.63535 
                 −63.27075 
                 −31.63539 
               
               
                 E T  (atom-atom, msp 3 .AO) (eV) 
                 −1.44915 
                 −1.85836 
                 −1.44915 
                 −1.44915 
                 −2.26759 
                 −0.56690 
               
               
                 E T  (MO) (eV) 
                 −33.08452 
                 −33.49373 
                 −33.08452 
                 −33.08452 
                 −65.53833 
                 −32.20226 
               
               
                 ω (10 15  rad/s) 
                 15.4846 
                 9.43699 
                 9.55643 
                 9.55643 
                 49.7272 
                 26.4826 
               
               
                 E K  (eV) 
                 10.19220 
                 6.21159 
                 6.29021 
                 6.29021 
                 32.73133 
                 17.43132 
               
               
                 Ē D  (eV) 
                 −0.20896 
                 −0.16515 
                 −0.16416 
                 −0.16416 
                 −0.35806 
                 −0.26130 
               
               
                 Ē Kvib  (eV) 
                 0.09944 
                 0.12312 
                 0.12312 
                 0.12312 
                 0.19649 
                 0.35532 
               
               
                   
                 [5] 
                 [2] 
                 [2] 
                 [2] 
                 [49] 
                 Eq. (13.458) 
               
               
                 Ē osc  (eV) 
                 −0.15924 
                 −0.10359 
                 −0.10260 
                 −0.10260 
                 −0.25982 
                 −0.08364 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                 E T  (Group) (eV) 
                 −33.24376 
                 −33.59732 
                 −33.18712 
                 −33.18712 
                 −49.54347 
                 −32.28590 
               
               
                 E initial  (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
               
               
                 E initial  (c 5  AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 −13.59844 
               
               
                 E D  (Group) (eV) 
                 3.97398 
                 4.17951 
                 3.62128 
                 3.91734 
                 5.63881 
                 3.90454 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 55 
               
               
                   
               
               
                 The total bond energies of alkyl phosphine oxides calculated using the functional group composition and the energies of 
               
               
                 Table 54 compared to the experimental values [68]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                 C—C 
                 C—C 
                 C—C 
               
               
                 Formula 
                 Name 
                 P═O 
                 P—C 
                 CH 3   
                 CH 2   
                 CH (i) 
                 (a) 
                 (b) 
                 (c) 
               
               
                   
               
               
                 C 3 H 9 PO 
                 Trimethylphosphine oxide 
                 1 
                 3 
                 3 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                 Calculated 
                   
                   
               
               
                   
                   
                   
                   
                   
                   
                   
                 Total Bond 
                 Experimental 
               
               
                   
                   
                 C—C 
                 C—C 
                 C—C 
                   
                   
                 Energy 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 (d) 
                 (e) 
                 (f) 
                 C 3e ═C 
                 CH (ii) 
                 (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 C 3 H 9 PO 
                 Trimethylphosphine oxide 
                 0 
                 0 
                 0 
                 0 
                 0 
                 53.00430 
                 52.91192 
                 −0.00175 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 56 
               
               
                   
               
               
                 The bond angle parameters of alkyl phosphine oxides and experimental values [1]. In the calculation of θ v , 
               
               
                 the parameters from the preceding angle were used. E T  is E T  (atom-atom, msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                 2c′ 
                   
                 Atom 1 
                   
                 Atom 2 
                   
                   
               
               
                   
                 2c′ 
                 2c′ 
                 Terminal 
                 E Coulombic   
                 Hybridization 
                   
                 Hybridization 
               
               
                 Atoms of 
                 Bond 1 
                 Bond 2 
                 Atoms 
                 or E 
                 Designation 
                 E Coulombic   
                 Designation 
                 c 2   
                 c 2   
               
               
                 Angle 
                 (a 0 ) 
                 (a 0 ) 
                 (a 0 ) 
                 Atom 1 
                 (Table 7) 
                 Atom 2 
                 (Table 7) 
                 Atom 1 
                 Atom 2 
               
               
                   
               
               
                 Methyl 
                 2.09711 
                 2.09711 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
                 1 
               
               
                 ∠HC a H 
               
               
                 ∠H a C a P 
               
               
                 ∠C a PC b   
                 3.52498 
                 3.52498 
                 5.4955 
                 −15.75493 
                 7 
                 −15.75493 
                 7 
                 0.86359 
                 0.86359 
               
               
                 ∠C a PO 
                 3.52498 
                 2.76885 
                 5.3104 
                 −15.95954 
                 10 
                 −15.95954 
                 10 
                 0.85252 
                 0.85252 
               
               
                 Methylene 
                 2.11106 
                 2.11106 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
                 1 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
               
               
                 ∠C a C b H 
               
               
                 Methyl 
                 2.09711 
                 2.09711 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
                 1 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
               
               
                 ∠C a C b H 
               
               
                 ∠C b C a C c   
                 2.91547 
                 2.91547 
                 4.7958 
                 −16.68412 
                 26 
                 −16.68412 
                 26 
                 0.81549 
                 0.81549 
               
               
                 iso C a   
                   
                   
                   
                 C b   
                   
                 C c   
               
               
                 ∠C b C a H 
                 2.91547 
                 2.11323 
                 4.1633 
                 −15.55033 
                 5 
                 −14.82575 
                 1 
                 0.87495 
                 0.91771 
               
               
                 iso C a   
                   
                   
                   
                 C a   
                   
                 C b   
               
               
                 ∠C a C b H 
                 2.91547 
                 2.09711 
                 4.1633 
                 −15.55033 
                 5 
                 −14.82575 
                 1 
                 0.87495 
                 0.91771 
               
               
                 iso C a   
                   
                   
                   
                 C b   
                   
                 C a   
               
               
                 ∠C b C a C b   
                 2.90327 
                 2.90327 
                 4.7958 
                 −16.68412 
                 26 
                 −16.68412 
                 26 
                 0.81549 
                 0.81549 
               
               
                 tert C a   
                   
                   
                   
                 C b   
                   
                 C b   
               
               
                 ∠C b C a C d   
               
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                 E T   
                 θ v   
                 θ 1   
                 θ 2   
                 Cal. θ 
                 Exp. θ 
               
               
                 Atoms of Angle 
                 C 1   
                 C 2   
                 c 1   
                 c 2 ′ 
                 (eV) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
               
               
                   
               
               
                 Methyl 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 109.50 
               
               
                 ∠HC a H 
               
               
                 ∠H a C a P 
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
                 110.7 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (trimethyl 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 phosphine) 
               
               
                 ∠C a PC b   
                 1 
                 1 
                 1 
                 0.86359 
                 −1.85836 
                   
                   
                   
                 102.43 
                 104.31 [72] 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (Ph 2 P(O)CH 2 OH) 
               
               
                 ∠C a PO 
                 1 
                 1 
                 1 
                 0.85252 
                 −1.85836 
                   
                   
                   
                 114.54 
                 114.03 [72] 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (Ph 2 P(O)CH 2 OH) 
               
               
                 Methylene 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 108.44 
                 107 
               
               
                 ∠HC a H 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (propane) 
               
               
                 ∠C a C b C c   
                   
                   
                   
                   
                   
                 69.51 
                   
                   
                 110.49 
                 112 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (propane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 113.8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (butane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 110.8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C a C b H 
                   
                   
                   
                   
                   
                 69.51 
                   
                   
                 110.49 
                 111.0 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (butane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 111.4 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 Methyl 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 109.50 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                 ∠C a C b H 
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                 ∠C b C a C c   
                 1 
                 1 
                 1 
                 0.81549 
                 −1.85836 
                   
                   
                   
                 110.67 
                 110.8 
               
               
                 iso C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C b C a H 
                 0.75 
                 1 
                 0.75 
                 1.04887 
                 0 
                   
                   
                   
                 110.76 
               
               
                 iso C a   
               
               
                 ∠C a C b H 
                 0.75 
                 1 
                 0.75 
                 1.04887 
                 0 
                   
                   
                   
                 111.27 
                 111.4 
               
               
                 iso C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C b C a C b   
                 1 
                 1 
                 1 
                 0.81549 
                 −1.85836 
                   
                   
                   
                 111.37 
                 110.8 
               
               
                 tert C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C b C a C d   
                   
                   
                   
                   
                   
                 72.50 
                   
                   
                 107.50 
               
               
                   
               
             
          
         
       
     
         [0239]    Alkyl Phosphates ((C n H 2n+1 O) 3 P═O, n=1,2,3,4,5 . . . ∞) 
         [0240]    The alkyl phosphates, (C n H 2n+1 O) 3 P═O, comprise P═O, P—O, and C—O functional groups. The P═O functional group is equivalent to that of alkyl phosphine oxides. The P—O and C—O functional groups are equivalent to those of alkyl phosphites. The alkyl portion of the alkyl phosphate may comprise at least two terminal methyl groups (CH 3 ) at each end of each chain, and may comprise methylene (CH 2 ), and methylyne (CH) functional groups as well as C bound by carbon-carbon single bonds. The methyl and methylene functional groups are equivalent to those of straight-chain alkanes. Six types of C—C bonds can be identified. The n-alkane C—C bond is the same as that of straight-chain alkanes. In addition, the C—C bonds within isopropyl ((CH 3 ) 2 CH) and t-butyl ((CH 3 ) 3 C) groups and the isopropyl to isopropyl, isopropyl to t-butyl, and t-butyl to t-butyl C—C bonds comprise functional groups. The branched-chain-alkane groups in alkyl phosphates are equivalent to those in branched-chain alkanes. 
         [0241]    The symbols of the functional groups of branched-chain alkyl phosphates are given in Table 57. The geometrical (Eqs. (15.1-15.5) and (15.51)), intercept (Eqs. (15.80-15.87)), and energy (Eqs. (15.6-15.11) and (15.17-15.65)) parameters of alkyl phosphates are given in Tables 58, 59, and 60, respectively. The total energy of each alkyl phosphate given in Table 61 was calculated as the sum over the integer multiple of each E D (Group) of Table 60 corresponding to functional-group composition of the molecule. The bond angle parameters of alkyl phosphates determined using Eqs. (15.88-15.117) are given in Table 63. The color scale, charge-density of exemplary alkyl phosphate, tri-isopropyl phosphate, comprising of atoms with the outer shell bridged by one or more H 2 -type ellipsoidal MOs or joined with one or more hydrogen MOs is shown in  FIG. 17 . 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 57 
               
             
             
               
                   
               
               
                 The symbols of functional groups of alkyl phosphates. 
               
             
          
           
               
                   
                 Functional Group 
                 Group Symbol 
               
               
                   
                   
               
               
                   
                 P═O 
                 P═O 
               
               
                   
                 P—O 
                 P—O 
               
               
                   
                 C—O (CH 3 —O— and (CH 3 ) 3 C—O—) 
                 C—O (i) 
               
               
                   
                 C—O (alkyl) 
                 C—O (ii) 
               
               
                   
                 CH 2  group 
                 C—H (CH 2 ) 
               
               
                   
                 CH 
                 C—H 
               
               
                   
                 CC bond (n-C) 
                 C—C (a) 
               
               
                   
                 CC bond (iso-C) 
                 C—C (b) 
               
               
                   
                 CC bond (tert-C) 
                 C—C (c) 
               
               
                   
                 CC (iso to iso-C) 
                 C—C (d) 
               
               
                   
                 CC (t to t-C) 
                 C—C (e) 
               
               
                   
                 CC (t to iso-C) 
                 C—C (f) 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 58 
               
               
                   
               
               
                 The geometrical bond parameters of alkyl phosphates and experimental values [1]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 P═O 
                 P—O 
                 C—O (i) 
                 C—O (ii) 
                 C—H (CH 3 ) 
                 C—H (CH 2 ) 
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 1.91663 
                 1.84714 
                 1.80717 
                 1.79473 
                 1.64920 
                 1.67122 
               
               
                 c′ (a 0 ) 
                 1.38442 
                 1.52523 
                 1.34431 
                 1.33968 
                 1.04856 
                 1.05553 
               
               
                 Bond Length 
                 1.46521E−10 
                 1.61423 
                 1.42276 
                 1.41785 
                 1.10974 
                 1.11713 
               
               
                 2c′ (Å) 
               
               
                 Exp. Bond 
                 1.48 [64] 
                 1.631 [69] 
                 1.416 
                 1.418 
                 1.107 
                 1.107 
               
               
                 Length 
                 (DNA) 
                 (MHP) 
                 (dimethyl ether) 
                 (ethyl methyl 
                 (C—H propane) 
                 (C—H propane) 
               
               
                 (Å) 
                 1.4759 
                 1.60 [64] 
                   
                 ether (avg.)) 
                 1.117 
                 1.117 
               
               
                   
                 (PO) 
                 (DNA) 
                   
                   
                 (C—H butane) 
                 (C—H butane) 
               
               
                 b, c (a 0 ) 
                 1.32546 
                 1.04192 
                 1.20776 
                 1.19429 
                 1.27295 
                 1.29569 
               
               
                 e 
                 0.72232 
                 0.82573 
                 0.74388 
                 0.74645 
                 0.63580 
                 0.63159 
               
               
                   
               
             
          
           
               
                   
                 C—H 
                 C—C (a) 
                 C—C (b) 
                 C—C (c) 
                 C—C (d) 
                 C—C (e) 
                 C—C (f) 
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 1.67465 
                 2.12499 
                 2.12499 
                 2.10725 
                 2.12499 
                 2.10725 
                 2.10725 
               
               
                 c′ (a 0 ) 
                 1.05661 
                 1.45744 
                 1.45744 
                 1.45164 
                 1.45744 
                 1.45164 
                 1.45164 
               
               
                 Bond Length 
                 1.11827 
                 1.54280 
                 1.54280 
                 1.53635 
                 1.54280 
                 1.53635 
                 1.53635 
               
               
                 2c′ (Å) 
               
               
                 Exp. Bond 
                 1.122 
                 1.532 
                 1.532 
                 1.532 
                 1.532 
                 1.532 
                 1.532 
               
               
                 Length 
                 (isobutane) 
                 (propane) 
                 (propane) 
                 (propane) 
                 (propane) 
                 (propane) 
                 (propane) 
               
               
                 (Å) 
                   
                 1.531 
                 1.531 
                 1.531 
                 1.531 
                 1.531 
                 1.531 
               
               
                   
                   
                 (butane) 
                 (butane) 
                 (butane) 
                 (butane) 
                 (butane) 
                 (butane) 
               
               
                 b, c (a 0 ) 
                 1.29924 
                 1.54616 
                 1.54616 
                 1.52750 
                 1.54616 
                 1.52750 
                 1.52750 
               
               
                 e 
                 0.63095 
                 0.68600 
                 0.68600 
                 0.68888 
                 0.68600 
                 0.68888 
                 0.68888 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 59 
               
               
                   
               
               
                 The MO to HO intercept geometrical bond parameters of alkyl phosphates. R, R′, R″ are H or alkyl groups. E T  is E T   
               
               
                 (atom-atom, msp 3 .A O). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                 E T   
                 E T   
                 E T   
               
               
                   
                   
                 (eV) 
                 (eV) 
                 (eV) 
               
               
                 Bond 
                 Atom 
                 Bond 1 
                 Bond 2 
                 Bond 3 
               
               
                   
               
               
                 (CH 3 ) 3 P═O 
                 O 
                 −1.13379 
                 0 
                 0 
               
               
                 (CH 3 O) 3 P═O 
                 P 
                 −1.13379 
                 −0.72457 
                 −0.72457 
               
               
                 (CH 3 O) 2 (O)P—OCH 3 (CH 3 O) 2 (O)P—OC(CH 3 ) 3 (C—O (i)) 
                 O 
                 −0.72457 
                 −0.72457 
                 0 
               
               
                 (CH 3 O) 2 (O)P—OCH 3 (CH 3 O) 2 (O)P—OC(CH 3 ) 3 (CH 3 O) 2 (O)P—OCH 2 R(C—O (i)) 
                 P 
                 −0.72457 
                 −0.72457 
                 −0.72457 
               
               
                 and (C—O (ii)) 
               
               
                 (CH 3 O) 2 (O)P—OCH 2 R(C—O (ii)) 
                 O 
                 −0.72457 
                 −0.82688 
                 0 
               
               
                 C—H (OC a H 3 ) 
                 C a   
                 −0.72457 
                 0 
                 0 
               
               
                 (CH 3 O) 2 (O)PO—C a H 3   
                 C a   
                 −0.72457 
                 0 
                 0 
               
               
                 (CH 3 O) 2 (O)PO—C a (CH 3 ) 3 (C—O (i)) 
                 C a   
                 −0.72457 
                 −0.72457 
                 −0.72457 
               
               
                 (H 3 CO) 2 (O)PO—C a H 3(CH   3 ) 3 C a —OP(O)(OC b H 3 ) 2 (C—O (i)) 
                 O 
                 −0.72457 
                 −0.72457 
                 0 
               
               
                 —H 2 C a —OP(O)(OCH 3 ) 2 (C—O (ii)) 
                 C a   
                 −0.82688 
                 −0.92918 
                 0 
               
               
                 (CH 3 O) 2 (O)PO—C a H(CH 3 ) 2 (C—O (ii)) 
                 C a   
                 −0.82688 
                 −0.92918 
                 −0.92918 
               
               
                 —H 2 C a —OP(O)(OCH 3 ) 2 (H 3 C) 2 HC a —OP(O)(OCH 3 ) 2 (C—O (ii)) 
                 O 
                 −0.72457 
                 −0.82688 
                 0 
               
               
                 C—H (CH 3 ) 
                 C 
                 −0.92918 
                 0 
                 0 
               
               
                 C—H (CH 2 ) 
                 C 
                 −0.92918 
                 −0.92918 
                 0 
               
               
                 C—H (CH) 
                 C 
                 −0.92918 
                 −0.92918 
                 −0.92918 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 C a   
                 −0.92918 
                 0 
                 0 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 0 
               
               
                 R—H 2 C a C b (H 2 C c —R′)HCH 2 —(C—C (b)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 −0.92918 
               
               
                 R—H 2 C a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (c)) 
                 C b   
                 −0.92918 
                 −0.72457 
                 −0.72457 
               
               
                 isoC a C b (H 2 C c —R′)HCH 2 —(C—C (d)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 −0.92918 
               
               
                 tertC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (e)) 
                 C b   
                 −0.72457 
                 −0.72457 
                 −0.72457 
               
               
                 tertC a C b (H 2 C c —R′)HCH 2 —(C—C (f)) 
                 C b   
                 −0.72457 
                 −0.92918 
                 −0.92918 
               
               
                 isoC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (f)) 
                 C b   
                 −0.72457 
                 −0.72457 
                 −0.72457 
               
               
                   
               
             
          
           
               
                   
                   
                 Final Total 
                   
                   
               
               
                   
                 E T   
                 Energy 
               
               
                   
                 (eV) 
                 C2sp 3   
                 r initial   
                 r final   
               
               
                 Bond 
                 Bond 4 
                 (eV) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 (CH 3 ) 3 P═O 
                 0 
                   
                 1.00000 
                 0.85252 
               
               
                 (CH 3 O) 3 P═O 
                 −0.72457 
                   
                 1.15350 
                 0.75032 
               
               
                 (CH 3 O) 2 (O)P—OCH 3 (CH 3 O) 2 (O)P—OC(CH 3 ) 3 (C—O (i)) 
                 0 
                   
                 1.00000 
                 0.83600 
               
               
                 (CH 3 O) 2 (O)P—OCH 3(CH   3 O) 2 (O)P—OC(CH 3 ) 3 (CH 3 O) 2 (O)P—OCH 2 R(C—O (i)) 
                 −1.13379 
                   
                 1.15350 
                 0.75032 
               
               
                 and (C—O (ii)) 
               
               
                 (CH 3 O) 2 (O)P—OCH 2 R(C—O (ii)) 
                 0 
                   
                 1.00000 
                 0.83078 
               
               
                 C—H (OC a H 3 ) 
                 0 
                 −152.34026 
                 0.91771 
                 0.87495 
               
               
                 (CH 3 O) 2 (O)PO—C a H 3   
                 0 
                 −152.34026 
                 0.91771 
                 0.87495 
               
               
                 (CH 3 O) 2 (O)PO—C a (CH 3 ) 3 (C—O (i)) 
                 −0.72457 
                 −154.51399 
                 0.91771 
                 0.76765 
               
               
                 (H 3 CO) 2 (O)PO—C a H 3 (CH 3 ) 3 C a —OP(O)(OC b H 3 ) 2 (C—O (i)) 
                 0 
                   
                 1.00000 
                 0.83600 
               
               
                 —H 2 C a —OP(O)(OCH 3 ) 2 (C—O (ii)) 
                 0 
                 −153.37175 
                 0.91771 
                 0.82053 
               
               
                 (CH 3 O) 2 (O)PO—C a H(CH 3 ) 2 (C—O (ii)) 
                 0 
                 −154.30093 
                 0.91771 
                 0.77699 
               
               
                 —H 2 C a —OP(O)(OCH 3 ) 2 (H 3 C) 2 HC a —OP(O)(OCH 3 ) 2 (C—O (ii)) 
                 0 
                   
                 1.00000 
                 0.83078 
               
               
                 C—H (CH 3 ) 
                 0 
                 −152.54487 
                 0.91771 
                 0.86359 
               
               
                 C—H (CH 2 ) 
                 0 
                 −153.47406 
                 0.91771 
                 0.81549 
               
               
                 C—H (CH) 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 0 
                 −152.54487 
                 0.91771 
                 0.86359 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 0 
                 −153.47406 
                 0.91771 
                 0.81549 
               
               
                 R—H 2 C a C b (H 2 C c —R′)HCH 2 —(C—C (b)) 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 R—H 2 C a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (c)) 
                 −0.72457 
                 −154.71860 
                 0.91771 
                 0.75889 
               
               
                 isoC a C b (H 2 C c —R′)HCH 2 —(C—C (d)) 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 tertC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (e)) 
                 −0.72457 
                 −154.51399 
                 0.91771 
                 0.76765 
               
               
                 tertC a C b (H 2 C c —R′)HCH 2 —(C—C (f)) 
                 0 
                 −154.19863 
                 0.91771 
                 0.78155 
               
               
                 isoC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (f)) 
                 −0.72457 
                 −154.51399 
                 0.91771 
                 0.76765 
               
               
                   
               
             
          
           
               
                   
                 E Coulomb   
                   
                 θ′ 
               
               
                 Bond 
                 (eV) Final 
                 E (C2sp 3 ) (eV) Final 
                 (°) 
               
               
                   
               
               
                 (CH 3 ) 3 P═O 
                 −15.95954 
                   
                 84.02 
               
               
                 (CH 3 O) 3 P═O 
                 −18.13326 
                   
                 72.13 
               
               
                 (CH 3 O) 2 (O)P—OCH 3 (CH 3 O) 2 (O)P—OC(CH 3 ) 3 (C—O (i)) 
                 −16.27489 
                   
                 111.08 
               
               
                 (CH 3 O) 2 (O)P—OCH 3 (CH 3 O) 2 (O)P—OC(CH 3 ) 3 (CH 3 O) 2 (O)P—OCH 2 R(C—O (i)) 
                 −18.13326 
                   
                 105.22 
               
               
                 and (C—O (ii)) 
               
               
                 (CH 3 O) 2 (O)P—OCH 2 R(C—O (ii)) 
                 −16.37720 
                   
                 110.75 
               
               
                 C—H (OC a H 3 ) 
                 −15.55033 
                 −15.35946 
                 78.85 
               
               
                 (CH 3 O) 2 (O)PO—C a H 3   
                 −15.55033 
                 −15.35946 
                 95.98 
               
               
                 (CH 3 O) 2 (O)PO—C a (CH 3 ) 3 (C—O (i)) 
                 −17.72405 
                   
                 86.03 
               
               
                 (H 3 CO) 2 (O)PO—C a H 3 (CH 3 ) 3 C a —OP(O)(OC b H 3 ) 2 (C—O (i)) 
                 −16.27490 
                   
                 92.66 
               
               
                 —H 2 C a —OP(O)(OCH 3 ) 2 (C—O (ii)) 
                 −16.58181 
                 −16.39095 
                 92.41 
               
               
                 (CH 3 O) 2 (O)PO—C a H(CH 3 ) 2 (C—O (ii)) 
                 −17.51099 
                 −17.32013 
                 88.25 
               
               
                 —H 2 C a —OP(O)(OCH 3 ) 2 (H 3 C) 2 HC a —OP(O)(OCH 3 ) 2 (C—O (ii)) 
                 −16.37720 
                   
                 93.33 
               
               
                 C—H (CH 3 ) 
                 −15.75493 
                 −15.56407 
                 77.49 
               
               
                 C—H (CH 2 ) 
                 −16.68412 
                 −16.49325 
                 68.47 
               
               
                 C—H (CH) 
                 −17.61330 
                 −17.42244 
                 61.10 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 −15.75493 
                 −15.56407 
                 63.82 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 −16.68412 
                 −16.49325 
                 56.41 
               
               
                 R—H 2 C a C b (H 2 C c —R′)HCH 2 —(C—C (b)) 
                 −17.61330 
                 −17.42244 
                 48.30 
               
               
                 R—H 2 C a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (c)) 
                 −17.92866 
                 −17.73779 
                 48.21 
               
               
                 isoC a C b (H 2 C c —R′)HCH 2 —(C—C (d)) 
                 −17.61330 
                 −17.42244 
                 48.30 
               
               
                 tertC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (e)) 
                 −17.92866 
                 −17.73779 
                 50.04 
               
               
                 tertC a C b (H 2 C c —R′)HCH 2 —(C—C (f)) 
                 −17.40869 
                 −17.21783 
                 52.78 
               
               
                 isoC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (f)) 
                 −17.92866 
                 −17.73779 
                 50.04 
               
               
                   
               
             
          
           
               
                   
                   
                 θ 1   
                 θ 2   
                 d 1   
                 d 2   
               
               
                   
                 Bond 
                 (°) 
                 (°) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
                   
               
               
                   
                 (CH 3 ) 3 P═O 
                 95.98 
                 39.77 
                 1.47318 
                 0.08876 
               
               
                   
                 (CH 3 O) 3 P═O 
                 107.87 
                 32.60 
                 1.61466 
                 0.23024 
               
               
                   
                 (CH 3 O) 2 (O)P—OCH 3 (CH 3 O) 2 (O)P—OC(CH 3 ) 3 (C—O (i)) 
                 68.92 
                 48.48 
                 1.22455 
                 0.30068 
               
               
                   
                 (CH 3 O) 2 (O)P—OCH 3 (CH 3 O) 2 (O)P—OC(CH 3 ) 3 (CH 3 O) 2 (O)P—OCH 2 R(C—O (i)) 
                 74.78 
                 44.02 
                 1.32831 
                 0.19692 
               
               
                   
                 and (C—O (ii)) 
               
               
                   
                 (CH 3 O) 2 (O)P—OCH 2 R(C—O (ii)) 
                 69.25 
                 48.21 
                 1.23087 
                 0.29436 
               
               
                   
                 C—H (OC a H 3 ) 
                 101.15 
                 42.40 
                 1.21777 
                 0.16921 
               
               
                   
                 (CH 3 O) 2 (O)PO—C a H 3   
                 84.02 
                 46.10 
                 1.25319 
                 0.09112 
               
               
                   
                 (CH 3 O) 2 (O)PO—C a (CH 3 ) 3 (C—O (i)) 
                 93.97 
                 39.35 
                 1.39744 
                 0.05313 
               
               
                   
                 (H 3 CO) 2 (O)PO—C a H 3 (CH 3 ) 3 C a —OP(O)(OC b H 3 ) 2 (C—O (i)) 
                 87.34 
                 43.74 
                 1.30555 
                 0.03876 
               
               
                   
                 —H 2 C a —OP(O)(OCH 3 ) 2 (C—O (ii)) 
                 87.59 
                 43.35 
                 1.30512 
                 0.03456 
               
               
                   
                 (CH 3 O) 2 (O)PO—C a H(CH 3 ) 2 (C—O (ii)) 
                 91.75 
                 40.56 
                 1.36345 
                 0.02377 
               
               
                   
                 —H 2 C a —OP(O)(OCH 3 ) 2 (H 3 C) 2 HC a —OP(O)(OCH 3 ) 2 (C—O (ii)) 
                 86.67 
                 43.98 
                 1.29138 
                 0.04829 
               
               
                   
                 C—H (CH 3 ) 
                 102.51 
                 41.48 
                 1.23564 
                 0.18708 
               
               
                   
                 C—H (CH 2 ) 
                 111.53 
                 35.84 
                 1.35486 
                 0.29933 
               
               
                   
                 C—H (CH) 
                 118.90 
                 31.37 
                 1.42988 
                 0.37326 
               
               
                   
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 116.18 
                 30.08 
                 1.83879 
                 0.38106 
               
               
                   
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 123.59 
                 26.06 
                 1.90890 
                 0.45117 
               
               
                   
                 R—H 2 C a C b (H 2 C c —R′)HCH 2 —(C—C (b)) 
                 131.70 
                 21.90 
                 1.97162 
                 0.51388 
               
               
                   
                 R—H 2 C a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (c)) 
                 131.79 
                 21.74 
                 1.95734 
                 0.50570 
               
               
                   
                 isoC a C b (H 2 C c —R′)HCH 2 —(C—C (d)) 
                 131.70 
                 21.90 
                 1.97162 
                 0.51388 
               
               
                   
                 tertC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (e)) 
                 129.96 
                 22.66 
                 1.94462 
                 0.49298 
               
               
                   
                 tertC a C b (H 2 C c —R′)HCH 2 —(C—C (f)) 
                 127.22 
                 24.04 
                 1.92443 
                 0.47279 
               
               
                   
                 isoC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (f)) 
                 129.96 
                 22.66 
                 1.94462 
                 0.49298 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 60 
               
               
                   
               
               
                 The energy parameters (eV) of functional groups of alkyl phosphates. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 P═O 
                 P—O 
                 C—O (i) 
                 C—O (ii) 
                 CH 3   
                 CH 2   
                 CH (i) 
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 n 1   
                 2 
                 1 
                 1 
                 1 
                 3 
                 2 
                 1 
               
               
                 n 2   
                 0 
                 0 
                 0 
                 0 
                 2 
                 1 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.75 
                 0.75 
                 0.75 
               
               
                 C 2   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 2   
                 0.79401 
                 0.79401 
                 0.85395 
                 0.85395 
                 0.91771 
                 0.91771 
                 0.91771 
               
               
                 c 3   
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
               
               
                 c 4   
                 4 
                 2 
                 2 
                 2 
                 1 
                 1 
                 1 
               
               
                 c 5   
                 0 
                 0 
                 0 
                 0 
                 3 
                 2 
                 1 
               
               
                 C 1o   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.75 
                 0.75 
                 0.75 
               
               
                 C 2o   
                 1 
                 0.79401 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 V e  (eV) 
                 −56.96374 
                 −33.27738 
                 −33.15757 
                 −33.47304 
                 −107.32728 
                 −70.41425 
                 −35.12015 
               
               
                 V p  (eV) 
                 9.82777 
                 8.92049 
                 10.12103 
                 10.15605 
                 38.92728 
                 25.78002 
                 12.87680 
               
               
                 T (eV) 
                 14.86039 
                 9.00781 
                 9.17389 
                 9.32537 
                 32.53914 
                 21.06675 
                 10.48582 
               
               
                 V m  (eV) 
                 −7.43020 
                 −4.50391 
                 −4.58695 
                 −4.66268 
                 −16.26957 
                 −10.53337 
                 −5.24291 
               
               
                 E (AO/HO) (eV) 
                 −23.56492 
                 −11.78246 
                 −14.63489 
                 −14.63489 
                 −15.56407 
                 −15.56407 
                 −14.63489 
               
               
                 ΔE H     2     MO  (AO/HO) (eV) 
                 0 
                 0 
                 −1.44915 
                 −1.65376 
                 0 
                 0 
                 0 
               
               
                 E T  (AO/HO) (eV) 
                 −23.56492 
                 −11.78246 
                 −13.18574 
                 −12.98113 
                 −15.56407 
                 −15.56407 
                 −14.63489 
               
               
                 E T  (H 2 MO) (eV) 
                 −63.27069 
                 −31.63544 
                 −31.63533 
                 −31.63544 
                 −67.69451 
                 −49.66493 
                 −31.63533 
               
               
                 E T  (atom-atom, msp 3 .AO) (eV) 
                 −2.26758 
                 −1.44914 
                 −1.44915 
                 −1.65376 
                 0 
                 0 
                 0 
               
               
                 E T  (MO) (eV) 
                 −65.53832 
                 −33.08451 
                 −33.08452 
                 −33.28912 
                 −67.69450 
                 −49.66493 
                 −31.63537 
               
               
                 ω (10 15  rad/s) 
                 11.0170 
                 10.3761 
                 12.0329 
                 12.1583 
                 24.9286 
                 24.2751 
                 24.1759 
               
               
                 E K  (eV) 
                 7.25157 
                 6.82973 
                 7.92028 
                 8.00277 
                 16.40846 
                 15.97831 
                 15.91299 
               
               
                 Ē D  (eV) 
                 −0.17458 
                 −0.17105 
                 −0.18420 
                 −0.18631 
                 −0.25352 
                 −0.25017 
                 −0.24966 
               
               
                 Ē Kvib  (eV) 
                 0.15292 
                 0.10477 
                 0.13663 
                 0.16118 
                 0.35532 
                 0.35532 
                 0.35532 
               
               
                   
                 [24] 
                 [70] 
                 [21] 
                 [4] 
                 (Eq. 
                 (Eq. 
                 (Eq. 
               
               
                   
                   
                   
                   
                   
                 (13.458)) 
                 (13.458)) 
                 (13.458)) 
               
               
                 Ē osc  (eV) 
                 −0.09812 
                 −0.11867 
                 −0.11589 
                 −0.10572 
                 −0.22757 
                 −0.14502 
                 −0.07200 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                 E T  (Group) (eV) 
                 −65.73455 
                 −33.20318 
                 −33.20040 
                 −33.39484 
                 −67.92207 
                 −49.80996 
                 −31.70737 
               
               
                 E initial  (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
               
               
                 E initial  (c 5  AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 −13.59844 
                 −13.59844 
                 −13.59844 
               
               
                 E D  (Group) (eV) 
                 7.19500 
                 3.93340 
                 3.93062 
                 4.12506 
                 12.49186 
                 7.83016 
                 3.32601 
               
               
                   
               
             
          
           
               
                   
                 C—C (a) 
                 C—C (b) 
                 C—C (c) 
                 C—C (d) 
                 C—C (e) 
                 C—C (f) 
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 n 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 n 2   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
               
               
                 C 2   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 2   
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
               
               
                 c 3   
                 0 
                 0 
                 0 
                 1 
                 1 
                 0 
               
               
                 c 4   
                 2 
                 2 
                 2 
                 2 
                 2 
                 2 
               
               
                 c 5   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1o   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
               
               
                 C 2o   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 V e  (eV) 
                 −28.79214 
                 −28.79214 
                 −29.10112 
                 −28.79214 
                 −29.10112 
                 −29.10112 
               
               
                 V p  (eV) 
                 9.33352 
                 9.33352 
                 9.37273 
                 9.33352 
                 9.37273 
                 9.37273 
               
               
                 T (eV) 
                 6.77464 
                 6.77464 
                 6.90500 
                 6.77464 
                 6.90500 
                 6.90500 
               
               
                 V m  (eV) 
                 −3.38732 
                 −3.38732 
                 −3.45250 
                 −3.38732 
                 −3.45250 
                 −3.45250 
               
               
                 E (AO/HO) (eV) 
                 −15.56407 
                 −15.56407 
                 −15.35946 
                 −15.56407 
                 −15.35946 
                 −15.35946 
               
               
                 ΔE H     2     MO  (AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 E T  (AO/HO) (eV) 
                 −15.56407 
                 −15.56407 
                 −15.35946 
                 −15.56407 
                 −15.35946 
                 −15.35946 
               
               
                 E T  (H 2 MO) (eV) 
                 −31.63537 
                 −31.63537 
                 −31.63535 
                 −31.63537 
                 −31.63535 
                 −31.63535 
               
               
                 E T  (atom-atom, msp 3 .AO) (eV) 
                 −1.85836 
                 −1.85836 
                 −1.44915 
                 −1.85836 
                 −1.44915 
                 −1.44915 
               
               
                 E T  (MO) (eV) 
                 −33.49373 
                 −33.49373 
                 −33.08452 
                 −33.49373 
                 −33.08452 
                 −33.08452 
               
               
                 ω (10 15  rad/s) 
                 9.43699 
                 9.43699 
                 15.4846 
                 9.43699 
                 9.55643 
                 9.55643 
               
               
                 E K  (eV) 
                 6.21159 
                 6.21159 
                 10.19220 
                 6.21159 
                 6.29021 
                 6.29021 
               
               
                 Ē D  (eV) 
                 −0.16515 
                 −0.16515 
                 −0.20896 
                 −0.16515 
                 −0.16416 
                 −0.16416 
               
               
                 Ē Kvib  (eV) 
                 0.12312 
                 0.17978 
                 0.09944 
                 0.12312 
                 0.12312 
                 0.12312 
               
               
                   
                 [2] 
                 [4] 
                 [5] 
                 [2] 
                 [2] 
                 [2] 
               
               
                 Ē osc  (eV) 
                 −0.10359 
                 −0.07526 
                 −0.15924 
                 −0.10359 
                 −0.10260 
                 −0.10260 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                 E T  (Group) (eV) 
                 −33.59732 
                 −33.49373 
                 −33.24376 
                 −33.59732 
                 −33.18712 
                 −33.18712 
               
               
                 E initial  (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
               
               
                 E initial  (c 5  AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 E D  (Group) (eV) 
                 4.32754 
                 4.29921 
                 3.97398 
                 4.17951 
                 3.62128 
                 3.91734 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 61 
               
               
                   
               
               
                 The total bond energies of alkyl phosphates calculated using the functional group composition 
               
               
                 and the energies of Table 60 compared to the experimental values [68]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                 C—O 
                   
                   
                   
                 C—C 
               
               
                 Formula 
                 Name 
                 P═O 
                 P—O 
                 C—O (i) 
                 (ii) 
                 CH 3   
                 CH 2   
                 CH (i) 
                 (a) 
               
               
                   
               
               
                 C 6 H 15 O 4 P 
                 Triethyl phosphate 
                 1 
                 3 
                 0 
                 3 
                 3 
                 3 
                 0 
                 3 
               
               
                 C 9 H 21 O 4 P 
                 Tri-n-propyl 
                 1 
                 3 
                 0 
                 3 
                 3 
                 6 
                 0 
                 6 
               
               
                   
                 phosphate 
               
               
                 C 9 H 21 O 4 P 
                 Tri-isopropyl 
                 1 
                 3 
                 0 
                 3 
                 6 
                 0 
                 3 
                 0 
               
               
                   
                 phosphate 
               
               
                 C 9 H 27 O 4 P 
                 Tri-n-butyl 
                 1 
                 3 
                 0 
                 3 
                 3 
                 9 
                 0 
                 9 
               
               
                   
                 phosphate 
               
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                 Calculated 
                   
                   
               
               
                   
                   
                   
                   
                   
                   
                   
                 Total Bond 
                 Experimental 
               
               
                   
                   
                 C—C 
                 C—C 
                 C—C 
                 C—C 
                 C—C 
                 Energy 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 (b) 
                 (c) 
                 (d) 
                 (e) 
                 (f) 
                 (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 C 6 H 15 O 4 P 
                 Triethyl phosphate 
                 0 
                 0 
                 0 
                 0 
                 0 
                 105.31906 
                 104.40400 
                 −0.00876 
               
               
                 C 9 H 21 O 4 P 
                 Tri-n-propyl 
                 0 
                 0 
                 0 
                 0 
                 0 
                 141.79216 
                 140.86778 
                 −0.00656 
               
               
                   
                 phosphate 
               
               
                 C 9 H 21 O 4 P 
                 Tri-isopropyl 
                 6 
                 0 
                 0 
                 0 
                 0 
                 142.09483 
                 141.42283 
                 −0.00475 
               
               
                   
                 phosphate 
               
               
                 C 9 H 27 O 4 P 
                 Tri-n-butyl phosphate 
                 0 
                 0 
                 0 
                 0 
                 0 
                 178.26526 
                 178.07742 
                 −0.00105 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 62 
               
               
                   
               
               
                 The bond angle parameters of alkyl phosphates and experimental values [1]. In the calculation of θ v , the parameters from 
               
               
                 the preceding angle were used. E T  is E T (atom-atom,msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                 2c′ 
                   
                 Atom 1 
                   
                 Atom 2 
                   
                   
               
               
                   
                 2c′ 
                 2c′ 
                 Terminal 
                 E Coulombic   
                 Hybridization 
                   
                 Hybridization 
               
               
                 Atoms of 
                 Bond 1 
                 Bond 2 
                 Atoms 
                 or E 
                 Designation 
                 E Coulombic   
                 Designation 
                 c 2   
                 c 2   
               
               
                 Angle 
                 (a 0 ) 
                 (a 0 ) 
                 (a 0 ) 
                 Atom 1 
                 (Table 7) 
                 Atom 2 
                 (Table 7) 
                 Atom 1 
                 Atom 2 
               
               
                   
               
               
                 ∠POC 
                 3.05046 
                 2.67935 
                 4.9904 
                 −11.78246 
                 Psp 3   
                 −15.75493 
                 7 
                 0.73885 
                 0.86359 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Eq. 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 (15.181) 
               
               
                 ∠O a PO a   
                 3.05046 
                 3.05046 
                 4.7539 
                 −15.95954 
                 10 
                 −15.95954 
                 10 
                 0.85252 
                 0.85252 
               
               
                 ∠O a PO b   
                 3.05046 
                 2.76885 
                 4.7539 
                 −15.95954 
                 10 
                 −15.95954 
                 10 
                 0.85252 
                 0.85252 
               
               
                 ∠C b C a O(C a —O 
                 2.91547 
                 2.67935 
                 4.5607 
                 −16.68412 
                 26 
                 −13.61806 
                 O 
                 0.81549 
                 0.85395 
               
               
                 (ii)) 
                   
                   
                   
                   
                   
                   
                   
                   
                 (Eq. 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (15.133)) 
               
               
                 Methylene 
                 2.11106 
                 2.11106 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
                 1 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
               
               
                 ∠C a C b H 
               
               
                 Methyl 
                 2.09711 
                 2.09711 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
                 1 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
               
               
                 ∠C a C b H 
               
               
                 ∠C b C a C c   
                 2.91547 
                 2.91547 
                 4.7958 
                 −16.68412 
                 26 
                 −16.68412 
                 26 
                 0.81549 
                 0.81549 
               
               
                 iso C a   
                   
                   
                   
                 C b   
                   
                 C c   
               
               
                 ∠C b C a H 
                 2.91547 
                 2.11323 
                 4.1633 
                 −15.55033 
                 5 
                 −14.82575 
                 1 
                 0.87495 
                 0.91771 
               
               
                 iso C a   
                   
                   
                   
                 C a   
                   
                 C b   
               
               
                 ∠C a C b H 
                 2.91547 
                 2.09711 
                 4.1633 
                 −15.55033 
                 5 
                 −14.82575 
                 1 
                 0.87495 
                 0.91771 
               
               
                 iso C a   
                   
                   
                   
                 C b   
                   
                 C a   
               
               
                 ∠C b C a C b   
                 2.90327 
                 2.90327 
                 4.7958 
                 −16.68412 
                 26 
                 −16.68412 
                 26 
                 0.81549 
                 0.81549 
               
               
                 tert C a   
                   
                   
                   
                 C b   
                   
                 C b   
               
               
                 ∠C b C a C d   
               
               
                   
               
             
          
           
               
                 Atoms of 
                   
                   
                   
                   
                 E T   
                 θ v   
                 θ 1   
                 θ 2   
                 Cal. θ 
                 Exp. θ 
               
               
                 Angle 
                 C 1   
                 C 2   
                 c 1   
                 c 2 ′ 
                 (eV) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
               
               
                   
               
               
                 ∠POC 
                 1 
                 0.73885 
                 1 
                 0.80122 
                 −0.72457 
                   
                   
                   
                 121.00 
                 122.2 [69] 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (MHPO) 
               
               
                 ∠O a PO a   
                 1 
                 1 
                 1 
                 0.85252 
                 −1.65376 
                   
                   
                   
                 102.38 
                 101.4 [64] 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (DNA) 
               
               
                 ∠O a PO b   
                 1 
                 1 
                 1 
                 0.85395 
                 −1.65376 
                   
                   
                   
                 109.46 
                 109.7 [64] 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (DNA) 
               
               
                 ∠C b C a O(C a —O 
                 1 
                 1 
                 1 
                 0.83472 
                 −1.65376 
                   
                   
                   
                 109.13 
                 109.4 
               
               
                 (ii)) 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (ethyl methyl 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 ether) 
               
               
                 Methylene 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 108.44 
                 107   
               
               
                 ∠HC a H 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (propane) 
               
               
                 ∠C a C b C c   
                   
                   
                   
                   
                   
                 69.51 
                   
                   
                 110.49 
                 112   
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (propane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 113.8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (butane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 110.8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C a C b H 
                   
                   
                   
                   
                   
                 69.51 
                   
                   
                 110.49 
                 111.0 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (butane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 111.4 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 Methyl 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 109.50 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                 ∠C a C b H 
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                 ∠C b C a C c   
                 1 
                 1 
                 1 
                 0.81549 
                 −1.85836 
                   
                   
                   
                 110.67 
                 110.8 
               
               
                 iso C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C b C a H 
                 0.75 
                 1 
                 0.75 
                 1.04887 
                 0 
                   
                   
                   
                 110.76 
               
               
                 iso C a   
               
               
                 ∠C a C b H 
                 0.75 
                 1 
                 0.75 
                 1.04887 
                 0 
                   
                   
                   
                 111.27 
                 111.4 
               
               
                 iso C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C b C a C b   
                 1 
                 1 
                 1 
                 0.81549 
                 −1.85836 
                   
                   
                   
                 111.37 
                 110.8 
               
               
                 tert C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C b C a C d   
                   
                   
                   
                   
                   
                 72.50 
                   
                   
                 107.50 
               
               
                   
               
             
          
         
       
     
         [0242]    Organic and Related Ions (RCO 2   − , ROSO 3   − , NO 3   − , (RO) 2 PO 2   − (RO) 3 SiO − , (R) 2 Si(O − ) 2 , RNH 3   + , R 2 NH 2   + ) 
         [0243]    Proteins comprising amino acids with amino and carboxylic acid groups are charged at physiological pH. Deoxyribonucleic acid (DNA), the genetic material of living organisms also comprises negatively charged phosphate groups. Thus, the bonding of organic ions is considered next. The molecular ions also comprise functional groups that have an additional electron or are deficient by an electron in the cases of monovalent molecular anions and cations, respectively. The molecular chemical bond typically comprises an even integer number of paired electrons, but with an excess of deficiency, the bonding may involve and odd number of electrons, and the electrons may be distributed over multiple bonds, solved as a linear combination of standard bonds. As given in the Benzene Molecule section and other sections on aromatic molecules such as naphthalene, toluene, chlorobenzene, phenol, aniline, nitrobenzene, benzoic acid, pyridine, pyrimidine, pyrazine, quinoline, isoquinoline, indole, and adenine, the paired electrons of MOs may be distributed over a linear combination of bonds such that the bonding between two atoms involves less than an integer multiple of two electrons. Specifically, the results of the derivation of the parameters of the benzene molecule given in the Benzene Molecule (C 6 H 6 ) section was generalized to any aromatic functional group of aromatic and heterocyclic compounds in the Aromatic and Heterocyclic Compounds section. Ethylene serves as a basis element for the C 3e ═C bonding of the aromatic bond wherein each of the C 3e ═C aromatic bonds comprises (0.75)(4)=3 electrons according to Eq. (15.161). Thus, in these aromatic cases, three electrons can be assigned to a given bond between two atoms wherein the electrons of the linear combination of bonded atoms are paired and comprise an integer multiple of two. 
         [0244]    In graphite, the minimum energy structure with equivalent carbon atoms wherein each carbon forms bonds with three other such carbons requires a redistribution of charge within an aromatic system of bonds. Considering that each carbon contributes four bonding electrons, the sum of electrons of a vertex-atom group is four from the vertex atom plus two from each of the two atoms bonded to the vertex atom where the latter also contribute two each to the juxtaposed group. These eight electrons are distributed equivalently over the three bonds of the group such that the electron number assignable to each bond is 8/3. Thus, the C 8/2e ═C functional group of graphite comprises the aromatic bond with the exception that the electron-number per bond is 8/3. 
         [0245]    As given in the Bridging Bonds of Boranes section and the Bridging Bonds of Organoaluminum Hydrides section, other examples of electron deficient bonding involving two paired electrons centered on three atoms are three-center bonds as opposed to the typical single bond, a two-center bond. The B2sp 3  HOs comprise four orbitals containing three electrons as given by Eq. (23.1) that can form three-center as well as two-center bonds. The designation for a three-center bond involving two B2sp 3  HOs and a H1s AO is B—H—B, and the designation for a three-center bond involving three B2sp 3  HOs is B—B—B. In the aluminum case, each Al—H—Al-bond MO and Al—C—Al-bond MO comprises the corresponding single bond and forms with further sharing of electrons between each Al3sp 3  HO and each H1s AO and C2sp 3  HO, respectively. Thus, the geometrical and energy parameters of the three-center bond are equivalent to those of the corresponding two-center bonds except that the bond energy is increased in the former case since the donation of electron density from the unoccupied Al3sp 3  HO to each Al—H—Al-bond MO and Al—C—Al-bond MO permits the participating orbital to decrease in size and energy. 
         [0246]    To match the energies of the AOs and MOs of the ionic functional group with the others within the molecular ion, the bonding in organic ions comprises a standard bond that serves as basis element and retains the same geometrical characteristics as that standard bond. In the case of organic oxyanions, the A-O −  (A=C, S, N, P, Si) bond is intermediate between a single and double bond, and the latter serves as a basis element. Similar to the case of the C 3e ═C aromatic bond wherein ethylene is the basis element, the A=O-bond functional group serves as the basis element for the A-O −  functional group of the oxyanion of carboxylates, sulfates, nitrates, phosphates, silanolates, and siloxanolates. This oxyanion group designated by A 3e =O −  comprises (0.75)(4)=3 electrons after Eq. (15.161). Thus, the energy parameters of the A 3e =O −  function group are given by the factor of (0.75)(4)=3 times those of the corresponding A=O functional group, and the geometric parameters are the same. The C═O, S═O, N═O 2 , P═O, and Si═O basis elements are given in the Carboxylic Acids, Sulfates, Alkyl Nitrates, Phosphates, and Silicon Oxides, Silicic Acids, Silanols, Siloxanes and Disiloxanes sections, respectively. A convenient means to obtain the final group energy parameters of E T (Group) and E D (Group) is by using Eqs. (15.165-15.166) with f 1 =0.75: 
         [0000]    
       
         
           
             
               
                 
                   
                     E 
                     
                       T 
                       
                         ( 
                         Group 
                         ) 
                       
                     
                   
                   = 
                   
                     
                       f 
                       1 
                     
                      
                     
                       ( 
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       
                                         
                                           
                                             E 
                                              
                                             
                                               ( 
                                               
                                                 basis 
                                                  
                                                 
                                                     
                                                 
                                                  
                                                 energies 
                                               
                                               ) 
                                             
                                           
                                           + 
                                         
                                       
                                     
                                     
                                       
                                         
                                           
                                             
                                               E 
                                               T 
                                             
                                              
                                             
                                               ( 
                                               
                                                 
                                                   atom 
                                                   - 
                                                   atom 
                                                 
                                                 , 
                                                 
                                                   
                                                     msp 
                                                     3 
                                                   
                                                   · 
                                                   AO 
                                                 
                                               
                                               ) 
                                             
                                           
                                           - 
                                         
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     31.63536831 
                                      
                                     
                                         
                                     
                                      
                                     eV 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   
                                     2 
                                      
                                     ℏ 
                                      
                                     
                                       
                                         
                                           
                                             C 
                                             
                                               1 
                                                
                                               o 
                                             
                                           
                                            
                                           
                                             C 
                                             
                                               2 
                                                
                                               o 
                                             
                                           
                                            
                                           
                                              
                                             2 
                                           
                                         
                                         
                                           4 
                                            
                                           
                                             πɛ 
                                             o 
                                           
                                            
                                           
                                             R 
                                             3 
                                           
                                         
                                       
                                       
                                         m 
                                         e 
                                       
                                     
                                   
                                   
                                     
                                       m 
                                       e 
                                     
                                      
                                     
                                       c 
                                       2 
                                     
                                   
                                 
                               
                               + 
                               
                                 
                                   n 
                                   1 
                                 
                                  
                                 
                                   
                                     E 
                                     _ 
                                   
                                   Kvib 
                                 
                               
                               + 
                               
                                 
                                   c 
                                   3 
                                 
                                  
                                 
                                   
                                     8 
                                      
                                     
                                       πμ 
                                       o 
                                     
                                      
                                     
                                       μ 
                                       B 
                                       2 
                                     
                                   
                                   
                                     r 
                                     3 
                                   
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   15.183 
                   ) 
                 
               
             
             
               
                 
                   
                     E 
                     
                       D 
                       
                         ( 
                         Group 
                         ) 
                       
                     
                   
                   = 
                   
                     - 
                     
                       ( 
                       
                         
                           
                             
                               
                                 
                                   f 
                                   1 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       
                                         
                                           
                                             
                                               
                                                 
                                                   
                                                     
                                                       
                                                         E 
                                                          
                                                         
                                                           ( 
                                                           
                                                             basis 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             energies 
                                                           
                                                           ) 
                                                         
                                                       
                                                       + 
                                                     
                                                   
                                                 
                                                 
                                                   
                                                     
                                                       
                                                         
                                                           E 
                                                           T 
                                                         
                                                          
                                                         
                                                           ( 
                                                           
                                                             
                                                             atom 
                                                             - 
                                                             atom 
                                                             
                                                             , 
                                                             
                                                             
                                                             msp 
                                                             3 
                                                             
                                                             · 
                                                             AO 
                                                             
                                                           
                                                           ) 
                                                         
                                                       
                                                       - 
                                                     
                                                   
                                                 
                                               
                                             
                                           
                                           
                                             
                                               
                                                 31.63536831 
                                                  
                                                 
                                                     
                                                 
                                                  
                                                 eV 
                                               
                                             
                                           
                                         
                                       
                                     
                                     
                                       
                                         
                                           
                                             
                                               
                                                 2 
                                                  
                                                 ℏ 
                                                  
                                                 
                                                   
                                                     
                                                       
                                                         
                                                           C 
                                                           
                                                             1 
                                                              
                                                             o 
                                                           
                                                         
                                                          
                                                         
                                                           C 
                                                           
                                                             2 
                                                              
                                                             o 
                                                           
                                                         
                                                          
                                                         
                                                            
                                                           2 
                                                         
                                                       
                                                       
                                                         4 
                                                          
                                                         
                                                           πɛ 
                                                           o 
                                                         
                                                          
                                                         
                                                           R 
                                                           3 
                                                         
                                                       
                                                     
                                                     
                                                       m 
                                                       e 
                                                     
                                                   
                                                 
                                               
                                               
                                                 
                                                   m 
                                                   e 
                                                 
                                                  
                                                 
                                                   c 
                                                   2 
                                                 
                                               
                                             
                                           
                                           + 
                                         
                                       
                                     
                                     
                                       
                                         
                                           
                                             
                                               n 
                                               1 
                                             
                                              
                                             
                                               
                                                 E 
                                                 _ 
                                               
                                               Kvib 
                                             
                                           
                                           + 
                                           
                                             
                                               c 
                                               3 
                                             
                                              
                                             
                                               
                                                 8 
                                                  
                                                 
                                                   πμ 
                                                   o 
                                                 
                                                  
                                                 
                                                   μ 
                                                   B 
                                                   2 
                                                 
                                               
                                               
                                                 r 
                                                 3 
                                               
                                             
                                           
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                               - 
                             
                           
                         
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     
                                       
                                         
                                           c 
                                           4 
                                         
                                          
                                         
                                           
                                             E 
                                             initial 
                                           
                                            
                                           
                                             ( 
                                             
                                               AO 
                                               / 
                                               HO 
                                             
                                             ) 
                                           
                                         
                                       
                                       + 
                                     
                                   
                                 
                                 
                                   
                                     
                                       
                                         c 
                                         5 
                                       
                                        
                                       
                                         
                                           E 
                                           initial 
                                         
                                          
                                         
                                           ( 
                                           
                                             
                                               c 
                                               5 
                                             
                                              
                                             
                                               AO 
                                               / 
                                               HO 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   15.184 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where c 4  is (0.75)(4)=3 when c 5 =0 and otherwise c 4  is (0.75)(2)=1.5 and c 5  is (0.75)(2)=1.5. 
         [0247]    The nature of the bonding of the amino functional group of protonated amines is similar to that in H 3   + . As given in the Triatomic Molecular Hydrogen-type Ion (H 3   + ) section, H 3   +  comprises two indistinguishable spin-paired electrons bound by three protons. The ellipsoidal molecular orbital (MO) satisfies the boundary constraints as shown in the Nature of the Chemical Bond of Hydrogen-Type Molecules section. Since the protons are indistinguishable, ellipsoidal MOs about each pair of protons taken one at a time are indistinguishable. H 3   +  is then given by a superposition or linear combinations of three equivalent ellipsoidal MOs that form a equilateral triangle where the points of contact between the prolate spheroids are equivalent in energy and charge density. The due to the equivalence of the H 2 -type ellipsoidal MOs and the linear superposition of their energies, the energy components defined previously for the H 2  molecule, Eqs. (11.207-11.212) apply in the case of the corresponding H 3   +  molecular ion. And, each molecular energy component is given by the integral of corresponding force in Eq. (13.5). Each energy component is the total for the two equivalent electrons with the exception that the total charge of the two electrons is normalized over the three basis set H 2 -type ellipsoidal MOs. Thus, the energies (Eqs. (13.12-13.17)) are those given for in the Energies of Hydrogen-Type Molecules section with the electron charge, where it appears, multiplied by a factor of 3/2, and the three sets of equivalent proton-proton pairs give rise to a factor of three times the proton-proton repulsion energy given by Eq. (11.208). 
         [0248]    With the protonation of the imidogen (NH) functional group, the minimum energy structure with equivalent hydrogen atoms comprises two protons bound to N by two paired electrons, one from H and one from N with the MO matched to the N2p AO. These two electrons are distributed equivalently over the two H—N bonds of the group such that the electron number assignable to each bond is 2/2. Thus, the NH 2   +  functional group has the imidogen energy parameters with the exception that each energy term is multiplied by the factor 2 due to the two bonds with electron-number per bond of 2/2 and has the same geometric parameters as the NH functional group given in the Secondary Amines section. A convenient means to obtain the final group energy parameters of E T (Group) and E D (Group) is by using Eqs. (15.165-15.166) (Eqs. (15.183-15.184)) with f 1 =2 and c 4  and c 5  multiplied by two. 
         [0249]    With the protonation of the amidogen (NH 2 ) functional group, the minimum energy structure with equivalent hydrogen atoms comprises three protons bound to N by four paired electrons, two from 2 H and two from N with the MO matched to the N2p AO. These four electrons are distributed equivalently over the three H—N bonds of the group such that the electron number assignable to each bond is 4/3. Thus, the NH 3   +  functional group has the amidogen energy parameters with the exception that each energy term is multiplied by the factor 3/2 due to the three bonds with electron-number per bond of 4/3 and has the same geometric parameters as the NH 2  functional group given in the Primary Amines section. A convenient means to obtain the final group energy parameters of E T (Group,) and E D (Group) is by using Eqs. (15.165-15.166) (Eqs. (15.183-15.184)) with f 1 =3/2 and c 4  and c 5  multiplied by 3/2. 
         [0250]    The symbols of the functional groups of organic and related ions are given in Table 63. The geometrical (Eqs. (15.1-15.5) and (15.51)), intercept (Eqs. (15.80-15.87)), and energy (Eqs. (15.6-15.11) and (15.17-15.65)) parameters are given in Tables 64, 65, and 66, respectively. Due to its charge, the bond angles of the organic and related ions that minimize the total energy are those that maximize the separation of the groups. For ions having three bonds to the central atom, the angles are 120°, and ions having four bonds are tetrahedral. The color scale, charge-density of exemplary organic ion, protonated lysine, comprising atoms with the outer shell bridged by one or more H 2 -type ellipsoidal MOs or joined with one or more hydrogen MOs is shown in  FIG. 18 . 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 63 
               
             
             
               
                   
               
               
                 The symbols of functional groups of organic and related ions. 
               
             
          
           
               
                   
                 Functional Group 
                 Group Symbol 
               
               
                   
                   
               
               
                   
                 (O)C—O −  (alkyl carboxylate) 
                 C—O −   
               
               
                   
                 (RO)(O) 2 S—O −  (alkyl sulfate) 
                 S—O −   
               
               
                   
                 (O) 2 N—O −  (nitrate) 
                 N—O −   
               
               
                   
                 (RO) 2 (O)P—O −  (alkyl phosphate) 
                 P—O −   
               
               
                   
                 (RO) 3 Si—O −  (alkyl siloxanolate) 
                 Si—O −   
               
               
                   
                 (R) 2 Si(—O − ) 2  (alkyl silanolate) 
               
               
                   
                 NH 2   +  group 
                 NH 2   +   
               
               
                   
                 NH 3   +  group 
                 NH 3   +   
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 64 
               
             
             
               
                   
               
               
                 The geometrical bond parameters of organic and related ions and experimental values of 
               
               
                 corresponding basis elements [1]. 
               
             
          
           
               
                   
                 C—O −   
                 S—O −   
                 N—O −   
                 P—O −   
                 Si—O −   
                 NH 2   +   
                 NH 3   +   
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 1.29907 
                 1.98517 
                 1.29538 
                 1.91663 
                 2.24744 
                 1.26224 
                 1.28083 
               
               
                 c′ (a 0 ) 
                 1.13977 
                 1.40896 
                 1.13815 
                 1.38442 
                 1.41056 
                 0.94811 
                 0.95506 
               
               
                 Bond Length 
                 1.20628 
                 1.49118 
                 1.20456 
                 1.46521 
                 1.49287 
                 1.00343 
                 1.0108  
               
               
                 2c′ (Å) 
               
               
                 Exp. Bond 
                 1.214  
                 1.485  
                 1.205  
                 1.48 [64] 
                 1.509  
                 1.00  
                 1.010  
               
               
                 Length 
                 (acetic acid) 
                 (dimethyl 
                 (methyl 
                 (DNA) 
                 (silicon 
                 (dimethylamine) 
                 (methylamine) 
               
               
                 (Å) 
                   
                 sulfoxide) 
                 nitrate) 
                   
                 oxide) 
               
               
                   
                   
                   
                 1.2   
                   
                 [73] 
               
               
                   
                   
                   
                 (HNO 2 ) 
               
               
                 b, c (a 0 ) 
                 0.62331 
                 1.39847 
                 0.61857 
                 1.32546 
                 1.74966 
                 0.83327 
                 0.85345 
               
               
                 e 
                 0.87737 
                 0.70974 
                 0.87862 
                 0.72232 
                 0.62763 
                 0.75113 
                 0.74566 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 65 
               
               
                   
               
               
                 The MO to HO intercept geometrical bond parameters of organic and related ions. E T  is E T (atom-atom,msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 Final Total 
                   
                   
               
               
                   
                   
                 E T   
                 E T   
                 E T   
                 E T   
                 Energy 
               
               
                   
                   
                 (eV) 
                 (eV) 
                 (eV) 
                 (eV) 
                 C2sp 3   
                 r initial   
                 r final   
               
               
                 Bond 
                 Atom 
                 Bond 1 
                 Bond 2 
                 Bond 3 
                 Bond 4 
                 (eV) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 RH 2 C b C a (O)—O −   
                 O 
                 −1.01210 
                 0 
                 0 
                 0 
                   
                 1.00000 
                 0.85907 
               
               
                 RH 2 C b C a (O)—O −   
                 C a   
                 −1.01210 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.48615 
                 0.91771 
                 0.76885 
               
               
                 (RO) 2 (O)S—O −   
                 S 
                 0 
                 −0.46459 
                 −0.46459 
                 0 
                   
                 1.32010 
                 0.86359 
               
               
                 (RO) 2 (O)S—O −   
                 O 
                 0 
                 0 
                 0 
                 0 
                   
                 1.00000 
                 0.91771 
               
               
                 O 2 N—O −   
                 O 
                 −0.69689 
                 0 
                 0 
                 0 
                   
                 1.00000 
                 0.87651 
               
               
                 O 2 N—O −   
                 N 
                 −0.92918 
                 −0.92918 
                 −0.69689 
                 0 
                   
                 0.93084 
                 0.78280 
               
               
                 (RO) 2 (O)P—O −   
                 P 
                 −0.72457 
                 −0.72457 
                 −1.13379 
                 −0.85034 
                   
                 1.15350 
                 0.74515 
               
               
                 (RO) 2 (O)P—O −   
                 O 
                 −0.85034 
                 0 
                 0 
                 0 
                   
                 1.00000 
                 0.86793 
               
               
                 (RO) 3 Si—O −   
                 Si 
                 −1.55205 
                 −0.62217 
                 −0.62217 
                 −0.62217 
                   
                 1.31926 
                 0.99082 
               
               
                 (RO) 3 Si—O −   
                 O 
                 −1.55205 
                 0 
                 0 
                 0 
                   
                 1.00000 
                 0.89688 
               
               
                 —H 2 C a NH(R alkyl )—H +   
                 N 
                 −0.56690 
                 −0.56690 
                 0 
                 0 
                   
                 0.93084 
                 0.85252 
               
               
                 —H 2 C a N(H 2 )—H +   
                 N 
                 −0.72457 
                 0 
                 0 
                 0 
                   
                 0.93084 
                 0.87495 
               
               
                   
               
             
          
           
               
                   
                 E Coulomb  (C2sp 3 ) 
                 E(C2sp 3 ) 
                   
                   
                   
                   
                   
               
               
                   
                 (eV) 
                 (eV) 
                 θ′ 
                 θ 1   
                 θ 2   
                 d 1   
                 d 2   
               
               
                 Bond 
                 Final 
                 Final 
                 (°) 
                 (°) 
                 (°) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 RH 2 C b C a (O)—O −   
                 −15.83785 
                   
                 137.99 
                 42.01 
                 67.29 
                 0.50150 
                 0.63827 
               
               
                 RH 2 C b C a (O)—O −   
                 −17.69621 
                 −17.50535 
                 134.14 
                 45.86 
                 62.28 
                 0.60433 
                 0.53544 
               
               
                 (RO) 2 (O)S—O −   
                 −15.75493 
                   
                 78.56 
                 101.44 
                 37.25 
                 1.58026 
                 0.17130 
               
               
                 (RO) 2 (O)S—O −   
                 −14.82575 
                   
                 84.06 
                 95.94 
                 40.75 
                 1.50400 
                 0.09504 
               
               
                 O 2 N—O −   
                 −15.52264 
                   
                 135.13 
                 44.87 
                 63.23 
                 0.58339 
                 0.55475 
               
               
                 O 2 N—O −   
                 −17.38100 
                   
                 138.99 
                 41.01 
                 68.41 
                 0.47673 
                 0.66142 
               
               
                 (RO) 2 (O)P—O −   
                 −18.25903 
                   
                 71.42 
                 108.58 
                 32.20 
                 1.62182 
                 0.23739 
               
               
                 (RO) 2 (O)P—O −   
                 −15.67609 
                   
                 85.55 
                 94.45 
                 40.76 
                 1.45184 
                 0.06742 
               
               
                 (RO) 3 Si—O −   
                 −13.73181 
                   
                 53.34 
                 126.66 
                 27.02 
                 2.00216 
                 0.59160 
               
               
                 (RO) 3 Si—O −   
                 −15.17010 
                   
                 34.26 
                 145.74 
                 16.77 
                 2.15183 
                 0.74128 
               
               
                 —H 2 C a NH(R alkyl )—H +   
                 −15.95954 
                   
                 118.18 
                 61.82 
                 64.40 
                 0.54546 
                 0.40264 
               
               
                 —H 2 C a N(H 2 )—H +   
                 −15.55033 
                   
                 118.00 
                 62.00 
                 64.85 
                 0.54432 
                 0.41075 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 66 
               
             
             
               
                   
               
               
                 The energy parameters (eV) of functional groups of organic and related ions. 
               
             
          
           
               
                   
                 C—O −   
                 S—O −   
                 N—O −   
                 P—O −   
                 Si—O −   
                 NH 2   +   
                 NH 3   +   
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
             
          
           
               
                 f 1   
                 0.75 
                 0.75 
                 0.75 
                 0.75 
                 0.75 
                 2 
                 3/2 
               
               
                 n 1   
                 2 
                 2 
                 2 
                 2 
                 2 
                 1 
                 2 
               
               
                 n 2   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
               
               
                 C 1   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.75 
                 0.75 
                 0.75 
               
               
                 C 2   
                 1 
                 1 
                 1 
                 1 
                 0.75304 
                 0.93613 
                 0.93613 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 0.75 
                 0.75 
               
               
                 c 2   
                 0.85395 
                 1.20632 
                 0.85987 
                 0.78899 
                 1 
                 0.93383 
                 0.94627 
               
               
                 c 3   
                 2 
                 0 
                 0 
                 0 
                 0 
                 1 
                 0 
               
               
                 c 4   
                 4 
                 4 
                 4 
                 4 
                 2 
                 1 
                 1 
               
               
                 c 5   
                 0 
                 1 
                 0 
                 0 
                 2 
                 1 
                 2 
               
               
                 C 1o   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.75 
                 0.75 
                 1.5 
               
               
                 C 2o   
                 1 
                 1 
                 1 
                 1 
                 0.75304 
                 1 
                 1 
               
               
                 V e  (eV) 
                 −111.25473 
                 −82.63003 
                 −112.63415 
                 −56.96374 
                 −56.90923 
                 −39.21967 
                 −77.89897 
               
               
                 V p  (eV) 
                 23.87467 
                 19.31325 
                 23.90868 
                 9.82777 
                 19.29141 
                 14.35050 
                 28.49191 
               
               
                 T (eV) 
                 42.82081 
                 20.81183 
                 43.47534 
                 14.86039 
                 12.66092 
                 15.53581 
                 30.40957 
               
               
                 V m  (eV) 
                 −21.41040 
                 −10.40592 
                 −21.73767 
                 −7.43020 
                 −6.33046 
                 −7.76790 
                 −15.20478 
               
               
                 E(AO/HO) (eV) 
                 0 
                 −11.52126 
                 0 
                 −11.78246 
                 −20.50975 
                 −14.53414 
                 −14.53414 
               
               
                 ΔE H     2     MO (AO/HO) (eV) 
                 −2.69893 
                 −1.16125 
                 −3.71673 
                 0 
                 0 
                 0 
                 0 
               
               
                 E(n 3  AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 −14.53414 
               
               
                 E T (AO/HO) (eV) 
                 2.69893 
                 −10.36001 
                 3.71673 
                 −11.78246 
                 −20.50975 
                 −14.53414 
                 −14.53414 
               
               
                 E T (H 2 MO) (eV) 
                 −63.27074 
                 −63.27088 
                 −63.27107 
                 −63.27069 
                 −51.79710 
                 −31.63541 
                 −48.73642 
               
               
                 E T (atom-atom,msp 3 .AO) (eV) 
                 −2.69893 
                 0 
                 −3.71673 
                 −2.26758 
                 −4.13881 
                 0 
                 0 
               
               
                 E T (MO) (eV) 
                 −65.96966 
                 −63.27074 
                 −66.98746 
                 −65.53832 
                 −55.93591 
                 −31.63537 
                 48.73660 
               
               
                 ω(10 15  rad/s) 
                 59.4034 
                 17.6762 
                 19.8278 
                 11.0170 
                 9.22130 
                 47.0696 
                 64.2189 
               
               
                 E K  (eV) 
                 39.10034 
                 11.63476 
                 13.05099 
                 7.25157 
                 6.06962 
                 30.98202 
                 42.27003 
               
               
                 Ē D  (eV) 
                 −0.40804 
                 −0.21348 
                 −0.23938 
                 −0.17458 
                 −0.13632 
                 −0.34836 
                 −0.40690 
               
               
                 Ē Kvib  (eV) 
                 0.21077 [12] 
                 0.12832 [43] 
                 0.19342 [45] 
                 0.12337 [74] 
                 0.15393 [24] 
                 0.40696 [24] 
                 0.40929 [22] 
               
               
                 Ē osc  (eV) 
                 −0.30266 
                 −0.14932 
                 −0.14267 
                 −0.11289 
                 −0.05935 
                 −0.14488 
                 −0.20226 
               
               
                 E mag  (eV) 
                 0.11441 
                 0.11441 
                 0.11441 
                 0.14803 
                 0.04983 
                 0.14803 
                 0.14803 
               
               
                 E T (Group) (eV) 
                 −49.93123 
                 −47.67703 
                 −50.45460 
                 −49.32308 
                 −42.04096 
                 −63.56050 
                 −73.71167 
               
               
                 E initial (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −10.25487 
                 −14.53414 
                 −14.53414 
               
               
                 E initial (c 5  AO/HO) (eV) 
                 0 
                 −1.16125 
                 0 
                 0 
                 −13.61805 
                 −13.59844 
                 −13.59844 
               
               
                 E D (Group) (eV) 
                 6.02656 
                 2.90142 
                 6.54994 
                 5.41841 
                 6.23157 
                 7.01164 
                 11.11514 
               
               
                   
               
             
          
         
       
     
         [0251]    Monosaccharides of DNA and RNA 
         [0252]    The simple sugar moiety of DNA and RNA comprises the alpha forms of 2-deoxy-D-ribose and D-ribose, respectively. The sugars comprise the alkyl CH 2 , CH, and C—C functional groups and the alkyl alcohol C—O and OH functional groups given in the Alcohols section. In addition, the alpha form of the sugars comprise the C—O ether functional group given in the Ethers section, and the open-chain forms further comprise the carbon to carbonyl C—C, the methylyne carbon of the aldehyde carbonyl CH, and the aldehyde carbonyl C═O functional groups given in the Aldehydes section. The total energy of each sugar given in Tables 67-70 was calculated as the sum over the integer multiple of each E D (Group) corresponding to the functional-group composition wherein the group identity and energy E D (Group) are given in each table. The color scale, charge-density of the monosaccharides, 2-deoxy-D-ribose, D-ribose, Alpha-2-deoxy-D-ribose and alpha-D-ribose, each comprising atoms with the outer shell bridged by one or more H 2 -type ellipsoidal MOs or joined with one or more hydrogen MOs are shown in  FIGS. 19-22 . 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 67 
               
               
                   
               
               
                 The total gaseous bond energy of 2-deoxy-D-ribose (C 5 H 10 O 4 ) calculated 
               
               
                 using the functional group composition and the energies given supra. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                 CH 
                   
                   
                 C—C(O) 
                 C═O 
               
               
                   
                 CH 2   
                 (alkyl) 
                 CH(HC═O) 
                 C—C(n-C) 
                 (aldehyde) 
                 (aldehyde) 
               
               
                 Formula 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 Energies E D (Group) 
                 7.83016 
                 3.32601 
                 3.47404 
                 4.32754 
                 4.41461 
                 7.80660 
               
               
                 of Functional Groups 
               
               
                 (eV) 
               
               
                 Composition 
                 2 
                 2 
                 1 
                 3 
                 1 
                 1 
               
               
                   
               
             
          
           
               
                   
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                 C—O(C—OH) 
                 OH 
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Group 
                 Group 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 Energies E D (Group) 
                 4.34572 
                 4.41035 
               
               
                 of Functional Groups 
               
               
                 (eV) 
               
               
                 Composition 
                 3 
                 3 
                 77.25842 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 68 
               
               
                   
               
               
                 The total gaseous bond energy of D-ribose (C 5 H 10 O 5 ) calculated using the 
               
               
                 functional group composition and the energies given supra. compared to the 
               
               
                 experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                 CH 
                   
                   
                 C—C(O) 
                 C═O 
               
               
                   
                 CH 2   
                 (alkyl) 
                 CH(HC═O) 
                 C—C(n-C) 
                 (aldehyde) 
                 (aldehyde) 
               
               
                 Formula 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 Energies E D (Group) 
                 7.83016 
                 3.32601 
                 3.47404 
                 4.32754 
                 4.41461 
                 7.80660 
               
               
                 of Functional Groups 
               
               
                 (eV) 
               
               
                 Composition 
                 1 
                 3 
                 1 
                 3 
                 1 
                 1 
               
               
                   
               
             
          
           
               
                   
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                 C—O(C—OH) 
                 OH 
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Group 
                 Group 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 Energies E D (Group) 
                 4.34572 
                 4.41035 
               
               
                 of Functional Groups 
               
               
                 (eV) 
               
               
                 Composition 
                 4 
                 4 
                 81.51034 
                 83.498 a   
                 0.02381 
               
               
                   
               
               
                   a Crystal. 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 69 
               
             
             
               
                   
               
               
                 The total gaseous bond energy of alpha-2-deoxy-D-ribose (C 5 H 10 O 4 ) calculated 
               
               
                 using the functional group composition and the energies given supra. 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                 Calculated 
                   
                   
               
               
                   
                   
                   
                   
                 C—O 
                   
                   
                 Total 
               
               
                   
                   
                 CH 
                   
                 (alkyl 
                   
                   
                 Bond 
                 Experimental 
               
               
                   
                 CH 2   
                 (alkyl) 
                 C—C(n-C) 
                 ether) 
                 C—O(C—OH) 
                 OH 
                 Energy 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 Energies 
                 7.83016 
                 3.32601 
                 4.32754 
                 4.12506 
                 4.34572 
                 4.41035 
                   
                   
                   
               
               
                 E D (Group) 
               
               
                 of Functional 
               
               
                 Groups (eV) 
               
               
                 Composition 
                 2 
                 3 
                 4 
                 2 
                 3 
                 3 
                 77.46684 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 70 
               
             
             
               
                   
               
               
                 The total gaseous bond energy of alpha-D-ribose (C 5 H 10 O 5 ) calculated 
               
               
                 using the functional group composition and the energies given supra. 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                 Calculated 
                   
                   
               
               
                   
                   
                   
                   
                 C—O 
                   
                   
                 Total 
               
               
                   
                   
                 CH 
                   
                 (alkyl 
                   
                   
                 Bond 
                 Experimental 
               
               
                   
                 CH 2   
                 (alkyl) 
                 C—C(n-C) 
                 ether) 
                 C—O(C—OH) 
                 OH 
                 Energy 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 Energies 
                 7.83016 
                 3.32601 
                 4.32754 
                 4.12506 
                 4.34572 
                 4.41035 
                   
                   
                   
               
               
                 E D (Group) 
               
               
                 of Functional 
               
               
                 Groups (eV) 
               
               
                 Composition 
                 1 
                 4 
                 4 
                 2 
                 4 
                 4 
                 82.31088 
               
               
                   
               
             
          
         
       
     
         [0253]    Nucleotide Bonds of DNA and RNA 
         [0254]    DNA and RNA comprise a backbone of alpha-2-deoxy-D-ribose and alpha-D-ribose, respectively, with a charged phosphate moiety at the 3′ and 5′ positions of two consecutive ribose units in the chain and a base bound at the 1′ position wherein the ribose H of each of the corresponding 3′ or 5′ O—H and 1′ C—H bonds is replaced by P and the base N, respectively. For the base, the H of the N—H at the pyrimidine 1 position or the purine 9 position is replaced by the sugar C. The basic repeating unit of DNA or RNA is a nucleotide that comprises a monosaccharide, a phosphate moiety and a base. The structure of the nucleotide bond is shown in  FIG. 23  with the designation of the corresponding atoms. The phosphate moiety comprises the P═O, P═O, and C—O functional groups given in the Phosphates section as well as the P—O −  group given in the Organic and Related Ions section. The nucleoside bond (sugar C to base N) comprises the tertiary amine C—N functional group given in the corresponding section. The bases, adenine, guanine, thymine, and cytosine are equivalent to those given in the corresponding sections. The symbols of the functional groups of the nucleotide bond are given in Table 71. The geometrical (Eqs. (15.1-15.5) and (15.51)), intercept (Eqs. (15.80-15.87)), and energy (Eqs. (15.6-15.11) and (15.17-15.65)) parameters are given in Tables 72, 73, and 74, respectively. The functional group composition and the corresponding energy E D (Group) of each group of the nucleotide bond of DNA and RNA are given in Table 75. The bond angle parameters of the nucleoside bond determined using Eqs. (15.88-15.117) are given in Table 15.388. The color scale rendering of the charge-density of the exemplary tetra-nucleotide, (deoxy)adenosine 3′-monophosphate-5′-(deoxy)thymidine 3′-monophosphate-5′-(deoxy)guanosine 3′-monophosphate-5′-(deoxy)cytidine monophosphate (ATGC) comprising atoms with the outer shell bridged by one or more H 2 -type ellipsoidal MOs or joined with one or more hydrogen MOs is shown in  FIG. 24 .  FIG. 25  shows the color scale rendering of the charge-density of the exemplary DNA fragment 
         [0000]                            ACTGACTGACTG                       TGACTGACTGAC            
wherein each complementary strand comprises a dodeca-nucleotide of the form (base (1)—deoxyribose) monophosphate—(base(2)—deoxyribose) monophosphate—with the phosphates bridging the 3′ and 5′ ribose carbons with the opposite order for the complementary stands.
 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 71 
               
             
             
               
                   
               
               
                 The symbols of functional groups of the nucleotide bond. 
               
             
          
           
               
                   
                 Functional Group 
                 Group Symbol 
               
               
                   
                   
               
               
                   
                 C—N 
                 C—N 
               
               
                   
                 C—O (alkyl) 
                 C—O 
               
               
                   
                 P═O 
                 P═O 
               
               
                   
                 P—O 
                 P—O 
               
               
                   
                 (RO) 2 (O)P—O −  (alkyl phosphate) 
                 P—O −   
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 72 
               
             
             
               
                   
               
               
                 The geometrical bond parameters of the nucleotide bond and experimental values [1]. 
               
             
          
           
               
                   
                 C—N 
                 C—O 
                 P═O 
                 P—O 
                 P—O −   
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 1.96313 
                 1.79473 
                 1.91663 
                 1.84714 
                 1.91663 
               
               
                 c′ (a 0 ) 
                 1.40112 
                 1.33968 
                 1.38442 
                 1.52523 
                 1.38442 
               
               
                 Bond Length 
                 1.48288 
                 1.41785 
                 1.46521E−10 
                 1.61423 
                 1.46521 
               
               
                 2c′ (Å) 
               
               
                 Exp. Bond Length 
                 1.458  
                 1.418  
                 1.48 [64] 
                 1.631 [69] 
                 1.48 [64] 
               
               
                 (Å) 
                 (trimethylamine) 
                 (ethyl methyl 
                 (DNA) 
                 (MHP) 
                 (DNA) 
               
               
                   
                   
                 ether (avg.)) 
                 1.4759  
                 1.60 [64] 
               
               
                   
                   
                   
                 (PO) 
                 (DNA) 
               
               
                 b, c (a 0 ) 
                 1.37505 
                 1.19429 
                 1.32546 
                 1.04192 
                 1.32546 
               
               
                 e 
                 0.71372 
                 0.74645 
                 0.72232 
                 0.82573 
                 0.72232 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 73 
               
               
                   
               
               
                 The MO to HO intercept geometrical bond parameters of the nucleotide bond. E T  is E T (atom-atom, msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 Final Total 
                   
                   
               
               
                   
                   
                 E T   
                 E T   
                 E T   
                 E T   
                 Energy 
               
               
                   
                   
                 (eV) 
                 (eV) 
                 (eV) 
                 (eV) 
                 C2sp 3   
                 r initial   
                 r final   
               
               
                 Bond 
                 Atom 
                 Bond 1 
                 Bond 2 
                 Bond 3 
                 Bond 4 
                 (eV) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 C e (H)N d —C c (N c )C d N e (H)C e —N d (H)C c   
                 N d   
                 −0.60631 
                 −0.60631 
                 −0.46459 
                 0 
                   
                 0.93084 
                 0.82445 
               
               
                 (adenine nucleoside) 
               
               
                 C e (H)N d —C c (N c )C d N e (H)C e —N d (H)C c   
                 N d   
                 −0.92918 
                 −0.92918 
                 −0.46459 
                 0 
                   
                 0.93084 
                 0.79340 
               
               
                 (guanine nucleoside) 
               
               
                 N b (O)C b —N c HC c C b HN c —HC c C d   
                 N c   
                 −0.92918 
                 −0.92918 
                 −0.46459 
                 0 
                   
                 −0.93084 
                 −0.79340 
               
               
                 (thymine nucleoside) 
               
               
                 N b (O)C b —N c HC c C b HN c —HC c C d   
                 N c   
                 −0.92918 
                 −0.92918 
                 −0.46459 
                 0 
                   
                 −0.93084 
                 −0.79340 
               
               
                 (cytosine nucleoside) 
               
               
                 N d —C ribose 
                 N d   
                 −0.46459 
                 −0.60631 
                 −0.60631 
                 0 
                   
                 0.93084 
                 0.82445 
               
               
                 (adenine nucleoside) 
               
               
                 N d —C ribose 
                 C ribose 
                 −0.46459 
                 −0.92918 
                 −0.82688 
                 0 
                 −153.83634 
                 −0.91771 
                 −0.79816 
               
               
                 (adenine nucleoside) 
               
               
                 N d —C ribose 
                 N d   
                 −0.46459 
                 −0.92918 
                 −0.92918 
                 0 
                   
                 0.93084 
                 0.79340 
               
               
                 (guanine nucleoside) 
               
               
                 N d —C ribose 
                 C ribose 
                 −0.46459 
                 −0.92918 
                 −0.82688 
                 0 
                 −153.83634 
                 −0.91771 
                 −0.79816 
               
               
                 (guanine nucleoside) 
               
               
                 N c —C ribose 
                 N c   
                 −0.46459 
                 −0.92918 
                 −0.92918 
                 0 
                   
                 0.93084 
                 0.79340 
               
               
                 (thymine nucleoside) 
               
               
                 N c —C ribose 
                 C ribose 
                 −0.46459 
                 −0.92918 
                 −0.82688 
                 0 
                 −153.83634 
                 −0.91771 
                 −0.79816 
               
               
                 (thymine nucleoside) 
               
               
                 N c —C ribose 
                 N c   
                 −0.46459 
                 −0.92918 
                 −0.92918 
                 0 
                   
                 0.93084 
                 0.79340 
               
               
                 (cytosine nucleoside) 
               
               
                 N c —C ribose 
                 C ribose 
                 −0.46459 
                 −0.92918 
                 −0.82688 
                 0 
                 −153.83634 
                 −0.91771 
                 −0.79816 
               
               
                 (cytosine nucleoside) 
               
               
                   
               
             
          
           
               
                   
                 E Coulomb (C2sp 3 ) 
                 E(C2sp 3 ) 
                   
                   
                   
                   
                   
               
               
                   
                 (eV) 
                 (eV) 
                 θ′ 
                 θ 1   
                 θ 2   
                 d 1   
                 d 2   
               
               
                 Bond 
                 Final 
                 Final 
                 (°) 
                 (°) 
                 (°) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 C e (H)N d —C c (N c )C d N e (H)C e —N d (H)C c   
                 −16.50297 
                   
                 138.15 
                 41.85 
                 61.57 
                 0.68733 
                 0.61411 
               
               
                 (adenine nucleoside) 
               
               
                 C e (H)N d —C c (N c )C d N e (H)C e —N d (H)C c   
                 −17.14871 
                   
                 138.07 
                 41.93 
                 60.47 
                 0.70588 
                 0.59026 
               
               
                 (guanine nucleoside) 
               
               
                 N b (O)C b —N c HC c C b HN c —HC c C d   
                 −17.14871 
                   
                 138.07 
                 41.93 
                 60.47 
                 0.70588 
                 0.59026 
               
               
                 (thymine nucleoside) 
               
               
                 N b (O)C b —N c HC c C b HN c —HC c C d   
                 −17.14871 
                   
                 138.07 
                 41.93 
                 60.47 
                 0.70588 
                 0.59026 
               
               
                 (cytosine nucleoside) 
               
               
                 N d —C ribose 
                 −16.50297 
                   
                 76.37 
                 103.63 
                 35.64 
                 1.59544 
                 0.19432 
               
               
                 (adenine nucleoside) 
               
               
                 N d —C ribose 
                 −17.04640 
                 −16.85554 
                 73.17 
                 106.83 
                 33.75 
                 1.63226 
                 0.23114 
               
               
                 (adenine nucleoside) 
               
               
                 N d —C ribose 
                 −17.14871 
                   
                 72.56 
                 107.44 
                 33.40 
                 1.63893 
                 0.23782 
               
               
                 (guanine nucleoside) 
               
               
                 N d —C ribose 
                 −17.04640 
                 −16.85554 
                 73.17 
                 106.83 
                 33.75 
                 1.63226 
                 0.23114 
               
               
                 (guanine nucleoside) 
               
               
                 N c —C ribose 
                 −17.14871 
                   
                 72.56 
                 107.44 
                 33.40 
                 1.63893 
                 0.23782 
               
               
                 (thymine nucleoside) 
               
               
                 N c —C ribose 
                 −17.04640 
                 −16.85554 
                 73.17 
                 106.83 
                 33.75 
                 1.63226 
                 0.23114 
               
               
                 (thymine nucleoside) 
               
               
                 N c —C ribose 
                 −17.14871 
                   
                 72.56 
                 107.44 
                 33.40 
                 1.63893 
                 0.23782 
               
               
                 (cytosine nucleoside) 
               
               
                 N c —C ribose 
                 −17.04640 
                 −16.85554 
                 73.17 
                 106.83 
                 33.75 
                 1.63226 
                 0.23114 
               
               
                 (cytosine nucleoside) 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 74 
               
             
             
               
                   
               
               
                 The energy parameters (eV) of functional groups of the nucleotide bond. 
               
             
          
           
               
                   
                 C—N 
                 C—O 
                 P═O 
                 P—O 
                 P—O −   
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
             
          
           
               
                 n 1   
                 1 
                 1 
                 2 
                 1 
                 2 
               
               
                 n 2   
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
               
               
                 C 2   
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 2   
                 0.91140 
                 0.85395 
                 0.79401 
                 0.79401 
                 0.78899 
               
               
                 c 3   
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 c 4   
                 2 
                 2 
                 4 
                 2 
                 4 
               
               
                 c 5   
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1o   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
               
               
                 C 2o   
                 1 
                 1 
                 1 
                 0.79401 
                 1 
               
               
                 V e  (eV) 
                 −31.67393 
                 −33.47304 
                 −56.96374 
                 −33.27738 
                 −56.96374 
               
               
                 V p  (eV) 
                 9.71067 
                 10.15605 
                 9.82777 
                 8.92049 
                 9.82777 
               
               
                 T (eV) 
                 8.06719 
                 9.32537 
                 14.86039 
                 9.00781 
                 14.86039 
               
               
                 V m  (eV) 
                 −4.03359 
                 −4.66268 
                 −7.43020 
                 −4.50391 
                 −7.43020 
               
               
                 E(AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −23.56492 
                 −11.78246 
                 −11.78246 
               
               
                 ΔE H     2     MO (AO/HO) (eV) 
                 −0.92918 
                 −1.65376 
                 0 
                 0 
                 0 
               
               
                 E T (AO/HO) (eV) 
                 −13.70571 
                 −12.98113 
                 −23.56492 
                 −11.78246 
                 −11.78246 
               
               
                 E T (H 2 MO) (eV) 
                 −31.63537 
                 −31.63544 
                 −63.27069 
                 −31.63544 
                 −63.27069 
               
               
                 E T (atom-atom,msp 3 .AO) (eV) 
                 −0.92918 
                 −1.65376 
                 −2.26758 
                 −1.44914 
                 −2.26758 
               
               
                 E T (MO) (eV) 
                 −32.56455 
                 −33.28912 
                 −65.53832 
                 −33.08451 
                 −65.53832 
               
               
                 ω(10 15  rad/s) 
                 18.1298 
                 12.1583 
                 11.0170 
                 10.3761 
                 11.0170 
               
               
                 E K  (eV) 
                 11.93333 
                 8.00277 
                 7.25157 
                 6.82973 
                 7.25157 
               
               
                 Ē D  (eV) 
                 −0.22255 
                 −0.18631 
                 −0.17458 
                 −0.17105 
                 −0.17458 
               
               
                 Ē Kvib  (eV) 
                 0.12944 [23] 
                 0.16118 [4] 
                 0.15292 [24] 
                 0.10477 [70] 
                 0.12337 [74] 
               
               
                 Ē osc  (eV) 
                 −0.15783 
                 −0.10572 
                 −0.09812 
                 −0.11867 
                 −0.11289 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                 E T (Group) (eV) 
                 −32.72238 
                 −33.39484 
                 −65.73455 
                 −33.20318 
                 −49.32308 
               
               
                 E initial (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
               
               
                 E initial (c 5  AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 E D (Group) (eV) 
                 3.45260 
                 4.12506 
                 7.19500 
                 3.93340 
                 5.41841 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 75 
               
             
             
               
                   
               
               
                 The functional group composition and the energy E D (Group) of each group of the nucleotide bond. 
               
             
          
           
               
                   
                 C—N 
                 C—O 
                 P═O 
                 P—O 
                 P—O −   
               
               
                   
                 (3° amine) 
                 (alkyl ether) 
                 (phosphate) 
                 (phosphate) 
                 (organic ions) 
               
               
                 Formula 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
             
          
           
               
                 Energies E D (Group) 
                 3.45260 
                 4.12506 
                 7.19500 
                 3.93340 
                 5.41841 
               
               
                 of Functional Groups (eV) 
               
               
                 Composition 
                 1 
                 2 
                 1 
                 2 
                 1 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 76 
               
               
                   
               
               
                 The bond angle parameters of the nucleotide bond and experimental values [1]. In the calculation of θ v , the parameters 
               
               
                 from the preceding angle were used. E T  is E T  (atom-atom, msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                 2c′ 
                   
                 Atom 1 
                   
                 Atom 2 
                   
                   
               
               
                   
                 2c′ 
                 2c′ 
                 Terminal 
                   
                 Hybridization 
                   
                 Hybridization 
               
               
                 Atoms of 
                 Bond 1 
                 Bond 2 
                 Atoms 
                 E Coulombic   
                 Designation 
                 E Coulombic   
                 Designation 
                 c 2   
                 c 2   
               
               
                 Angle 
                 (a 0 ) 
                 (a 0 ) 
                 (a 0 ) 
                 Atom 1 
                 (Table 7) 
                 Atom 2 
                 (Table 7) 
                 Atom 1 
                 Atom 2 
               
               
                   
               
               
                 ∠(P)OCN 
                 2.67935 
                 2.80224 
                 4.5277 
                 −16.47951 
                 22 
                 −16.47951 
                 22 
                 0.82562 
                 0.82562 
               
               
                 ∠POC 
                 3.05046 
                 2.67935 
                 4.9904 
                 −11.78246 
                 Psp 3   
                 −15.75493 
                 7 
                 0.73885 
                 0.86359 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Eq. 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                 (15.181) 
               
               
                 ∠O a PO b   
                 3.05046 
                 3.05046 
                 4.7539 
                 −15.95954 
                 10 
                 −15.95954 
                 10 
                 0.85252 
                 0.85252 
               
               
                 ∠O b PO c   
                 3.05046 
                 2.76885 
                 4.7539 
                 −15.95954 
                 10 
                 −15.95954 
                 10 
                 0.85252 
                 0.85252 
               
               
                 ∠O c PO d   
                 2.76885 
                 2.76885 
                 4.7539 
                 −15.95954 
                 10 
                 −15.95954 
                 10 
                 0.85252 
                 0.85252 
               
               
                 ∠C a OC b (C a —O (i))(C b —O (ii)) 
                 2.68862 
                 2.67935 
                 4.4385 
                 −17.51099 
                 48 
                 −17.51099 
                 48 
                 0.77699 
                 0.77699 
               
               
                 ∠C b C a O(C a —O (ii)) 
                 2.91547 
                 2.67935 
                 4.5607 
                 −16.68412 
                 26 
                 −13.61806 
                 O 
                 0.81549 
                 0.85395 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (Eq. 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (15.133)) 
               
               
                 ∠C a OH(C a —O (ii)) 
                 2.67024 
                 1.83616 
                 3.6515 
                 −14.82575 
                 1 
                 −14.82575 
                 1 
                 1 
                 0.91771 
               
               
                 ∠C b C a O(C a —O (ii)) 
                 2.91547 
                 2.67024 
                 4.5826 
                 −16.68412 
                 26 
                 −13.61806 
                 O 
                 0.81549 
                 0.85395 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (Eq. 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (15.114)) 
               
               
                 ∠CNC 
                 2.80224 
                 2.80224 
                 4.6043 
                 −17.14871 
                 36 
                 −17.14871 
                 36 
                 0.79340 
                 0.79340 
               
               
                 (3° amine) 
               
               
                 Methylene 
                 2.11106 
                 2.11106 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
                 1 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
               
               
                 ∠C a C b H 
               
               
                 Methyl 
                 2.09711 
                 2.09711 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
                 1 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
               
               
                 ∠C a C b H 
               
               
                 ∠C b C a C c   
                 2.91547 
                 2.91547 
                 4.7958 
                 −16.68412 
                 26 
                 −16.68412 
                 26 
                 0.81549 
                 0.81549 
               
               
                 iso C a   
                   
                   
                   
                 C b   
                   
                 C c   
               
               
                 ∠C b C a H 
                 2.91547 
                 2.11323 
                 4.1633 
                 −15.55033 
                 5 
                 −14.82575 
                 1 
                 0.87495 
                 0.91771 
               
               
                 iso C a   
                   
                   
                   
                 C a   
                   
                 C b   
               
               
                 ∠C a C b H 
                 2.91547 
                 2.09711 
                 4.1633 
                 −15.55033 
                 5 
                 −14.82575 
                 1 
                 0.87495 
                 0.91771 
               
               
                 iso C a   
                   
                   
                   
                 C b   
                   
                 C a   
               
               
                   
               
             
          
           
               
                 Atoms of 
                   
                   
                   
                   
                 E T   
                 θ v   
                 θ 1   
                 θ 2   
                 Cal. θ 
                 Exp. θ 
               
               
                 Angle 
                 C 1   
                 C 2   
                 c 1   
                 c 2 ′ 
                 (eV) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
               
               
                   
               
               
                 ∠(P)OCN 
                 1 
                 1 
                 1 
                 0.82562 
                 −1.65376 
                   
                   
                   
                 111.36 
                 111.3 [64] 
               
               
                 ∠POC 
                 1 
                 0.73885 
                 1 
                 0.80122 
                 −0.72457 
                   
                   
                   
                 121.00 
                 121.3 [64] 
               
               
                 ∠O a PO b   
                 1 
                 1 
                 1 
                 0.85252 
                 −1.65376 
                   
                   
                   
                 102.38 
                 101.4 [64] 
               
               
                 ∠O b PO c   
                 1 
                 1 
                 1 
                 0.85395 
                 −1.65376 
                   
                   
                   
                 109.46 
                 109.7 [64] 
               
               
                 ∠O c PO d   
                 1 
                 1 
                 1 
                 0.85252 
                 −1.65376 
                   
                   
                   
                 118.29 
                 116.0 [64] 
               
               
                 ∠C a OC b (C a —O (i))(C b —O (ii)) 
                 1 
                 1 
                 1 
                 0.77699 
                 −1.85836 
                   
                   
                   
                 111.55 
                 111.9 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (ethyl methyl ether) 
               
               
                 ∠C b C a O(C a —O (ii)) 
                 1 
                 1 
                 1 
                 0.83472 
                 −1.65376 
                   
                   
                   
                 109.13 
                 109.4 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (ethyl methyl ether) 
               
               
                 ∠C a OH(C a —O (ii)) 
                 0.75 
                 1 
                 0.75 
                 0.91771 
                 0 
                   
                   
                   
                 106.78 
                 105   
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (ethanol) 
               
               
                 ∠C b C a O(C a —O (ii)) 
                 1 
                 1 
                 1 
                 0.83472 
                 −1.65376 
                   
                   
                   
                 110.17 
                 107.8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (ethanol) 
               
               
                 ∠CNC 
                 1 
                 1 
                 1 
                 0.79340 
                 −1.85836 
                   
                   
                   
                 110.48 
                 110.9 
               
               
                 (3° amine) 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (trimethyl amine) 
               
               
                 Methylene 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 108.44 
                 107   
               
               
                 ∠HC a H 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (propane) 
               
               
                 ∠C a C b C c   
                   
                   
                   
                   
                   
                 69.51 
                   
                   
                 110.49 
                 112 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (propane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 113.8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (butane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 110.8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C a C b H 
                   
                   
                   
                   
                   
                 69.51 
                   
                   
                 110.49 
                 111.0 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (butane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 111.4 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 Methyl 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 109.50 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                 ∠C a C b H 
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                 ∠C b C a C c   
                 1 
                 1 
                 1 
                 0.81549 
                 −1.85836 
                   
                   
                   
                 110.67 
                 110.8 
               
               
                 iso C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C b C a H 
                 0.75 
                 1 
                 0.75 
                 1.04887 
                 0 
                   
                   
                   
                 110.76 
               
               
                 iso C a   
               
               
                 ∠C a C b H 
                 0.75 
                 1 
                 0.75 
                 1.04887 
                 0 
                   
                   
                   
                 111.27 
                 111.4 
               
               
                 iso C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 77 
               
               
                   
               
               
                 The total bond energy of aspartic acid (C 4 H 7 NO 4 ) calculated using 
               
               
                 the functional group composition and the energies given supra. compared 
               
               
                 to the experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                 C—C 
                 C—C(O) 
                 C═O 
                   
               
               
                   
                 CH 2   
                 CH 
                 (iso-C) 
                 (alkyl carboxylic 
                 (alkyl carboxylic 
                 C—O((O)C—O) 
               
               
                 Formula 
                 Group 
                 Group 
                 Group 
                 acid) Group 
                 acid) Group 
                 Group 
               
               
                   
               
               
                 Energies E D (Group) of 
                 7.83016 
                 3.32601 
                 4.29921 
                 4.43110 
                 7.80660 
                 4.41925 
               
               
                 Functional Groups (eV) 
               
               
                 Composition 
                 1 
                 1 
                 1 
                 2 
                 2 
                 2 
               
               
                   
               
             
          
           
               
                   
                   
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                 OH 
                 NH 2   
                 C—N 
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Group 
                 Group 
                 (1° amine) 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 Energies E D (Group) of 
                 4.41035 
                 7.41010 
                 3.98101 
               
               
                 Functional Groups (eV) 
               
               
                 Composition 
                 2 
                 1 
                 1 
                 68.98109 
                 70.843 a   
                 0.02628 
               
               
                   
               
               
                   a Crystal. 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 78 
               
               
                   
               
               
                 The total bond energy of glutamic acid (C 5 H 9 NO 4 ) calculated using 
               
               
                 the functional group composition and the energies 
               
               
                 given supra. compared to the experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                   
                   
                 C—C(O) 
                 C═O 
                   
               
               
                   
                   
                   
                 C—C 
                 C—C 
                 (alkyl 
                 (alkyl 
                   
               
               
                   
                 CH 2   
                 CH 
                 (n-C) 
                 (iso-C) 
                 carboxylic acid) 
                 carboxylic acid) 
                 C—O((O)C—O) 
               
               
                   
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 Energies E D  (Group) of 
                 7.83016 
                 3.32601 
                 4.32754 
                 4.29921 
                 4.43110 
                 7.80660 
                 4.41925 
               
               
                 Functional Groups (eV) 
               
               
                 Composition 
                 2 
                 1 
                 1 
                 1 
                 2 
                 2 
                 2 
               
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 OH 
                 NH 2   
                 C—N 
                 Total Bond 
                 Total Bond 
               
               
                   
                   
                 Group 
                 Group 
                 (1° amine) 
                 Energy (eV) 
                 Energy (eV) 
                 Relative Error 
               
               
                   
                   
               
               
                   
                 Energies E D  (Group) of 
                 4.41035 
                 7.41010 
                 3.98101 
               
               
                   
                 Functional Groups (eV) 
               
               
                   
                 Composition 
                 2 
                 1 
                 1 
                 81.13879 
                 83.167 a   
                 0.02438 
               
               
                   
                   
               
               
                   
                   a Crystal. 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 79 
               
               
                   
               
               
                 The total bond energy of cysteine (C 3 H 7 NO 4 S) calculated using the functional 
               
               
                 group composition and the energies given supra. compared to the experimental values [3]. 
               
               
                 79 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                   
                 C—C(O) 
                 C═O 
                   
               
               
                   
                   
                   
                   
                 (alkyl 
                 (alkyl 
               
               
                   
                   
                   
                 C—C 
                 carboxylic 
                 carboxylic 
                   
               
               
                   
                 CH 2   
                 CH 
                 (iso-C) 
                 acid) 
                 acid) 
                 C—O((O)C—O) 
               
               
                   
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 Energies E D  (Group) of 
                 7.83016 
                 3.32601 
                 4.29921 
                 4.43110 
                 7.80660 
                 4.41925 
               
               
                 Functional Groups (eV) 
               
               
                 Composition 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                   
                   
                 C—S 
                 Calculated 
                 Experimental 
                   
               
               
                   
                 OH 
                 NH 2   
                 C—N 
                 SH 
                 (thiol) 
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                   
                 Group 
                 Group 
                 (1° amine) 
                 Group 
                 Group 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 Energies E D  (Group) 
                 4.41035 
                 7.41010 
                 3.98101 
                 3.77430 
                 3.33648 
               
               
                 of Functional 
               
               
                 Groups (eV) 
               
               
                 Composition 
                 1 
                 1 
                 1 
                 1 
                 1 
                 55.02457 
                 56.571 a   
                 0.02733 
               
               
                   
               
               
                   a Crystal 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 80 
               
               
                   
               
               
                 The total bond energy of lysine (C 6 H 14 N 2 O 2 ) calculated using the functional group 
               
               
                 composition and the energies given supra. compared to the experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                   
                   
                 C—C(O) 
                 C═O 
                   
               
               
                   
                   
                   
                   
                   
                 (alkyl 
                 (alkyl 
               
               
                   
                   
                   
                 C—C 
                 C—C 
                 carboxylic 
                 carboxylic 
                   
               
               
                   
                 CH 2   
                 CH 
                 (n-C) 
                 (iso-C) 
                 acid) 
                 acid) 
                 C—O((O)C—O) 
               
               
                   
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 Energies E D  (Group) of 
                 7.83016 
                 3.32601 
                 4.32754 
                 4.29921 
                 4.43110 
                 7.80660 
                 4.41925 
               
               
                 Functional Groups (eV) 
               
               
                 Composition 
                 4 
                 1 
                 3 
                 1 
                 1 
                 1 
                 1 
               
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                 OH 
                 NH 2   
                 C—N 
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                   
                 Group 
                 Group 
                 (1° amine) 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 Energies E D  (Group) of Functional 
                 4.41035 
                 7.41010 
                 3.98101 
               
               
                 Groups (eV) 
               
               
                 Composition 
                 1 
                 2 
                 2 
                 95.77799 
                 98.194 a   
                 0.02461 
               
               
                   
               
               
                   a Crystal. 
               
             
          
         
       
     
         [0255]    Amino Acids (H 2 N—CH(R)—COOH) 
         [0256]    The amino acids, H 2 NCH(R)COOH, each have a primary amine moiety comprised of NH 2  and C—N functional groups, an alkyl carboxylic acid moiety comprised of a C═O functional group, and the single bond of carbon to the carbonyl carbon atom, C—C(O), is also a functional group. The carboxylic acid moiety further comprises a C—OH moiety that comprises C—O and OH functional groups. The alpha carbon comprises a methylyne (CH) functional group bound to a side chain R group by an isopropyl C—C bond functional group. These groups common to all amino acids are given in the Primary Amines section, the Carboxylic Acids section, and the Branched Alkanes section, respectively. The R group is unique for each amino acid and determines its characteristic hydrophilic, hydrophobic, acidic, and basic properties. These characteristic functional groups are given in the prior organic functional group sections. The total energy of each amino acid given in Tables 77-96 was calculated as the sum over the integer multiple of each E D (Group) corresponding to the functional-group composition of the amino acid wherein the group identity and energy Group, E D (Group) are given in each table. The structure and the color scale, charge-density of the amino acids, each comprising atoms with the outer shell bridged by one or more H 2 -type ellipsoidal MOs or joined with one or more hydrogen MOs are shown in  FIGS. 26-65 . 
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 81 
               
               
                   
               
               
                 The total bond energy of arginine (C 6 H 14 N 2 O 2 ) calculated using the functional 
               
               
                 group composition and the energies given supra. compared to the experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                   
                   
                 C—C(O) 
                 C═O 
                   
                   
                   
               
               
                   
                   
                   
                   
                   
                 (alkyl 
                 (alkyl 
               
               
                   
                   
                   
                 C—C 
                 C—C 
                 carboxylic 
                 carboxylic 
               
               
                   
                 CH 2   
                 CH 
                 (n-C) 
                 (iso-C) 
                 acid) 
                 acid) 
                 C—O((O)C—O) 
                 OH 
                 NH 2   
               
               
                   
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 Energies of 
                 7.83016 
                 3.32601 
                 4.32754 
                 4.29921 
                 4.43110 
                 7.80660 
                 4.41925 
                 4.41035 
                 7.41010 
               
               
                 Functional Groups 
               
               
                 (eV) 
               
               
                 Composition 
                 3 
                 1 
                 2 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                 N═C 
                 NH 
                 C—N 
                 C—N((O)C—N 
                   
                 Calculated 
                   
                   
               
               
                   
                 C—N 
                 (N b ═C c   
                 (heterocyclic 
                 (N alkyl 
                 alkyl 
                 NH 2   
                 Total Bond 
                 Experimental 
               
               
                   
                 (1° 
                 imidazole) 
                 imidazole) 
                 amide) 
                 amide) 
                 (amide) 
                 Energy 
                 Total Bond 
                 Relative 
               
               
                   
                 amine) 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 Energies of 
                 3.98101 
                 6.79303 
                 3.51208 
                 3.40044 
                 4.12212 
                 7.37901 
               
               
                 Functional 
               
               
                 Groups (eV) 
               
               
                 Composition 
                 1 
                 1 
                 2 
                 1 
                 2 
                 1 
                 105.07007 
                 107.420 a   
                 0.02188 
               
               
                   
               
               
                   a Crystal. 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 82 
               
               
                   
               
               
                 The total bond energy of histidine (C 6 H 9 N 3 O 2 ) calculated using the functional group 
               
               
                 composition and the energies given supra. compared to the experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                   
                 C—C(O) 
                 C═O 
                   
                   
                   
                   
                   
                   
               
               
                   
                   
                   
                   
                 (alkyl 
                 (alkyl 
               
               
                   
                   
                   
                 C—C 
                 carboxylic 
                 carboxylic 
                   
                   
                   
                 C—N 
                   
                 CH 
               
               
                   
                 CH 2   
                 CH 
                 (iso-C) 
                 acid) 
                 acid) 
                 C—O((O)C—O) 
                 OH 
                 NH 2   
                 (1° 
                 C—C(—C(C)═C) 
                 (imidazole) 
               
               
                   
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 amine) 
                 Group 
                 Group 
               
               
                   
               
               
                 Energies 
                 7.83016 
                 3.32601 
                 4.29921 
                 4.43110 
                 7.80660 
                 4.41925 
                 4.41035 
                 7.41010 
                 3.98101 
                 3.75498 
                 3.32988 
               
               
                 E D  (Group) 
               
               
                 of 
               
               
                 Functional 
               
               
                 Groups (eV) 
               
               
                 Composition 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 2 
               
               
                   
               
             
          
           
               
                   
                 Formula 
                   
               
             
          
           
               
                   
                   
                 C═C 
                 N═C 
                 C—N 
                 NH 
                 C—N—C 
                 Calculated 
                   
                   
               
               
                   
                   
                 (C a ═C b   
                 (N b ═C c   
                 (C b —N b   
                 (heterocyclic 
                 (C a —N a —C c   
                 Total Bond 
                 Experimental 
               
               
                   
                   
                 imidazole) 
                 imidazole) 
                 imidazole) 
                 imidazole) 
                 imidazole) 
                 Energy 
                 Total Bond 
                 Relative 
               
               
                   
                   
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
                   
               
               
                   
                 Energies 
                 7.23317 
                 6.79303 
                 3.47253 
                 3.51208 
                 8.76298 
               
               
                   
                 E D  (Group) of 
               
               
                   
                 Functional 
               
               
                   
                 Groups (eV) 
               
               
                   
                 Composition 
                 1 
                 1 
                 1 
                 1 
                 1 
                 88.10232 
                 89.599 a   
                 0.01671 
               
               
                   
                   
               
               
                   
                   a Crystal. 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 83 
               
               
                   
               
               
                 The total bond energy of asparagine (C 4 H 8 N 2 O 2 ) calculated using the functional group 
               
               
                 composition and the energies given supra. compared to the experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                   
                 C—C(O) 
                 C═O 
                   
                   
                   
               
               
                   
                   
                   
                   
                 (alkyl 
                 (alkyl 
               
               
                   
                   
                   
                 C—C 
                 carboxylic 
                 carboxylic 
               
               
                   
                 CH 2   
                 CH 
                 (iso-C) 
                 acid) 
                 acid) 
                 C—O((O)C—O) 
                 OH 
                 NH 2   
               
               
                   
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 Energies E D  (Group) 
                 7.83016 
                 3.32601 
                 4.29921 
                 4.43110 
                 7.80660 
                 4.41925 
                 4.41035 
                 7.41010 
               
               
                 of Functional Groups 
               
               
                 (eV) 
               
               
                 Composition 
                 1 
                 1 
                 1 
                 1 
                 2 
                 1 
                 1 
                 1 
               
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                 C—C(O) 
                   
                   
                   
                   
                   
               
               
                   
                   
                 (alkyl 
                 C—N((O)C—N 
                 NH 2   
                 Calculated 
                 Experimental 
               
               
                   
                 C—N 
                 amide) 
                 alkyl amide) 
                 (amide) 
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                   
                 (1° amine) 
                 Group 
                 Group 
                 Group 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 Energies E D  (Group) 
                 3.98101 
                 4.35263 
                 4.12212 
                 7.37901 
               
               
                 of Functional Groups 
               
               
                 (eV) 
               
               
                 Composition 
                 1 
                 1 
                 1 
                 1 
                 71.57414 
                 73.513 a   
                 0.02637 
               
               
                   
               
               
                   a Crystal. 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 84 
               
               
                   
               
               
                 The total bond energy of glutamine (C 5 H 10 N 2 O 2 ) calculated using the functional group 
               
               
                 composition and the energies given supra. compared to the experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                   
                   
                 C—C(O) 
                 C═O 
                   
                   
               
               
                   
                   
                   
                   
                   
                 (alkyl 
                 (alkyl 
               
               
                   
                   
                   
                 C—C 
                 C—C 
                 carboxylic 
                 carboxylic 
               
               
                   
                 CH 2   
                 CH 
                 (n-C) 
                 (iso-C) 
                 acid) 
                 acid) 
                 C—O((O)C—O) 
                 OH 
               
               
                   
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 Energies E D  (Group) 
                 7.83016 
                 3.32601 
                 4.32754 
                 4.29921 
                 4.43110 
                 7.80660 
                 4.41925 
                 4.41035 
               
               
                 of Functional Groups 
               
               
                 (eV) 
               
               
                 Composition 
                 2 
                 1 
                 1 
                 1 
                 1 
                 2 
                 1 
                 1 
               
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                 C—C(O) 
                 C—N((O)C—N 
                   
                   
                   
                   
               
               
                   
                   
                   
                 (alkyl 
                 alkyl 
                 NH 2   
                 Calculated 
                 Experimental 
               
               
                   
                 NH 2   
                 C—N 
                 amide) 
                 amide) 
                 (amide) 
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                   
                 Group 
                 (1° amine) 
                 Group 
                 Group 
                 Group 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 Energies 
                 7.41010 
                 3.98101 
                 4.35263 
                 4.12212 
                 7.37901 
               
               
                 E D  (Group) of 
               
               
                 Functional 
               
               
                 Groups (eV) 
               
               
                 Composition 
                 1 
                 1 
                 1 
                 1 
                 1 
                 83.73184 
                 85.843 a   
                 0.02459 
               
               
                   
               
               
                   a Crystal. 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 85 
               
               
                   
               
               
                 The total bond energy of threonine (C 4 H 9 NO 3 ) calculated using the functional group 
               
               
                 composition and the energies given supra. compared to the experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                   
                 C—C(O) 
                 C═O 
                   
                   
               
               
                   
                   
                   
                   
                 (alkyl 
                 (alkyl 
               
               
                   
                   
                   
                 C—C 
                 carboxylic 
                 carboxylic 
               
               
                   
                 CH 3   
                 CH 
                 (iso-C) 
                 acid) 
                 acid) 
                 C—O((O)C—O) 
                 OH 
               
               
                   
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 Energies E D  (Group) of 
                 12.49186 
                 3.32601 
                 4.29921 
                 4.43110 
                 7.80660 
                 4.41925 
                 4.41035 
               
               
                 Functional Groups (eV) 
               
               
                 Composition 
                 1 
                 2 
                 2 
                 1 
                 1 
                 1 
                 2 
               
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                 C—O 
                 Calculated 
                 Experimental 
                   
               
               
                   
                 NH 2   
                 C—N 
                 (alkyl alcohol) 
                 Total Bond 
                 Total Bond 
               
               
                   
                 Group 
                 (1° amine) 
                 Group 
                 Energy (eV) 
                 Energy (eV) 
                 Relative Error 
               
               
                   
               
               
                 Energies 
                 7.41010 
                 3.98101 
                 4.34572 
               
               
                 E D  (Group) of 
               
               
                 Functional 
               
               
                 Groups (eV) 
               
               
                 Composition 
                 1 
                 1 
                 1 
                 68.95678 
                 71.058 a   
                 0.02956 
               
               
                   
               
               
                   a Crystal. 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 86 
               
               
                   
               
               
                 The total bond energy of tyrosine (C 9 H 11 NO 3 ) calculated using the functional group 
               
               
                 composition and the energies given supra. compared to the experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                   
                 C—C(O) 
                 C═O 
                   
                   
                   
               
               
                   
                   
                   
                   
                 (alkyl 
                 (alkyl 
               
               
                   
                   
                   
                 C—C 
                 carboxylic 
                 carboxylic 
                   
               
               
                   
                 CH 2   
                 CH 
                 (iso-C) 
                 acid) 
                 acid) 
                 C—O((O)C—O) 
                 OH 
                 NH 2   
               
               
                   
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 Energies E D  (Group) of 
                 7.83016 
                 3.32601 
                 4.29921 
                 4.43110 
                 7.80660 
                 4.41925 
                 4.41035 
                 7.41010 
               
               
                 Functional Groups (eV) 
               
               
                 Composition 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 2 
                 1 
               
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                 C 3e ═C 
                 CH 
                 C—C 
                 C—O 
                   
                   
                   
               
               
                   
                 C—N 
                 (CC aromatic 
                 (CH 
                 (C alkyl to 
                 (Aryl C—O 
                 Calculated 
                 Experimental 
               
               
                   
                 (1° 
                 bond) 
                 aromatic) 
                 aryl toluene) 
                 phenol) 
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                   
                 amine) 
                 Group 
                 Group 
                 Group 
                 Group 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 Energies 
                 3.98101 
                 5.63881 
                 3.90454 
                 3.63685 
                 3.99228 
               
               
                 E D  (Group) of 
               
               
                 Functional 
               
               
                 Groups (eV) 
               
               
                 Composition 
                 1 
                 6 
                 4 
                 1 
                 1 
                 109.40427 
                 111.450 a   
                 0.01835 
               
               
                   
               
               
                   a Crystal. 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 87 
               
               
                   
               
               
                 The total bond energy of serine (C 3 H 7 NO 3 ) calculated using the functional group 
               
               
                 composition and the energies given supra. compared to the experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                   
                 C—C(O) 
                 C═O 
                   
                   
               
               
                   
                   
                   
                   
                 (alkyl 
                 (alkyl 
               
               
                   
                   
                   
                 C—C 
                 carboxylic 
                 carboxylic 
               
               
                   
                 CH 2   
                 CH 
                 (iso-C) 
                 acid) 
                 acid) 
                 C—O((O)C—O) 
                 OH 
               
               
                   
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 Energies E D  (Group) of 
                 7.83016 
                 3.32601 
                 4.29921 
                 4.43110 
                 7.80660 
                 4.41925 
                 4.41035 
               
               
                 Functional Groups (eV) 
               
               
                 Composition 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 2 
               
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                 C—O 
                 Calculated 
                 Experimental 
                   
               
               
                   
                 NH 2   
                 C—N 
                 (alkyl alcohol) 
                 Total Bond 
                 Total Bond 
               
               
                   
                 Group 
                 (1° amine) 
                 Group 
                 Energy (eV) 
                 Energy (eV) 
                 Relative Error 
               
               
                   
               
               
                 Energies 
                 7.41010 
                 3.98101 
                 4.34572 
               
               
                 E D  (Group) of 
               
               
                 Functional 
               
               
                 Groups (eV) 
               
               
                 Composition 
                 1 
                 1 
                 1 
                 56.66986 
                 58.339 a   
                 0.02861 
               
               
                   
               
               
                   a Crystal. 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 88 
               
               
                   
               
               
                 The total bond energy of tryptophan (C 11 H 12 N 2 O 2 ) calculated using the functional group 
               
               
                 composition and the energies given supra. compared to the experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                   
                 C—C(O) 
                 C═O 
                   
               
               
                   
                   
                   
                 C—C 
                 (alkyl carboxylic 
                 (alkyl carboxylic 
               
               
                   
                 CH 2   
                 CH 
                 (iso-C) 
                 acid) 
                 acid) 
                 C—O((O)C—O) 
               
               
                   
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 Energies E D  (Group) of 
                 7.83016 
                 3.32601 
                 4.29921 
                 4.43110 
                 7.80660 
                 4.41925 
               
               
                 Functional Groups (eV) 
               
               
                 Composition 
                 1 
                 1 
                 2 
                 1 
                 1 
                 1 
               
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                   
                 C 3e ═C 
                   
                   
                   
               
               
                   
                   
                   
                   
                 (CC aromatic 
                 CH 
                 C—C(C b —C d   
                 C═C(C d ═C e   
               
               
                   
                 OH 
                 NH 2   
                 C—N 
                 bond) 
                 (CH aromatic) 
                 indole) 
                 indole) 
               
               
                   
                 Group 
                 Group 
                 (1° amine) 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 Energies 
                 4.41035 
                 7.41010 
                 3.98101 
                 5.63881 
                 3.90454 
                 3.47253 
                 6.79303 
               
               
                 E D  (Group) 
               
               
                 of 
               
               
                 Functional 
               
               
                 Groups (eV) 
               
               
                 Composition 
                 2 
                 1 
                 1 
                 6 
                 4 
                 1 
                 1 
               
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                   
                 C—C 
                   
                   
                   
               
               
                   
                 CH 
                 C—N—C 
                 NH 
                 (C alkyl to 
                 Calculated 
                 Experimental 
               
               
                   
                 (CH indole) 
                 (indole) 
                 (indole) 
                 aryl toluene) 
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                   
                 Group 
                 Group 
                 Group 
                 Group 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 Energies 
                   
                   
                 3.63685 
                 3.63685 
               
               
                 E D  (Group) of 
               
               
                 Functional 
               
               
                 Groups (eV) 
               
               
                 Composition 
                 1 
                 1 
                 1 
                 1 
                 126.74291 
                 128.084 a   
                 0.01047 
               
               
                   
               
               
                   a Crystal. 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 89 
               
               
                   
               
               
                 The total bond energy of phenylalanine (C 9 H 11 NO 2 ) calculated using the functional group 
               
               
                 composition and the energies given supra. compared to the experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                   
                 C—C(O) 
                 C═O 
                   
                   
                   
               
               
                   
                   
                   
                   
                 (alkyl 
                 (alkyl 
               
               
                   
                   
                   
                 C—C 
                 carboxylic 
                 carboxylic 
               
               
                   
                 CH 2   
                 CH 
                 (iso-C) 
                 acid) 
                 acid) 
                 C—O((O)C—O) 
                 OH 
                 NH 2   
               
               
                   
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 Energies E D  (Group) of 
                 7.83016 
                 3.32601 
                 4.29921 
                 4.43110 
                 7.80660 
                 4.41925 
                 4.41035 
                 7.41010 
               
               
                 Functional Groups (eV) 
               
               
                 Composition 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 2 
                 1 
               
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                 CH 
                 C—C 
                   
                   
                   
               
               
                   
                   
                 C 3e ═C 
                 (CH 
                 (C alkyl to 
                 Calculated 
                 Experimental 
               
               
                   
                 C—N 
                 (CC aromatic bond) 
                 aromatic) 
                 aryl toluene) 
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                   
                 (1° amine) 
                 Group 
                 Group 
                 Group 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 Energies E D  (Group) 
                 3.98101 
                 5.63881 
                 3.90454 
                 3.63685 
               
               
                 of Functional 
               
               
                 Groups (eV) 
               
               
                 Composition 
                 1 
                 6 
                 5 
                 1 
                 104.90618 
                 105.009 
                 0.00098 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 90 
               
               
                   
               
               
                 The total bond energy of proline (C 5 H 9 NO 2 ) calculated using the functional group 
               
               
                 composition and the energies given supra. compared to the experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                   
                   
                 C—C(O) 
                 C═O 
                   
               
               
                   
                   
                   
                   
                   
                 (alkyl 
                 (alkyl 
               
               
                   
                   
                   
                 C—C 
                 C—C 
                 carboxylic 
                 carboxylic 
               
               
                   
                 CH 2   
                 CH 
                 (n-C) 
                 (iso-C) 
                 acid) 
                 acid) 
                 C—O((O)C—O) 
               
               
                   
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 Energies E D  (Group) of 
                 7.83016 
                 3.32601 
                 4.32754 
                 4.29921 
                 4.43110 
                 7.80660 
                 4.41925 
               
               
                 Functional Groups (eV) 
               
               
                 Composition 
                 3 
                 1 
                 2 
                 1 
                 1 
                 1 
                 1 
               
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                 OH 
                 NH 
                 C—N 
                 Total Bond 
                 Total Bond 
               
               
                   
                 Group 
                 (2° amine) 
                 (2° amine) 
                 Energy (eV) 
                 Energy (eV) 
                 Relative Error 
               
               
                   
               
               
                 Energies E D  (Group) of 
                 4.41035 
                 3.50582 
                 3.71218 
               
               
                 Functional Groups (eV) 
               
               
                 Composition 
                 1 
                 1 
                 2 
                 71.76826 
                 71.332 
                 −0.00611 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 91 
               
               
                   
               
               
                 The total bond energy of methionine (C 5 H 11 NO 2 S) calculated using the functional group 
               
               
                 composition and the energies given supra. compared to the experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 C—C(O) 
                 C═O 
                   
               
               
                   
                   
                   
                   
                   
                   
                 (alkyl 
                 (alkyl 
               
               
                   
                   
                   
                   
                 C—C 
                 C—C 
                 carboxylic 
                 carboxylic 
               
               
                   
                 CH 3   
                 CH 2   
                 CH 
                 (n-C) 
                 (iso-C) 
                 acid) 
                 acid) 
                 C—O((O)C—O) 
               
               
                   
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 Energies E D  (Group) of 
                 12.49186 
                 7.83016 
                 3.32601 
                 4.32754 
                 4.29921 
                 4.43110 
                 7.80660 
                 4.41925 
               
               
                 Functional Groups (eV) 
               
               
                 Composition 
                 1 
                 2 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                   
                 C—S 
                 Calculated 
                 Experimental 
                   
               
               
                   
                 OH 
                 NH 2   
                 C—N 
                 (alkyl 
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                   
                 Group 
                 Group 
                 (1° amine) 
                 sulfide) 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 Energies E D  (Group) of 
                 4.41035 
                 7.41010 
                 3.98101 
                 3.33648 
               
               
                 Functional Groups (eV) 
               
               
                 Composition 
                 1 
                 1 
                 1 
                 2 
                 79.23631 
                 79.214 
                 −0.00028 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 92 
               
               
                   
               
               
                 The total bond energy of leucine (C 6 H 13 NO 2 ) calculated using the functional group 
               
               
                 composition and the energies given supra. compared to the experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                   
                   
                   
                   
                 C—C(O) 
                 C═O 
                   
               
               
                   
                   
                   
                   
                 C—C 
                 (alkyl carboxylic 
                 (alkyl carboxylic 
               
               
                   
                 CH 3   
                 CH 2   
                 CH 
                 (iso-C) 
                 acid) 
                 acid) 
                 C—O((O)C—O) 
               
               
                   
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 Energies E D  (Group) of 
                 12.49186 
                 7.83016 
                 3.32601 
                 4.29921 
                 4.43110 
                 7.80660 
                 4.41925 
               
               
                 Functional Groups (eV) 
               
               
                 Composition 
                 2 
                 1 
                 2 
                 4 
                 1 
                 1 
                 1 
               
               
                   
               
             
          
           
               
                   
                 Formula 
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 OH 
                 NH 2   
                 C—N 
                 Total Bond 
                 Total Bond 
               
               
                   
                   
                 Group 
                 Group 
                 (1° amine) 
                 Energy (eV) 
                 Energy (eV) 
                 Relative Error 
               
               
                   
                   
               
               
                   
                 Energies E D  (Group) of 
                 4.41035 
                 7.41010 
                 3.98101 
               
               
                   
                 Functional Groups (eV) 
               
               
                   
                 Composition 
                 1 
                 1 
                 1 
                 89.12115 
                 89.047 
                 −0.00083 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 93 
               
               
                   
               
               
                 The total bond energy of isoleucine (C 6 H 13 NO 2 ) calculated using the 
               
               
                 functional group composition and the energies given supra. compared to the experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 C—C(O) 
                   
                 C═O 
               
               
                   
                   
                   
                   
                   
                   
                 (alkyl 
                   
                 (alkyl 
               
               
                   
                   
                   
                   
                 C—C 
                 C—C 
                 carboxylic 
                 C—C 
                 carboxylic 
               
               
                   
                 CH 3   
                 CH 2   
                 CH 
                 (n-C) 
                 (iso-C) 
                 acid) 
                 (iso to iso-C) 
                 acid) 
               
               
                 Formula 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 Energies E D (Group) of 
                 12.49186 
                 7.83016 
                 3.32601 
                 4.32754 
                 4.29921 
                 4.43110 
                 4.17951 
                 7.80660 
               
               
                 Functional Groups (eV) 
               
               
                 Composition 
                 2 
                 1 
                 2 
                 1 
                 2 
                 1 
                 1 
                 1 
               
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                 C—O((O)C—O) 
                 OH 
                 NH 2   
                 C—N 
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Group 
                 Group 
                 Group 
                 (1° amine) 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 Energies E D (Group) of 
                 4.41925 
                 4.41035 
                 7.41010 
                 3.98101 
               
               
                 Functional Groups (eV) 
               
               
                 Composition 
                 1 
                 1 
                 1 
                 1 
                 89.02978 
                 90.612 
                 0.01746 
               
               
                   
               
               
                   a Crystal. 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 94 
               
               
                   
               
               
                 The total bond energy of valine (C 5 H 11 NO 2 ) calculated using the functional group 
               
               
                 composition and the energies given supra. compared to the experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                 C—C(O) 
                 C═O 
               
               
                   
                   
                   
                 C—C 
                 C—C 
                 (alkyl carboxylic 
                 (alkyl carboxylic 
               
               
                   
                 CH 3   
                 CH 
                 (iso-C) 
                 (iso to iso-C) 
                 acid) 
                 acid) 
               
               
                 Formula 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 Energies E D (Group) of 
                 12.49186 
                 3.32601 
                 4.29921 
                 4.17951 
                 4.43110 
                 7.80660 
               
               
                 Functional Groups (eV) 
               
               
                 Composition 
                 2 
                 2 
                 2 
                 1 
                 1 
                 1 
               
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                 C—O((O)C—O) 
                 OH 
                 NH 2   
                 C—N 
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Group 
                 Group 
                 Group 
                 (1° amine) 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 Energies E D (Group) of 
                 4.41925 
                 4.41035 
                 7.41010 
                 3.98101 
               
               
                 Functional Groups (eV) 
               
               
                 Composition 
                 1 
                 1 
                 1 
                 1 
                 76.87208 
                 76.772 
                 −0.00130 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 95 
               
               
                   
               
               
                 The total bond energy of alanine (C 3 H 7 NO 2 ) calculated using the functional group 
               
               
                 composition and the energies given supra. compared to the experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                 C—C(O) 
                 C═O 
                   
               
               
                   
                   
                   
                 C—C 
                 (alkyl carboxylic 
                 (alkyl carboxylic 
               
               
                   
                 CH 3   
                 CH 
                 (iso-C) 
                 acid) 
                 acid) 
                 C—O((O)C—O) 
               
               
                 Formula 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 Energies E D (Group) of 
                 12.49186 
                 3.32601 
                 4.29921 
                 4.43110 
                 7.80660 
                 4.41925 
               
               
                 Functional Groups (eV) 
               
               
                 Composition 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                   
               
             
          
           
               
                   
                   
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                 OH 
                 NH 2   
                 C—N 
                 Total Bond 
                 Total Bond 
               
               
                 Formula 
                 Group 
                 Group 
                 (1° amine) 
                 Energy (eV) 
                 Energy (eV) 
                 Relative Error 
               
               
                   
               
               
                 Energies E D (Group) of 
                 4.41035 
                 7.41010 
                 3.98101 
               
               
                 Functional Groups (eV) 
               
               
                 Composition 
                 1 
                 1 
                 1 
                 52.57549 
                 52.991 
                 0.00785 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 96 
               
               
                   
               
               
                 The total bond energy of glycine (C 2 H 5 NO 2 ) calculated using the functional group 
               
               
                 composition and the energies given supra. compared to the experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                 C—C(O) 
                 C═O 
                   
                   
               
               
                   
                   
                 (alkyl carboxylic 
                 (alkyl carboxylic 
               
               
                   
                 CH 2   
                 acid) 
                 acid) 
                 C—O((O)C—O) 
                 OH 
               
               
                 Formula 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 Energies E D (Group) of 
                 7.83016 
                 4.43110 
                 7.80660 
                 4.41925 
                 4.41035 
               
               
                 Functional Groups (eV) 
               
               
                 Composition 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                   
               
             
          
           
               
                   
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                 NH 2   
                 C—N 
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Group 
                 (1° amine) 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 Energies E D (Group) of 
                 7.41010 
                 3.98101 
               
               
                 Functional Groups (eV) 
               
               
                 Composition 
                 1 
                 1 
                 40.28857 
                 40.280 
                 −0.00021 
               
               
                   
               
             
          
         
       
     
         [0257]    Polypeptides (—[HN—CH(R)—C(O)] n —) 
         [0258]    The amino acids can be polymerized by reaction of the OH group from the carboxylic acid moiety of one amino acid with H from the alpha-carbon NH 2  of another amino acid to form H 2 O and an amide bond as part of a polyamide chain of a polypeptide or protein. Each amide bond that forms by the condensation of two amino acids is called a peptide bond. It comprises a C═O functional group, and the single bond of carbon to the carbonyl carbon atom, C—C(O), is also a functional group. The peptide bond further comprises a C—NH(R) moiety that comprises NH and C—N functional groups where R is the characteristic side chain of each amino acid that is unchanged in terms of its functional group composition upon the formation of the peptide bond. From the N-Alkyl and N,N-Dialkyl-Amides section, the functional group composition and the corresponding energy E D (Group) of each group of the peptide bond is given in Table 97. The color scale, charge-density of the exemplary polypeptide, phenylalanine-leucine-glutamine-asparic acid (phe-leu-gln-asp) comprising the atoms with the outer shell bridged by one or more H 2 -type ellipsoidal MOs or joined with one or more hydrogen MOs is shown in  FIG. 66 . 
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 97 
               
             
             
               
                   
               
               
                 The functional group composition and the energy 
               
               
                 E D  (Group) of each group of the peptide bond. 
               
             
          
           
               
                   
                 Formula 
               
             
          
           
               
                   
                 C—C(O) 
                 C—N((O)C—N 
                 C—N 
                 NH 
               
               
                   
                 (alkyl 
                 alkyl 
                 (N alkyl 
                 (N alkyl 
               
               
                   
                 amide) 
                 amide) 
                 amide) 
                 amide) 
               
               
                   
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
                   
               
             
          
           
               
                 Energies E D  (Group) 
                 4.35263 
                 4.12212 
                 3.40044 
                 3.49788 
               
               
                 of Functional Groups 
               
               
                 (eV) 
               
               
                 Composition 
                 1 
                 1 
                 1 
                 1 
               
               
                   
               
             
          
         
       
     
         [0259]    Summary Tables of Organic Molecules 
         [0260]    The bond energies, calculated using closed-form equations having integers and fundamental constants only for classes of molecules whose designation is based on the main functional group, are given in the following tables with the experimental values. 
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 98 
               
             
             
               
                   
               
               
                 Summary results of n-alkanes. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 3 H 8   
                 propane 
                 41.46896 
                 41.434 
                 −0.00085 
               
               
                 C 4 H 10   
                 butane 
                 53.62666 
                 53.61 
                 −0.00036 
               
               
                 C 5 H 12   
                 pentane 
                 65.78436 
                 65.77 
                 −0.00017 
               
               
                 C 6 H 14   
                 hexane 
                 77.94206 
                 77.93 
                 −0.00019 
               
               
                 C 7 H 16   
                 heptane 
                 90.09976 
                 90.09 
                 −0.00013 
               
               
                 C 8 H 18   
                 octane 
                 102.25746 
                 102.25 
                 −0.00006 
               
               
                 C 9 H 20   
                 nonane 
                 114.41516 
                 114.40 
                 −0.00012 
               
               
                 C 10 H 22   
                 decane 
                 126.57286 
                 126.57 
                 −0.00003 
               
               
                 C 11 H 24   
                 undecane 
                 138.73056 
                 138.736 
                 0.00004 
               
               
                 C 12 H 26   
                 dodecane 
                 150.88826 
                 150.88 
                 −0.00008 
               
               
                 C 18 H 38   
                 octadecane 
                 223.83446 
                 223.85 
                 0.00008 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 99 
               
             
             
               
                   
               
               
                 Summary results of branched alkanes. 
               
             
          
           
               
                   
                   
                   
                 Experi- 
                   
               
               
                   
                   
                 Calculated 
                 mental 
               
               
                   
                   
                 Total 
                 Total 
               
               
                   
                   
                 Bond 
                 Bond 
               
               
                   
                   
                 Energy 
                 Energy 
                 Relative 
               
               
                 Formula 
                 Name 
                 (eV) 
                 (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 4 H 10   
                 isobutane 
                 53.69922 
                 53.695 
                 −0.00007 
               
               
                 C 5 H 12   
                 isopentane 
                 65.85692 
                 65.843 
                 −0.00021 
               
               
                 C 5 H 12   
                 neopentane 
                 65.86336 
                 65.992 
                 0.00195 
               
               
                 C 6 H 14   
                 2-methylpentane 
                 78.01462 
                 78.007 
                 −0.00010 
               
               
                 C 6 H 14   
                 3-methylpentane 
                 78.01462 
                 77.979 
                 −0.00046 
               
               
                 C 6 H 14   
                 2,2-dimethylbutane 
                 78.02106 
                 78.124 
                 0.00132 
               
               
                 C 6 H 14   
                 2,3-dimethylbutane 
                 77.99581 
                 78.043 
                 0.00061 
               
               
                 C 7 H 16   
                 2-methylhexane 
                 90.17232 
                 90.160 
                 −0.00014 
               
               
                 C 7 H 16   
                 3-methylhexane 
                 90.17232 
                 90.127 
                 −0.00051 
               
               
                 C 7 H 16   
                 3-ethylpentane 
                 90.17232 
                 90.108 
                 −0.00072 
               
               
                 C 7 H 16   
                 2,2-dimethylpentane 
                 90.17876 
                 90.276 
                 0.00107 
               
               
                 C 7 H 16   
                 2,2,3-trimethylbutane 
                 90.22301 
                 90.262 
                 0.00044 
               
               
                 C 7 H 16   
                 2,4-dimethylpentane 
                 90.24488 
                 90.233 
                 −0.00013 
               
               
                 C 7 H 16   
                 3,3-dimethylpentane 
                 90.17876 
                 90.227 
                 0.00054 
               
               
                 C 8 H 18   
                 2-methylheptane 
                 102.33002 
                 102.322 
                 −0.00008 
               
               
                 C 8 H 18   
                 3-methylheptane 
                 102.33002 
                 102.293 
                 −0.00036 
               
               
                 C 8 H 18   
                 4-methylheptane 
                 102.33002 
                 102.286 
                 −0.00043 
               
               
                 C 8 H 18   
                 3-ethylhexane 
                 102.33002 
                 102.274 
                 −0.00055 
               
               
                 C 8 H 18   
                 2,2-dimethylhexane 
                 102.33646 
                 102.417 
                 0.00079 
               
               
                 C 8 H 18   
                 2,3-dimethylhexane 
                 102.31121 
                 102.306 
                 −0.00005 
               
               
                 C 8 H 18   
                 2,4-dimethylhexane 
                 102.40258 
                 102.362 
                 −0.00040 
               
               
                 C 8 H 18   
                 2,5-dimethylhexane 
                 102.40258 
                 102.396 
                 −0.00006 
               
               
                 C 8 H 18   
                 3,3-dimethylhexane 
                 102.33646 
                 102.369 
                 0.00032 
               
               
                 C 8 H 18   
                 3,4-dimethylhexane 
                 102.31121 
                 102.296 
                 −0.00015 
               
               
                 C 8 H 18   
                 3-ethyl-2-methylpentane 
                 102.31121 
                 102.277 
                 −0.00033 
               
               
                 C 8 H 18   
                 3-ethyl-3-methylpentane 
                 102.33646 
                 102.317 
                 −0.00019 
               
               
                 C 8 H 18   
                 2,2,3-trimethylpentane 
                 102.38071 
                 102.370 
                 −0.00010 
               
               
                 C 8 H 18   
                 2,2,4-trimethylpentane 
                 102.40902 
                 102.412 
                 0.00003 
               
               
                 C 8 H 18   
                 2,3,3-trimethylpentane 
                 102.38071 
                 102.332 
                 −0.00048 
               
               
                 C 8 H 18   
                 2,3,4-trimethylpentane 
                 102.29240 
                 102.342 
                 0.00049 
               
               
                 C 8 H 18   
                 2,2,3,3-tetramethylbutane 
                 102.41632 
                 102.433 
                 0.00016 
               
               
                 C 9 H 20   
                 2,3,5-trimethylhexane 
                 114.54147 
                 114.551 
                 0.00008 
               
               
                 C 9 H 20   
                 3,3-diethylpentane 
                 114.49416 
                 114.455 
                 −0.00034 
               
               
                 C 9 H 20   
                 2,2,3,3-tetramethylpentane 
                 114.57402 
                 114.494 
                 −0.00070 
               
               
                 C 9 H 20   
                 2,2,3,4-tetramethylpentane 
                 114.51960 
                 114.492 
                 −0.00024 
               
               
                 C 9 H 20   
                 2,2,4,4-tetramethylpentane 
                 114.57316 
                 114.541 
                 −0.00028 
               
               
                 C 9 H 20   
                 2,3,3,4-tetramethylpentane 
                 114.58266 
                 114.484 
                 −0.00086 
               
               
                 C 10 H 22   
                 2-methylnonane 
                 126.64542 
                 126.680 
                 0.00027 
               
               
                 C 10 H 22   
                 5-methylnonane 
                 126.64542 
                 126.663 
                 0.00014 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 100 
               
             
             
               
                   
               
               
                 Summary results of alkenes. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 3 H 6   
                 propene 
                 35.56033 
                 35.63207 
                 0.00201 
               
               
                 C 4 H 8   
                 1-butene 
                 47.71803 
                 47.78477 
                 0.00140 
               
               
                 C 4 H 8   
                 trans-2-butene 
                 47.93116 
                 47.90395 
                 −0.00057 
               
               
                 C 4 H 8   
                 isobutene 
                 47.90314 
                 47.96096 
                 0.00121 
               
               
                 C 5 H 10   
                 1-pentene 
                 59.87573 
                 59.95094 
                 0.00125 
               
               
                 C 5 H 10   
                 trans-2-pentene 
                 60.08886 
                 60.06287 
                 −0.00043 
               
               
                 C 5 H 10   
                 2-methyl-1-butene 
                 60.06084 
                 60.09707 
                 0.00060 
               
               
                 C 5 H 10   
                 2-methyl-2-butene 
                 60.21433 
                 60.16444 
                 −0.00083 
               
               
                 C 5 H 10   
                 3-methyl-1-butene 
                 59.97662 
                 60.01727 
                 0.00068 
               
               
                 C 6 H 12   
                 1-hexene 
                 72.03343 
                 72.12954 
                 0.00133 
               
               
                 C 6 H 12   
                 trans-2-hexene 
                 72.24656 
                 72.23733 
                 −0.00013 
               
               
                 C 6 H 12   
                 trans-3-hexene 
                 72.24656 
                 72.24251 
                 −0.00006 
               
               
                 C 6 H 12   
                 2-methyl-1-pentene 
                 72.21854 
                 72.29433 
                 0.00105 
               
               
                 C 6 H 12   
                 2-methyl-2-pentene 
                 72.37203 
                 72.37206 
                 0.00000 
               
               
                 C 6 H 12   
                 3-methyl-1-pentene 
                 72.13432 
                 72.19173 
                 0.00080 
               
               
                 C 6 H 12   
                 4-methyl-1-pentene 
                 72.10599 
                 72.21038 
                 0.00145 
               
               
                 C 6 H 12   
                 3-methyl-trans-2-pentene 
                 72.37203 
                 72.33268 
                 −0.00054 
               
               
                 C 6 H 12   
                 4-methyl-trans-2-pentene 
                 72.34745 
                 72.31610 
                 −0.00043 
               
               
                 C 6 H 12   
                 2-ethyl-1-butene 
                 72.21854 
                 72.25909 
                 0.00056 
               
               
                 C 6 H 12   
                 2,3-dimethyl-1-butene 
                 72.31943 
                 72.32543 
                 0.00008 
               
               
                 C 6 H 12   
                 3,3-dimethyl-1-butene 
                 72.31796 
                 72.30366 
                 −0.00020 
               
               
                 C 6 H 12   
                 2,3-dimethyl-2-butene 
                 72.49750 
                 72.38450 
                 −0.00156 
               
               
                 C 7 H 14   
                 1-heptene 
                 84.19113 
                 84.27084 
                 0.00095 
               
               
                 C 7 H 14   
                 5-methyl-1-hexene 
                 84.26369 
                 84.30608 
                 0.00050 
               
               
                 C 7 H 14   
                 trans-3-methyl-3-hexene 
                 84.52973 
                 84.42112 
                 −0.00129 
               
               
                 C 7 H 14   
                 2,4-dimethyl-1-pentene 
                 84.44880 
                 84.49367 
                 0.00053 
               
               
                 C 7 H 14   
                 4,4-dimethyl-1-pentene 
                 84.27012 
                 84.47087 
                 0.00238 
               
               
                 C 7 H 14   
                 2,4-dimethyl-2-pentene 
                 84.63062 
                 84.54445 
                 −0.00102 
               
               
                 C 7 H 14   
                 trans-4,4-dimethyl-2-pentene 
                 84.54076 
                 84.54549 
                 0.00006 
               
               
                 C 7 H 14   
                 2-ethyl-3-methyl-1-butene 
                 84.47713 
                 84.44910 
                 −0.00033 
               
               
                 C 7 H 14   
                 2,3,3-trimethyl-1-butene 
                 84.51274 
                 84.51129 
                 −0.00002 
               
               
                 C 8 H 16   
                 1-octene 
                 96.34883 
                 96.41421 
                 0.00068 
               
               
                 C 8 H 16   
                 trans-2,2-dimethyl-3-hexene 
                 96.69846 
                 96.68782 
                 −0.00011 
               
               
                 C 8 H 16   
                 3-ethyl-2-methyl-1-pentene 
                 96.63483 
                 96.61113 
                 −0.00025 
               
               
                 C 8 H 16   
                 2,4,4-trimethyl-1-pentene 
                 96.61293 
                 96.71684 
                 0.00107 
               
               
                 C 8 H 16   
                 2,4,4-trimethyl-2-pentene 
                 96.67590 
                 96.65880 
                 −0.00018 
               
               
                 C 10 H 20   
                 1-decene 
                 120.66423 
                 120.74240 
                 0.00065 
               
               
                 C 12 H 24   
                 1-dodecene 
                 144.97963 
                 145.07163 
                 0.00063 
               
               
                 C 16 H 32   
                 1-hexadecene 
                 193.61043 
                 193.71766 
                 0.00055 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 101 
               
             
             
               
                   
               
               
                 Summary results of alkynes. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 3 H 4   
                 propyne 
                 29.42932 
                 29.40432 
                 −0.00085 
               
               
                 C 4 H 6   
                 1-butyne 
                 41.58702 
                 41.55495 
                 −0.00077 
               
               
                 C 4 H 6   
                 2-butyne 
                 41.72765 
                 41.75705 
                 0.00070 
               
               
                 C 9 H 16   
                 1-nonyne 
                 102.37552 
                 102.35367 
                 −0.00021 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 102 
               
             
             
               
                   
               
               
                 Summary results of alkyl fluorides. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 CF 4   
                 tetrafluoromethane 
                 21.07992 
                 21.016 
                 −0.00303 
               
               
                 CHF 3   
                 trifluoromethane 
                 19.28398 
                 19.362 
                 0.00405 
               
               
                 CH 2 F 2   
                 difluoromethane 
                 18.22209 
                 18.280 
                 0.00314 
               
               
                 C 3 H 7 F 
                 1-fluoropropane 
                 41.86745 
                 41.885 
                 0.00041 
               
               
                 C 3 H 7 F 
                 2-fluoropropane 
                 41.96834 
                 41.963 
                 −0.00012 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 103 
               
             
             
               
                   
               
               
                 Summary results of alkyl chlorides. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 CCl 4   
                 tetrachloromethane 
                 13.43181 
                 13.448 
                 0.00123 
               
               
                 CHCl 3   
                 trichloromethane 
                 14.49146 
                 14.523 
                 0.00217 
               
               
                 CH 2 Cl 2   
                 dichloromethane 
                 15.37248 
                 15.450 
                 0.00499 
               
               
                 CH 3 Cl 
                 chloromethane 
                 16.26302 
                 16.312 
                 0.00299 
               
               
                 C 2 H 5 Cl 
                 chloroethane 
                 28.61064 
                 28.571 
                 −0.00138 
               
               
                 C 3 H 7 Cl 
                 1-chloropropane 
                 40.76834 
                 40.723 
                 −0.00112 
               
               
                 C 3 H 7 Cl 
                 2-chloropropane 
                 40.86923 
                 40.858 
                 −0.00028 
               
               
                 C 4 H 9 Cl 
                 1-chlorobutane 
                 52.92604 
                 52.903 
                 −0.00044 
               
               
                 C 4 H 9 Cl 
                 2-chlorobutane 
                 53.02693 
                 52.972 
                 −0.00104 
               
               
                 C 4 H 9 Cl 
                 1-chloro-2- 
                 52.99860 
                 52.953 
                 −0.00085 
               
               
                   
                 methylpropane 
               
               
                 C 4 H 9 Cl 
                 2-chloro-2- 
                 53.21057 
                 53.191 
                 −0.00037 
               
               
                   
                 methylpropane 
               
               
                 C 5 H 11 Cl 
                 1-chloropentane 
                 65.08374 
                 65.061 
                 −0.00034 
               
               
                 C 5 H 11 Cl 
                 1-chloro-3- 
                 65.15630 
                 65.111 
                 −0.00069 
               
               
                   
                 methylbutane 
               
               
                 C 5 H 11 Cl 
                 2-chloro-2- 
                 65.36827 
                 65.344 
                 −0.00037 
               
               
                   
                 methylbutane 
               
               
                 C 5 H 11 Cl 
                 2-chloro-3- 
                 65.16582 
                 65.167 
                 0.00002 
               
               
                   
                 methylbutane 
               
               
                 C 6 H 13 Cl 
                 2-chlorohexane 
                 77.34233 
                 77.313 
                 −0.00038 
               
               
                 C 8 H 17 Cl 
                 1-chlorooctane 
                 101.55684 
                 101.564 
                 0.00007 
               
               
                 C 12 H 25 Cl 
                 1-chlorododecane 
                 150.18764 
                 150.202 
                 0.00009 
               
               
                 C 18 H 37 Cl 
                 1-chlorooctadecane 
                 223.13384 
                 223.175 
                 0.00018 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 104 
               
             
             
               
                   
               
               
                 Summary results of alkyl bromides. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 CBr 4   
                 tetrabromomethane 
                 11.25929 
                 11.196 
                 −0.00566 
               
               
                 CHBr 3   
                 tribromomethane 
                 12.87698 
                 12.919 
                 0.00323 
               
               
                 CH 3 Br 
                 bromomethane 
                 15.67551 
                 15.732 
                 0.00360 
               
               
                 C 2 H 5 Br 
                 bromoethane 
                 28.03939 
                 27.953 
                 −0.00308 
               
               
                 C 3 H 7 Br 
                 1-bromopropane 
                 40.19709 
                 40.160 
                 −0.00093 
               
               
                 C 3 H 7 Br 
                 2-bromopropane 
                 40.29798 
                 40.288 
                 −0.00024 
               
               
                 C 5 H 10 Br 2   
                 2,3-dibromo-2- 
                 63.53958 
                 63.477 
                 −0.00098 
               
               
                   
                 methylbutane 
               
               
                 C 6 H 13 Br 
                 1-bromohexane 
                 76.67019 
                 76.634 
                 −0.00047 
               
               
                 C 7 H 15 Br 
                 1-bromoheptane 
                 88.82789 
                 88.783 
                 −0.00051 
               
               
                 C 8 H 17 Br 
                 1-bromooctane 
                 100.98559 
                 100.952 
                 −0.00033 
               
               
                 C 12 H 25 Br 
                 1-bromododecane 
                 149.61639 
                 149.573 
                 −0.00029 
               
               
                 C 16 H 33 Br 
                 1-bromohexadecane 
                 198.24719 
                 198.192 
                 −0.00028 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 105 
               
             
             
               
                   
               
               
                 Summary results of alkyl iodides. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 CHI 3   
                 triiodomethane 
                 10.35888 
                 10.405 
                 0.00444 
               
               
                 CH 2 I 2   
                 diiodomethane 
                 12.94614 
                 12.921 
                 −0.00195 
               
               
                 CH 3 I 
                 iodomethane 
                 15.20294 
                 15.163 
                 −0.00263 
               
               
                 C 2 H 5 I 
                 iodoethane 
                 27.36064 
                 27.343 
                 −0.00066 
               
               
                 C 3 H 7 I 
                 1-iodopropane 
                 39.51834 
                 39.516 
                 −0.00006 
               
               
                 C 3 H 7 I 
                 2-iodopropane 
                 39.61923 
                 39.623 
                 0.00009 
               
               
                 C 4 H 9 I 
                 2-iodo-2- 
                 51.96057 
                 51.899 
                 −0.00119 
               
               
                   
                 methylpropane 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 106 
               
             
             
               
                   
               
               
                 Summary results of alkene halides. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 2 H 3 Cl 
                 chloroethene 
                 22.46700 
                 22.505 
                 0.00170 
               
               
                 C 3 H 5 Cl 
                 2-chloropropene 
                 35.02984 
                 35.05482 
                 0.00071 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 107 
               
             
             
               
                   
               
               
                 Summary results of alcohols. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 CH 4 O 
                 methanol 
                 21.11038 
                 21.131 
                 0.00097 
               
               
                 C 2 H 6 O 
                 ethanol 
                 33.40563 
                 33.428 
                 0.00066 
               
               
                 C 3 H 8 O 
                 1-propanol 
                 45.56333 
                 45.584 
                 0.00046 
               
               
                 C 3 H 8 O 
                 2-propanol 
                 45.72088 
                 45.766 
                 0.00098 
               
               
                 C 4 H 10 O 
                 1-butanol 
                 57.72103 
                 57.736 
                 0.00026 
               
               
                 C 4 H 10 O 
                 2-butanol 
                 57.87858 
                 57.922 
                 0.00074 
               
               
                 C 4 H 10 O 
                 2-methyl-1- 
                 57.79359 
                 57.828 
                 0.00060 
               
               
                   
                 propananol 
               
               
                 C 4 H 10 O 
                 2-methyl-2- 
                 58.15359 
                 58.126 
                 −0.00048 
               
               
                   
                 propananol 
               
               
                 C 5 H 12 O 
                 1-pentanol 
                 69.87873 
                 69.887 
                 0.00011 
               
               
                 C 5 H 12 O 
                 2-pentanol 
                 70.03628 
                 70.057 
                 0.00029 
               
               
                 C 5 H 12 O 
                 3-pentanol 
                 70.03628 
                 70.097 
                 0.00087 
               
               
                 C 5 H 12 O 
                 2-methyl-1- 
                 69.95129 
                 69.957 
                 0.00008 
               
               
                   
                 butananol 
               
               
                 C 5 H 12 O 
                 3-methyl-1- 
                 69.95129 
                 69.950 
                 −0.00002 
               
               
                   
                 butananol 
               
               
                 C 5 H 12 O 
                 2-methyl-2- 
                 70.31129 
                 70.246 
                 −0.00092 
               
               
                   
                 butananol 
               
               
                 C 5 H 12 O 
                 3-methyl-2- 
                 69.96081 
                 70.083 
                 0.00174 
               
               
                   
                 butananol 
               
               
                 C 6 H 14 O 
                 1-hexanol 
                 82.03643 
                 82.054 
                 0.00021 
               
               
                 C 6 H 14 O 
                 2-hexanol 
                 82.19398 
                 82.236 
                 0.00052 
               
               
                 C 7 H 16 O 
                 1-heptanol 
                 94.19413 
                 94.214 
                 0.00021 
               
               
                 C 8 H 18 O 
                 1-octanol 
                 106.35183 
                 106.358 
                 0.00006 
               
               
                 C 8 H 18 O 
                 2-ethyl-1-hexananol 
                 106.42439 
                 106.459 
                 0.00032 
               
               
                 C 9 H 20 O 
                 1-nonanol 
                 118.50953 
                 118.521 
                 0.00010 
               
               
                 C 10 H 22 O 
                 1-decanol 
                 130.66723 
                 130.676 
                 0.00007 
               
               
                 C 12 H 26 O 
                 1-dodecanol 
                 154.98263 
                 154.984 
                 0.00001 
               
               
                 C 16 H 34 O 
                 1-hexadecanol 
                 203.61343 
                 203.603 
                 −0.00005 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 108 
               
             
             
               
                   
               
               
                 Summary results of ethers. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 2 H 6 O 
                 dimethyl ether 
                 32.84496 
                 32.902 
                 0.00174 
               
               
                 C 3 H 8 O 
                 ethyl methyl ether 
                 45.19710 
                 45.183 
                 −0.00030 
               
               
                 C 4 H 10 O 
                 diethyl ether 
                 57.54924 
                 57.500 
                 −0.00086 
               
               
                 C 4 H 10 O 
                 methyl propyl ether 
                 57.35480 
                 57.355 
                 0.00000 
               
               
                 C 4 H 10 O 
                 isopropyl methyl ether 
                 57.45569 
                 57.499 
                 0.00075 
               
               
                 C 6 H 14 O 
                 dipropyl ether 
                 81.86464 
                 81.817 
                 −0.00059 
               
               
                 C 6 H 14 O 
                 diisopropyl ether 
                 82.06642 
                 82.088 
                 0.00026 
               
               
                 C 6 H 14 O 
                 t-butyl ethyl ether 
                 82.10276 
                 82.033 
                 −0.00085 
               
               
                 C 7 H 16 O 
                 t-butyl isopropyl ether 
                 94.36135 
                 94.438 
                 0.00081 
               
               
                 C 8 H 18 O 
                 dibutyl ether 
                 106.18004 
                 106.122 
                 −0.00055 
               
               
                 C 8 H 18 O 
                 di-sec-butyl ether 
                 106.38182 
                 106.410 
                 0.00027 
               
               
                 C 8 H 18 O 
                 di-t-butyl ether 
                 106.36022 
                 106.425 
                 0.00061 
               
               
                 C 8 H 18 O 
                 t-butyl isobutyl ether 
                 106.65628 
                 106.497 
                 −0.00218 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 109 
               
             
             
               
                   
               
               
                 Summary results of 1° amines. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 CH 5 N 
                 methylamine 
                 23.88297 
                 23.857 
                 −0.00110 
               
               
                 C 2 H 7 N 
                 ethylamine 
                 36.04067 
                 36.062 
                 0.00060 
               
               
                 C 3 H 9 N 
                 propylamine 
                 48.19837 
                 48.243 
                 0.00092 
               
               
                 C 4 H 11 N 
                 butylamine 
                 60.35607 
                 60.415 
                 0.00098 
               
               
                 C 4 H 11 N 
                 sec-butylamine 
                 60.45696 
                 60.547 
                 0.00148 
               
               
                 C 4 H 11 N 
                 t-butylamine 
                 60.78863 
                 60.717 
                 −0.00118 
               
               
                 C 4 H 11 N 
                 isobutylamine 
                 60.42863 
                 60.486 
                 0.00094 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 110 
               
             
             
               
                   
               
               
                 Summary results of 2° amines. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 2 H 7 N 
                 dimethylamine 
                 35.76895 
                 35.765 
                 −0.00012 
               
               
                 C 4 H 11 N 
                 diethylamine 
                 60.22930 
                 60.211 
                 −0.00030 
               
               
                 C 6 H 15 N 
                 dipropylamine 
                 84.54470 
                 84.558 
                 0.00016 
               
               
                 C 6 H 15 N 
                 diisopropylamine 
                 84.74648 
                 84.846 
                 0.00117 
               
               
                 C 8 H 19 N 
                 dibutylamine 
                 108.86010 
                 108.872 
                 0.00011 
               
               
                 C 8 H 19 N 
                 diisobutylamine 
                 109.00522 
                 109.106 
                 0.00092 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 111 
               
             
             
               
                   
               
               
                 Summary results of 3° amines. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 3 H 9 N 
                 trimethylamine 
                 47.83338 
                 47.761 
                 −0.00152 
               
               
                 C 6 H 15 N 
                 triethylamine 
                 84.30648 
                 84.316 
                 0.00012 
               
               
                 C 9 H 21 N 
                 tripropylamine 
                 120.77958 
                 120.864 
                 0.00070 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 112 
               
             
             
               
                   
               
               
                 Summary results of aldehydes. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 CH 2 O 
                 formaldehyde 
                 15.64628 
                 15.655 
                 0.00056 
               
               
                 C 2 H 4 O 
                 acetaldehyde 
                 28.18711 
                 28.198 
                 0.00039 
               
               
                 C 3 H 6 O 
                 propanal 
                 40.34481 
                 40.345 
                 0.00000 
               
               
                 C 4 H 8 O 
                 butanal 
                 52.50251 
                 52.491 
                 −0.00022 
               
               
                 C 4 H 8 O 
                 isobutanal 
                 52.60340 
                 52.604 
                 0.00001 
               
               
                 C 5 H 10 O 
                 pentanal 
                 64.66021 
                 64.682 
                 0.00034 
               
               
                 C 7 H 14 O 
                 heptanal 
                 88.97561 
                 88.942 
                 −0.00038 
               
               
                 C 8 H 16 O 
                 octanal 
                 101.13331 
                 101.179 
                 0.00045 
               
               
                 C 8 H 16 O 
                 2-ethylhexanal 
                 101.23420 
                 101.259 
                 0.00025 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 113 
               
             
             
               
                   
               
               
                 Summary results of ketones. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 3 H 6 O 
                 acetone 
                 40.68472 
                 40.672 
                 −0.00031 
               
               
                 C 4 H 8 O 
                 2-butanone 
                 52.84242 
                 52.84 
                 −0.00005 
               
               
                 C 5 H 10 O 
                 2-pentanone 
                 65.00012 
                 64.997 
                 −0.00005 
               
               
                 C 5 H 10 O 
                 3-pentanone 
                 65.00012 
                 64.988 
                 −0.00005 
               
               
                 C 5 H 10 O 
                 3-methyl-2-butanone 
                 65.10101 
                 65.036 
                 −0.00099 
               
               
                 C 6 H 12 O 
                 2-hexanone 
                 77.15782 
                 77.152 
                 −0.00008 
               
               
                 C 6 H 12 O 
                 3-hexanone 
                 77.15782 
                 77.138 
                 −0.00025 
               
               
                 C 6 H 12 O 
                 2-methyl-3-pentanone 
                 77.25871 
                 77.225 
                 −0.00043 
               
               
                 C 6 H 12 O 
                 3,3-dimethyl-2- 
                 77.29432 
                 77.273 
                 −0.00028 
               
               
                   
                 butanone 
               
               
                 C 7 H 14 O 
                 3-heptanone 
                 89.31552 
                 89.287 
                 −0.00032 
               
               
                 C 7 H 14 O 
                 4-heptanone 
                 89.31552 
                 89.299 
                 −0.00018 
               
               
                 C 7 H 14 O 
                 2,2-dimethyl-3- 
                 89.45202 
                 89.458 
                 0.00007 
               
               
                   
                 pentanone 
               
               
                 C 7 H 14 O 
                 2,4-dimethyl-3- 
                 89.51730 
                 89.434 
                 −0.00093 
               
               
                   
                 pentanone 
               
               
                 C 8 H 16 O 
                 2,2,4-trimethyl-3- 
                 101.71061 
                 101.660 
                 −0.00049 
               
               
                   
                 pentanone 
               
               
                 C 9 H 18 O 
                 2-nonanone 
                 113.63092 
                 113.632 
                 0.00001 
               
               
                 C 9 H 18 O 
                 5-nonanone 
                 113.63092 
                 113.675 
                 0.00039 
               
               
                 C 9 H 18 O 
                 2,6-dimethyl-4- 
                 113.77604 
                 113.807 
                 0.00027 
               
               
                   
                 heptanone 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 114 
               
             
             
               
                   
               
               
                 Summary results of carboxylic acids. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 CH 2 O 2   
                 formic acid 
                 21.01945 
                 21.036 
                 0.00079 
               
               
                 C 2 H 4 O 2   
                 acetic acid 
                 33.55916 
                 33.537 
                 −0.00066 
               
               
                 C 3 H 6 O 2   
                 propanoic acid 
                 45.71686 
                 45.727 
                 0.00022 
               
               
                 C 4 H 8 O 2   
                 butanoic acid 
                 57.87456 
                 57.883 
                 0.00015 
               
               
                 C 5 H 10 O 2   
                 pentanoic acid 
                 70.03226 
                 69.995 
                 −0.00053 
               
               
                 C 5 H 10 O 2   
                 3-methylbutanoic 
                 70.10482 
                 70.183 
                 0.00111 
               
               
                   
                 acid 
               
               
                 C 5 H 10 O 2   
                 2,2- 
                 70.31679 
                 69.989 
                 −0.00468 
               
               
                   
                 dimethylpropanoic 
               
               
                   
                 acid 
               
               
                 C 6 H 12 O 2   
                 hexanoic acid 
                 82.18996 
                 82.149 
                 −0.00050 
               
               
                 C 7 H 14 O 2   
                 heptanoic acid 
                 94.34766 
                 94.347 
                 0.00000 
               
               
                 C 8 H 16 O 2   
                 octanoic acid 
                 106.50536 
                 106.481 
                 −0.00022 
               
               
                 C 9 H 18 O 2   
                 nonanoic acid 
                 118.66306 
                 118.666 
                 0.00003 
               
               
                 C 10 H 20 O 2   
                 decanoic acid 
                 130.82076 
                 130.795 
                 −0.00020 
               
               
                 C 12 H 24 O 2   
                 dodecanoic acid 
                 155.13616 
                 155.176 
                 0.00026 
               
               
                 C 14 H 28 O 2   
                 tetradecanoic acid 
                 179.45156 
                 179.605 
                 0.00085 
               
               
                 C 15 H 30 O 2   
                 pentadecanoic acid 
                 191.60926 
                 191.606 
                 −0.00002 
               
               
                 C 16 H 32 O 2   
                 hexadecanoic acid 
                 203.76696 
                 203.948 
                 0.00089 
               
               
                 C 18 H 36 O 2   
                 stearic acid 
                 228.08236 
                 228.298 
                 0.00094 
               
               
                 C 20 H 40 O 2   
                 eicosanoic acid 
                 252.39776 
                 252.514 
                 0.00046 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 115 
               
             
             
               
                   
               
               
                 Summary results of carboxylic acid esters. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 2 H 4 O 2   
                 methyl formate 
                 32.71076 
                 32.762 
                 0.00156 
               
               
                 C 3 H 6 O 2   
                 methyl acetate 
                 45.24849 
                 45.288 
                 0.00087 
               
               
                 C 6 H 12 O 2   
                 methyl pentanoate 
                 81.72159 
                 81.726 
                 0.00005 
               
               
                 C 7 H 14 O 2   
                 methyl hexanoate 
                 93.87929 
                 93.891 
                 0.00012 
               
               
                 C 8 H 16 O 2   
                 methyl heptanoate 
                 106.03699 
                 106.079 
                 0.00040 
               
               
                 C 9 H 18 O 2   
                 methyl octanoate 
                 118.19469 
                 118.217 
                 0.00018 
               
               
                 C 10 H 20 O 2   
                 methyl nonanoate 
                 130.35239 
                 130.373 
                 0.00016 
               
               
                 C 11 H 22 O 2   
                 methyl decanoate 
                 142.51009 
                 142.523 
                 0.00009 
               
               
                 C 12 H 24 O 2   
                 methyl undecanoate 
                 154.66779 
                 154.677 
                 0.00006 
               
               
                 C 13 H 26 O 2   
                 methyl dodecanoate 
                 166.82549 
                 166.842 
                 0.00010 
               
               
                 C 14 H 28 O 2   
                 methyl tridecanoate 
                 178.98319 
                 179.000 
                 0.00009 
               
               
                 C 15 H 30 O 2   
                 methyl 
                 191.14089 
                 191.170 
                 0.00015 
               
               
                   
                 tetradecanoate 
               
               
                 C 16 H 32 O 2   
                 methyl 
                 203.29859 
                 203.356 
                 0.00028 
               
               
                   
                 pentadecanoate 
               
               
                 C 4 H 8 O 2   
                 propyl formate 
                 57.76366 
                 57.746 
                 −0.00030 
               
               
                 C 4 H 8 O 2   
                 ethyl acetate 
                 57.63888 
                 57.548 
                 −0.00157 
               
               
                 C 5 H 10 O 2   
                 isopropyl acetate 
                 69.89747 
                 69.889 
                 −0.00013 
               
               
                 C 5 H 10 O 2   
                 ethyl propanoate 
                 69.79658 
                 69.700 
                 −0.00139 
               
               
                 C 6 H 12 O 2   
                 butyl acetate 
                 81.95428 
                 81.873 
                 −0.00099 
               
               
                 C 6 H 12 O 2   
                 t-butyl acetate 
                 82.23881 
                 82.197 
                 −0.00051 
               
               
                 C 6 H 12 O 2   
                 methyl 2,2- 
                 82.00612 
                 81.935 
                 −0.00087 
               
               
                   
                 dimethylpropanoate 
               
               
                 C 7 H 14 O 2   
                 ethyl pentanoate 
                 94.11198 
                 94.033 
                 −0.00084 
               
               
                 C 7 H 14 O 2   
                 ethyl 
                 94.18454 
                 94.252 
                 0.00072 
               
               
                   
                 3-methylbutanoate 
               
               
                 C 7 H 14 O 2   
                 ethyl 2,2- 
                 94.39651 
                 94.345 
                 −0.00054 
               
               
                   
                 dimethylpropanoate 
               
               
                 C 8 H 16 O 2   
                 isobutyl 
                 106.44313 
                 106.363 
                 −0.00075 
               
               
                   
                 isobutanoate 
               
               
                 C 8 H 16 O 2   
                 propyl pentanoate 
                 106.26968 
                 106.267 
                 −0.00003 
               
               
                 C 8 H 16 O 2   
                 isopropyl pentanoate 
                 106.37057 
                 106.384 
                 0.00013 
               
               
                 C 9 H 18 O 2   
                 butyl pentanoate 
                 118.42738 
                 118.489 
                 0.00052 
               
               
                 C 9 H 18 O 2   
                 sec-butyl pentanoate 
                 118.52827 
                 118.624 
                 0.00081 
               
               
                 C 9 H 18 O 2   
                 isobutyl pentanoate 
                 118.49994 
                 118.576 
                 0.00064 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 116 
               
             
             
               
                   
               
               
                 Summary results of amides. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 CH 3 NO 
                 formamide 
                 23.68712 
                 23.697 
                 0.00041 
               
               
                 C 2 H 5 NO 
                 acetamide 
                 36.15222 
                 36.103 
                 −0.00135 
               
               
                 C 3 H 7 NO 
                 propanamide 
                 48.30992 
                 48.264 
                 −0.00094 
               
               
                 C 4 H 9 NO 
                 butanamide 
                 60.46762 
                 60.449 
                 −0.00030 
               
               
                 C 4 H 9 NO 
                 2- 
                 60.51509 
                 60.455 
                 −0.00099 
               
               
                   
                 methylpropanamide 
               
               
                 C 5 H 11 NO 
                 pentanamide 
                 72.62532 
                 72.481 
                 −0.00200 
               
               
                 C 5 H 11 NO 
                 2,2- 
                 72.67890 
                 72.718 
                 0.00054 
               
               
                   
                 dimethyl- 
               
               
                   
                 propanamide 
               
               
                 C 6 H 13 NO 
                 hexanamide 
                 84.78302 
                 84.780 
                 −0.00004 
               
               
                 C 8 H 17 NO 
                 octanamide 
                 109.09842 
                 109.071 
                 −0.00025 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 117 
               
             
             
               
                   
               
               
                 Summary results of N-alkyl and N,N-dialkyl amides. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 3 H 7 NO 
                 N,N- 
                 47.679454 
                 47.574 
                 0.00221 
               
               
                   
                 dimethylformamide 
               
               
                 C 4 H 9 NO 
                 N,N- 
                 60.14455 
                 59.890 
                 −0.00426 
               
               
                   
                 dimethylacetamide 
               
               
                 C 6 H 13 NO 
                 N-butylacetamide 
                 84.63649 
                 84.590 
                 −0.00055 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 118 
               
             
             
               
                   
               
               
                 Summary results of urea. 
               
             
          
           
               
                   
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                   
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
                   
               
               
                   
                 CH 4 N 2 O 
                 urea 
                 31.35919 
                 31.393 
                 0.00108 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE 119 
               
             
             
               
                   
               
               
                 Summary results of acid halide. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 C 2 H 3 ClO 
                 acetyl chloride 
                 28.02174 
                 27.990 
                 −0.00115 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE 120 
               
             
             
               
                   
               
               
                 Summary results of acid anhydrides. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 C 4 H 6 O 3   
                 acetic anhydride 
                 56.94096 
                 56.948 
                 0.00013 
               
               
                 C 6 H 10 O 3   
                 propanoic anhydride 
                 81.25636 
                 81.401 
                 0.00177 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 121 
               
             
             
               
                   
               
               
                 Summary results of nitriles. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 2 H 3 N 
                 acetonitrile 
                 25.72060 
                 25.77 
                 0.00174 
               
               
                 C 3 H 5 N 
                 propanenitrile 
                 37.87830 
                 37.94 
                 0.00171 
               
               
                 C 4 H 7 N 
                 butanenitrile 
                 50.03600 
                 50.08 
                 0.00082 
               
               
                 C 4 H 7 N 
                 2-methyl- 
                 50.13689 
                 50.18 
                 0.00092 
               
               
                   
                 propanenitrile 
               
               
                 C 5 H 9 N 
                 pentanenitrile 
                 62.19370 
                 62.26 
                 0.00111 
               
               
                 C 5 H 9 N 
                 2,2-dimethyl- 
                 62.47823 
                 62.40 
                 −0.00132 
               
               
                   
                 propanenitrile 
               
               
                 C 7 H 13 N 
                 heptanenitrile 
                 86.50910 
                 86.59 
                 0.00089 
               
               
                 C 8 H 15 N 
                 octanenitrile 
                 98.66680 
                 98.73 
                 0.00069 
               
               
                 C 10 H 19 N 
                 decanenitrile 
                 122.98220 
                 123.05 
                 0.00057 
               
               
                 C 14 H 27 N 
                 tetradecanenitrile 
                 171.61300 
                 171.70 
                 0.00052 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 122 
               
             
             
               
                   
               
               
                 Summary results of thiols. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 HS 
                 hydrogen sulfide 
                 3.77430 
                 3.653 
                 −0.03320 
               
               
                 H 2 S 
                 dihydrogen sulfide 
                 7.56058 
                 7.605 
                 0.00582 
               
               
                 CH 4 S 
                 methanethiol 
                 19.60264 
                 19.575 
                 −0.00141 
               
               
                 C 2 H 6 S 
                 ethanethiol 
                 31.76034 
                 31.762 
                 0.00005 
               
               
                 C 3 H 8 S 
                 1-propanethiol 
                 43.91804 
                 43.933 
                 0.00035 
               
               
                 C 3 H 8 S 
                 2-propanethiol 
                 44.01893 
                 44.020 
                 0.00003 
               
               
                 C 4 H 10 S 
                 1-butanethiol 
                 56.07574 
                 56.089 
                 0.00024 
               
               
                 C 4 H 10 S 
                 2-butanethiol 
                 56.17663 
                 56.181 
                 0.00009 
               
               
                 C 4 H 10 S 
                 2-methyl-1- 
                 56.14830 
                 56.186 
                 0.00066 
               
               
                   
                 propanethiol 
               
               
                 C 4 H 10 S 
                 2-methyl-2- 
                 56.36027 
                 56.313 
                 −0.00084 
               
               
                   
                 propanethiol 
               
               
                 C 5 H 12 S 
                 2-methyl-1- 
                 68.30600 
                 68.314 
                 0.00012 
               
               
                   
                 butanethiol 
               
               
                 C 5 H 12 S 
                 1-pentanethiol 
                 68.23344 
                 68.264 
                 0.00044 
               
               
                 C 5 H 12 S 
                 2-methyl-2- 
                 68.51797 
                 68.441 
                 −0.00113 
               
               
                   
                 butanethiol 
               
               
                 C 5 H 12 S 
                 3-methyl-2- 
                 68.31552 
                 68.381 
                 0.00095 
               
               
                   
                 butanethiol 
               
               
                 C 5 H 12 S 
                 2,2-dimethyl-1- 
                 68.16441 
                 68.461 
                 0.00433 
               
               
                   
                 propanethiol 
               
               
                 C 6 H 14 S 
                 1-hexanethiol 
                 80.39114 
                 80.416 
                 0.00031 
               
               
                 C 6 H 14 S 
                 2-methyl-2- 
                 80.67567 
                 80.607 
                 −0.00085 
               
               
                   
                 pentanethiol 
               
               
                 C 7 H 16 S 
                 1-heptanethiol 
                 92.54884 
                 92.570 
                 0.00023 
               
               
                 C 10 H 22 S 
                 1-decanethiol 
                 129.02194 
                 129.048 
                 0.00020 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 123 
               
             
             
               
                   
               
               
                 Summary results of sulfides. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 2 H 6 S 
                 dimethyl sulfide 
                 31.65668 
                 31.672 
                 0.00048 
               
               
                 C 3 H 8 S 
                 ethyl methyl sulfide 
                 43.81438 
                 43.848 
                 0.00078 
               
               
                 C 4 H 10 S 
                 diethyl sulfide 
                 55.97208 
                 56.043 
                 0.00126 
               
               
                 C 4 H 10 S 
                 methyl propyl 
                 55.97208 
                 56.029 
                 0.00102 
               
               
                   
                 sulfide 
               
               
                 C 4 H 10 S 
                 isopropyl methyl 
                 56.07297 
                 56.115 
                 0.00075 
               
               
                   
                 sulfide 
               
               
                 C 5 H 12 S 
                 butyl methyl sulfide 
                 68.12978 
                 68.185 
                 0.00081 
               
               
                 C 5 H 12 S 
                 t-butyl methyl 
                 68.28245 
                 68.381 
                 0.00144 
               
               
                   
                 sulfide 
               
               
                 C 5 H 12 S 
                 ethyl propyl sulfide 
                 68.12978 
                 68.210 
                 0.00117 
               
               
                 C 5 H 12 S 
                 ethyl isopropyl 
                 68.23067 
                 68.350 
                 0.00174 
               
               
                   
                 sulfide 
               
               
                 C 6 H 14 S 
                 diisopropyl sulfide 
                 80.48926 
                 80.542 
                 0.00065 
               
               
                 C 6 H 14 S 
                 butyl ethyl sulfide 
                 80.28748 
                 80.395 
                 0.00133 
               
               
                 C 6 H 14 S 
                 methyl pentyl 
                 80.28748 
                 80.332 
                 0.00056 
               
               
                   
                 sulfide 
               
               
                 C 8 H 18 S 
                 dibutyl sulfide 
                 104.60288 
                 104.701 
                 0.00094 
               
               
                 C 8 H 18 S 
                 di-sec-butyl sulfide 
                 104.80466 
                 104.701 
                 −0.00099 
               
               
                 C 8 H 18 S 
                 di-t-butyl sulfide 
                 104.90822 
                 104.920 
                 0.00011 
               
               
                 C 8 H 18 S 
                 diisobutyl sulfide 
                 104.74800 
                 104.834 
                 0.00082 
               
               
                 C 10 H 22 S 
                 dipentyl sulfide 
                 128.91828 
                 128.979 
                 0.00047 
               
               
                 C 10 H 22 S 
                 diisopentyl sulfide 
                 129.06340 
                 129.151 
                 0.00068 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 124 
               
             
             
               
                   
               
               
                 Summary results of disulfides. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 2 H 6 S 2   
                 dimethyl disulfide 
                 34.48127 
                 34.413 
                 −0.00199 
               
               
                 C 4 H 10 S 2   
                 diethyl disulfide 
                 58.79667 
                 58.873 
                 0.00129 
               
               
                 C 6 H 14 S 2   
                 dipropyl disulfide 
                 83.11207 
                 83.169 
                 0.00068 
               
               
                 C 8 H 18 S 2   
                 di-t-butyl disulfide 
                 107.99653 
                 107.919 
                 −0.00072 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 125 
               
             
             
               
                   
               
               
                 Summary results of sulfoxides. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 2 H 6 SO 
                 dimethyl sulfoxide 
                 35.52450 
                 35.435 
                 −0.00253 
               
               
                 C 4 H 10 SO 
                 diethyl sulfoxide 
                 59.83990 
                 59.891 
                 0.00085 
               
               
                 C 6 H 14 SO 
                 dipropyl sulfoxide 
                 84.15530 
                 84.294 
                 0.00165 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE 126 
               
             
             
               
                   
               
               
                 Summary results of sulfones. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 C 2 H 6 SO 2   
                 dimethyl sulfone 
                 40.27588 
                 40.316 
                 0.00100 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 127 
               
             
             
               
                   
               
               
                 Summary results of sulfites. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 2 H 6 SO 3   
                 dimethyl sulfite 
                 43.95058 
                 44.042 
                 0.00207 
               
               
                 C 4 H 10 SO 3   
                 diethyl sulfite 
                 68.54939 
                 68.648 
                 0.00143 
               
               
                 C 8 H 18 SO 3   
                 dibutyl sulfite 
                 117.18019 
                 117.191 
                 0.00009 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 128 
               
             
             
               
                   
               
               
                 Summary results of sulfates. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 2 H 6 SO 4   
                 dimethyl sulfate 
                 48.70196 
                 48.734 
                 0.00067 
               
               
                 C 4 H 10 SO 4   
                 diethyl sulfate 
                 73.30077 
                 73.346 
                 0.00061 
               
               
                 C 6 H 14 SO 4   
                 dipropyl sulfate 
                 97.61617 
                 97.609 
                 −0.00008 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 129 
               
             
             
               
                   
               
               
                 Summary results of nitro alkanes. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 CH 3 NO 2   
                 nitromethane 
                 25.14934 
                 25.107 
                 −0.00168 
               
               
                 C 2 H 5 NO 2   
                 nitroethane 
                 37.30704 
                 37.292 
                 −0.00040 
               
               
                 C 3 H 7 NO 2   
                 1-nitropropane 
                 49.46474 
                 49.451 
                 −0.00028 
               
               
                 C 3 H 7 NO 2   
                 2-nitropropane 
                 49.56563 
                 49.602 
                 0.00074 
               
               
                 C 4 H 9 NO 2   
                 1-nitrobutane 
                 61.62244 
                 61.601 
                 −0.00036 
               
               
                 C 4 H 9 NO 2   
                 2-nitroisobutane 
                 61.90697 
                 61.945 
                 0.00061 
               
               
                 C 5 H 11 NO 2   
                 1-nitropentane 
                 73.78014 
                 73.759 
                 −0.00028 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE 130 
               
             
             
               
                   
               
               
                 Summary results of nitrite. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 CH 3 NO 2   
                 methyl nitrite 
                 24.92328 
                 24.955 
                 0.00126 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 131 
               
             
             
               
                   
               
               
                 Summary results of nitrate. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 CH 3 NO 3   
                 methyl nitrate 
                 28.18536 
                 28.117 
                 −0.00244 
               
               
                 C 2 H 5 NO 3   
                 ethyl nitrate 
                 40.34306 
                 40.396 
                 0.00131 
               
               
                 C 3 H 7 NO 3   
                 propyl nitrate 
                 52.50076 
                 52.550 
                 0.00093 
               
               
                 C 3 H 7 NO 3   
                 isopropyl nitrate 
                 52.60165 
                 52.725 
                 0.00233 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE 132 
               
             
             
               
                   
               
               
                 Summary results of conjugated alkenes. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 C 5 H 8   
                 cyclopentene 
                 54.83565 
                 54.86117 
                 0.00047 
               
               
                 C 4 H 6   
                 1,3 butadiene 
                 42.09159 
                 42.12705 
                 0.00084 
               
               
                 C 5 H 8   
                 1,3 pentadiene 
                 54.40776 
                 54.42484 
                 0.00031 
               
               
                 C 5 H 8   
                 1,4 pentadiene 
                 54.03745 
                 54.11806 
                 0.00149 
               
               
                 C 5 H 6   
                 1,3 cyclopentadiene 
                 49.27432 
                 49.30294 
                 0.00058 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 133 
               
             
             
               
                   
               
               
                 Summary results of aromatics and heterocyclic aromatics. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 6 H 6   
                 benzene 
                 57.26008 
                 57.26340 
                 0.00006 
               
               
                 C 6 H 5 Cl 
                 fluorobenzene 
                 57.93510 
                 57.887 
                 −0.00083 
               
               
                 C 6 H 5 Cl 
                 chlorobenzene 
                 56.55263 
                 56.581 
                 0.00051 
               
               
                 C 6 H 4 Cl 2   
                 m-dichlorobenzene 
                 55.84518 
                 55.852 
                 0.00012 
               
               
                 C 6 H 3 Cl 3   
                 1,2,3- 
                 55.13773 
                 55.077 
                 −0.00111 
               
               
                   
                 trichlorobenzene 
               
               
                 C 6 H 3 Cl 3   
                 1,3,5- 
                 55.29542 
                 55.255 
                 −0.00073 
               
               
                   
                 trichlorbenzene 
               
               
                 C 6 Cl 6   
                 hexachlorobenzene 
                 52.57130 
                 52.477 
                 −0.00179 
               
               
                 C 6 H 5 Br 
                 bromobenzene 
                 56.17932 
                 56.391 a   
                 0.00376 
               
               
                 C 6 H 5 I 
                 iodobenzene 
                 55.25993 
                 55.261 
                 0.00001 
               
               
                 C 6 H 5 NO 2   
                 nitrobenzene 
                 65.18754 
                 65.217 
                 0.00046 
               
               
                 C 7 H 8   
                 toluene 
                 69.48425 
                 69.546 
                 0.00088 
               
               
                 C 7 H 6 O 2   
                 benzoic acid 
                 73.76938 
                 73.762 
                 −0.00009 
               
               
                 C 7 H 5 ClO 2   
                 2-chlorobenzoic 
                 73.06193 
                 73.082 
                 0.00027 
               
               
                   
                 acid 
               
               
                 C 7 H 5 ClO 2   
                 3-chlorobenzoic 
                 73.26820 
                 73.261 
                 −0.00010 
               
               
                   
                 acid 
               
               
                 C 6 H 7 N 
                 aniline 
                 64.43373 
                 64.374 
                 −0.00093 
               
               
                 C 7 H 9 N 
                 2-methylaniline 
                 76.62345 
                 76.643 
                 −0.00025 
               
               
                 C 7 H 9 N 
                 3-methylaniline 
                 76.62345 
                 76.661 
                 0.00050 
               
               
                 C 7 H 9 N 
                 4-methylaniline 
                 76.62345 
                 76.654 
                 0.00040 
               
               
                 C 6 H 6 N 2 O 2   
                 2-nitroaniline 
                 72.47476 
                 72.424 
                 −0.00070 
               
               
                 C 6 H 6 N 2 O 2   
                 3-nitroaniline 
                 72.47476 
                 72.481 
                 −0.00009 
               
               
                 C 6 H 6 N 2 O 2   
                 4-nitroaniline 
                 72.47476 
                 72.476 
                 −0.00002 
               
               
                 C 7 H 7 NO 2   
                 aniline-2-carboxylic 
                 80.90857 
                 80.941 
                 0.00041 
               
               
                   
                 acid 
               
               
                 C 7 H 7 NO 2   
                 aniline-3-carboxylic 
                 80.90857 
                 80.813 
                 −0.00118 
               
               
                   
                 acid 
               
               
                 C 7 H 7 NO 2   
                 aniline-4-carboxylic 
                 80.90857 
                 80.949 
                 0.00050 
               
               
                   
                 acid 
               
               
                 C 6 H 6 O 
                 phenol 
                 61.75817 
                 61.704 
                 −0.00087 
               
               
                 C 6 H 4 N 2 O 5   
                 2,4-dinitrophenol 
                 77.61308 
                 77.642 
                 0.00037 
               
               
                 C 6 H 8 O 
                 anisole 
                 73.39006 
                 73.355 
                 −0.00047 
               
               
                 C 10 H 8   
                 naphthalene 
                 90.74658 
                 90.79143 
                 0.00049 
               
               
                 C 4 H 5 N 
                 pyrrole 
                 44.81090 
                 44.785 
                 −0.00057 
               
               
                 C 4 H 4 O 
                 furan 
                 41.67782 
                 41.692 
                 0.00033 
               
               
                 C 4 H 4 S 
                 thiophene 
                 40.42501 
                 40.430 
                 0.00013 
               
               
                 C 3 H 4 N 2   
                 imidazole 
                 39.76343 
                 39.74106 
                 −0.00056 
               
               
                 C 5 H 5 N 
                 pyridine 
                 51.91802 
                 51.87927 
                 −0.00075 
               
               
                 C 4 H 4 N 2   
                 pyrimidine 
                 46.57597 
                 46.51794 
                 −0.00125 
               
               
                 C 4 H 4 N 2   
                 pyrazine 
                 46.57597 
                 46.51380 
                 0.00095 
               
               
                 C 9 H 7 N 
                 quinoline 
                 85.40453 
                 85.48607 
                 0.00178 
               
               
                 C 9 H 7 N 
                 isoquinoline 
                 85.40453 
                 85.44358 
                 0.00046 
               
               
                 C 8 H 7 N 
                 indole 
                 78.52215 
                 78.514 
                 −0.00010 
               
               
                   
               
               
                   a Liquid. 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 134 
               
             
             
               
                   
               
               
                 Summary results of DNA bases. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 5 H 5 N 5   
                 adenine 
                 70.85416 
                 70.79811 
                 −0.00079 
               
               
                 C 5 H 6 N 2 O 2   
                 thymine 
                 69.08792 
                 69.06438 
                 −0.00034 
               
               
                 C 5 H 5 N 5 O 
                 guanine 
                 76.88212 
                 77.41849 
                 −0.00055 
               
               
                 C 4 H 5 N 3 O 
                 cytosine 
                 59.53378 
                 60.58056 
                 0.01728 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 135 
               
             
             
               
                   
               
               
                 Summary results of alkyl phosphines. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 3 H 9 P 
                 trimethylphosphine 
                 45.80930 
                 46.87333 
                 0.02270 
               
               
                 C 6 H 15 P 
                 triethylphosphine 
                 82.28240 
                 82.24869 
                 −0.00041 
               
               
                 C 18 H 15 P 
                 triphenylphosphine 
                 168.40033 
                 167.46591 
                 −0.00558 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 136 
               
             
             
               
                   
               
               
                 Summary results of alkyl phosphites. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 3 H 9 O 3 P 
                 trimethyl phosphite 
                 61.06764 
                 60.94329 
                 −0.00204 
               
               
                 C 6 H 15 O 3 P 
                 triethyl phosphite 
                 98.12406 
                 97.97947 
                 −0.00148 
               
               
                 C 9 H 21 O 3 P 
                 tri-isopropyl 
                 134.89983 
                 135.00698 
                 0.00079 
               
               
                   
                 phosphite 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE 137 
               
             
             
               
                   
               
               
                 Summary results of alkyl phosphine oxides. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 C 3 H 9 PO 
                 trimethylphosphine 
                 53.00430 
                 52.91192 
                 −0.00175 
               
               
                   
                 oxide 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE 138 
               
             
             
               
                   
               
               
                 Summary results of alkyl phosphates. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 C 6 H 15 O 4 P 
                 triethyl phosphate 
                 105.31906 
                 104.40400 
                 −0.00876 
               
               
                 C 9 H 21 O 4 P 
                 tri-n-propyl 
                 141.79216 
                 140.86778 
                 −0.00656 
               
               
                   
                 phosphate 
               
               
                 C 9 H 21 O 4 P 
                 tri-isopropyl 
                 142.09483 
                 141.42283 
                 −0.00475 
               
               
                   
                 phosphate 
               
               
                 C 9 H 27 O 4 P 
                 tri-n-butyl 
                 178.26526 
                 178.07742 
                 −0.00105 
               
               
                   
                 phosphate 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE 139 
               
             
             
               
                   
               
               
                 Summary results of monosaccharides of DNA and RNA. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 C 5 H 10 O 4   
                 2-deoxy-D-ribose 
                 77.25842 
                   
                   
               
               
                 C 5 H 10 O 5   
                 D-ribose 
                 81.51034 
                 83.498 a   
                 0.02381 
               
               
                 C 5 H 10 O 4   
                 alpha-2-deoxy-D- 
                 77.46684 
               
               
                   
                 ribose 
               
               
                 C 5 H 10 O 5   
                 alpha-D-ribose 
                 82.31088 
               
               
                   
               
               
                   a Crystal 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 140 
               
             
             
               
                   
               
               
                 Summary results of amino acids. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 4 H 7 NO 4   
                 aspartic acid 
                 68.98109 
                 70.843 a   
                 0.02628 
               
               
                 C 5 H 9 NO 4   
                 glutamic acid 
                 81.13879 
                 83.167 a   
                 0.02438 
               
               
                 C 3 H 7 NO 4 S 
                 cysteine 
                 55.02457 
                 56.571 a   
                 0.02733 
               
               
                 C 6 H 14 N 2 O 2   
                 lysine 
                 95.77799 
                 98.194 a   
                 0.02461 
               
               
                 C 6 H 14 N 2 O 2   
                 arginine 
                 105.07007 
                 107.420 a   
                 0.02188 
               
               
                 C 6 H 9 N 3 O 2   
                 histidine 
                 88.10232 
                 89.599 a   
                 0.01671 
               
               
                 C 4 H 8 N 2 O 2   
                 asparagine 
                 71.57414 
                 73.513 a   
                 0.02637 
               
               
                 C 5 H 10 N 2 O 2   
                 glutamine 
                 83.73184 
                 85.843 a   
                 0.02459 
               
               
                 C 4 H 9 NO 3   
                 threonine 
                 68.95678 
                 71.058 a   
                 0.02956 
               
               
                 C 9 H 11 NO 3   
                 tyrosine 
                 109.40427 
                 111.450 a   
                 0.01835 
               
               
                 C 3 H 7 NO 3   
                 serine 
                 56.66986 
                 58.339 a   
                 0.02861 
               
               
                 C 11 H 12 N 2 O 2   
                 tryptophan 
                 126.74291 
                 128.084 a   
                 0.01047 
               
               
                 C 9 H 11 NO 2   
                 phenylalanine 
                 104.90618 
                 105.009 
                 0.00098 
               
               
                 C 5 H 9 NO 2   
                 proline 
                 71.76826 
                 71.332 
                 −0.00611 
               
               
                 C 5 H 9 NO 2   
                 methionine 
                 79.23631 
                 79.214 
                 −0.00028 
               
               
                 C 6 H 13 NO 2   
                 leucine 
                 89.12115 
                 89.047 
                 −0.00083 
               
               
                 C 6 H 13 NO 2   
                 isoleucine 
                 89.02978 
                 90.612 
                 0.01746 
               
               
                 C 6 H 13 NO 2   
                 valine 
                 76.87208 
                 76.772 
                 −0.00130 
               
               
                 C 3 H 7 NO 2   
                 alanine 
                 52.57549 
                 52.991 
                 0.00785 
               
               
                 C 2 H 5 NO 2   
                 glycine 
                 40.28857 
                 40.280 
                 −0.00021 
               
               
                   
               
               
                   a Crystal 
               
             
          
         
       
     
       REFERENCES 
       [0000]    
       
         1. D. R. Lide,  CRC Handbook of Chemistry and Physics,  86th Edition, CRC Press, Taylor &amp; Francis, Boca Raton, (2005-6), pp. 9-19 to 9-45. 
         2. G. Herzberg,  Molecular Spectra and Molecular Structure II. Infrared and Raman Spectra of Polyatomic Molecules,  Van Nostrand Reinhold Company, New York, N.Y., (1945), p. 344. 
         3. D. R. Lide,  CRC Handbook of Chemistry and Physics,  86th Edition, CRC Press, Taylor &amp; Francis, Boca Raton, (2005-6), pp. 9-63; 5-18 to 5-42. 
         4. R. J. Fessenden, J. S. Fessenden,  Organic Chemistry,  Willard Grant Press. Boston, Mass., (1979), p. 320. 
         5. cyclohexane at http://webbook.nist.gov/. 
         6. G. Herzberg,  Molecular Spectra and Molecular Structure II. Infrared and Raman Spectra of Polyatomic Molecules,  Van Nostrand Reinhold Company, New York, N.Y., (1945), p. 326. 
         7. b1 2-methyl-1-propene at http://webbook.nist.gov/. 
         8. a1 2-methyl-1-propene at http://webbook.nist.gov/. 
         9. 2-butyne at http://webbook.nist.gov/. 
         10. trifluoromethane at http://webbook.nist.gov/. 
         11. fluoroethane at http://webbook.nist.gov/. 
         12. G. Herzberg,  Molecular Spectra and Molecular Structure II. Infrared and Raman Spectra of Polyatomic Molecules,  Krieger Publishing Company, Malabar, Fla., (1991), p. 195. 
         13. chloromethane at http://webbook.nist.gov/. 
         14. methyl bromide at http://webbook.nist.gov/. 
         15. tetrabromomethane at http://webbook.nist.gov/. 
         16. methyl iodide at http://webbook.nist.gov/. 
         17. K. P. Huber, G. Herzberg,  Molecular Spectra and Molecular Structure, IV. Constants of Diatomic Molecules,  Van Nostrand Reinhold Company, New York, (1979). 
         18. J. Crovisier, Molecular Database—Constants for molecules of astrophysical interest in the gas phase: photodissociation, microwave and infrared spectra, Ver. 4.2, Observatoire de Paris, Section de Meudon, Meudon, France, May 2002, pp. 34-37, available at http://wwwusr.obspm.fr/˜crovisie/. 
         19. methanol at http://webbook.nist.gov/. 
         20. D. Lin-Vien. N. B. Colthup, W. G. Fateley, J. G. Grasselli,  The Handbook of Infrared and Raman Frequencies of Organic Molecules,  Academic Press, Inc., Harcourt Brace Jovanovich, Boston, (1991), p. 46. 
         21. dimethyl ether at http://webbook.nist.gov/. 
         22. T. Amano, P. F. Bernath, R. W. McKellar, “Direct observation of the v 1  and v 3  fundamental bands of NH 2  by difference frequency laser spectroscopy,” J. Mol. Spectrosc., Vol. 94, (1982), pp. 100-113. 
         23. methylamine at http://webbook.nist.gov/. 
         24. D. R. Lide,  CRC Handbook of Chemistry and Physics,  79th Edition, CRC Press, Boca Raton, Fla., (1998-9), pp. 9-80 to 9-86. 
         25. D. Lin-Vien. N. B. Colthup, W. G. Fateley, J. G. Grasselli,  The Handbook of Infrared and Raman Frequencies of Organic Molecules,  Academic Press, Inc., Harcourt Brace Jovanovich, Boston, (1991), p. 482. 
         26. acetaldehyde at http://webbook.nist.gov/. 
         27. acetone at http://webbook.nist.gov/. 
         28. 2-butanone at http://webbook.nist.gov/. 
         29. acetic acid at http://webbook.nist.gov/. 
         30. formic acid at http://webbook.nist.gov/. 
         31. D. Lin-Vien. N. B. Colthup, W. G. Fateley, J. G. Grasselli,  The Handbook of Infrared and Raman Frequencies of Organic Molecules,  Academic Press, Inc., Harcourt Brace Jovanovich, Boston, (1991), p. 138. 
         32. methyl formate at http://webbook.nist.gov/. 
         33. D. Lin-Vien. N. B. Colthup, W. G. Fateley, J. G. Grasselli,  The Handbook of Infrared and Raman Frequencies of Organic Molecules,  Academic Press, Inc., Harcourt Brace Jovanovich, Boston, (1991), p. 144. 
         34. D. Lin-Vien. N. B. Colthup, W. G. Fateley, J. G. Grasselli,  The Handbook of Infrared and Raman Frequencies of Organic Molecules,  Academic Press, Inc., Harcourt Brace Jovanovich, Boston, (1991), p. 147. 
         35. D. Lin-Vien. N. B. Colthup, W. G. Fateley, J. G. Grasselli,  The Handbook of Infrared and Raman Frequencies of Organic Molecules,  Academic Press, Inc., Harcourt Brace Jovanovich, Boston, (1991), p. 143. 
         36. H. J. Vledder, F. C. Mijlhoff, J. C. Leyte, C. Romers, “An electron diffraction investigation of the molecular structure of gaseous acetic anhydride,” Journal of Molecular Structure, Vol. 7, Issues 3-4, (1971), pp. 421-429. 
         37. acetonitrile at http://webbook.nist.gov/. 
         38. D. R. Lide,  CRC Handbook of Chemistry and Physics,  86th Edition, CRC Press, Taylor &amp; Francis, Boca Raton, (2005-6), pp. 10-202 to 10-204. 
         39. D. R. Lide,  CRC Handbook of Chemistry and Physics,  86th Edition, CRC Press, Taylor &amp; Francis, Boca Raton, (2005-6), p. 9-79. 
         40. D. R. Lide,  CRC Handbook of Chemistry and Physics,  86th Edition, CRC Press, Taylor &amp; Francis, Boca Raton, (2005-6), pp. 9-82 to 9-86. 
         41. thiirane at http://webbook.nist.gov/. 
         42. D. Lin-Vien. N. B. Colthup, W. G. Fateley, J. G. Grasselli,  The Handbook of Infrared and Raman Frequencies of Organic Molecules,  Academic Press, Inc., Harcourt Brace Jovanovich, Boston, (1991), p. 242. 
         43. D. Lin-Vien. N. B. Colthup, W. G. Fateley, J. G. Grasselli,  The Handbook of Infrared and Raman Frequencies of Organic Molecules,  Academic Press, Inc., Harcourt Brace Jovanovich, Boston, (1991), p. 241. 
         44. R. M. Ibberson, M. T. F. Telling, S. Parsons, “Structural determination and phase transition behavior of dimethyl sulfate,” Acta. Cryst., Vol. B62, (2006), pp. 280-286. 
         45. D. Lin-Vien. N. B. Colthup, W. G. Fateley, J. G. Grasselli,  The Handbook of Infrared and Raman Frequencies of Organic Molecules,  Academic Press, Inc., Harcourt Brace Jovanovich, Boston, (1991), p. 187. 
         46. D. Lin-Vien. N. B. Colthup, W. G. Fateley, J. G. Grasselli,  The Handbook of Infrared and Raman Frequencies of Organic Molecules,  Academic Press, Inc., Harcourt Brace Jovanovich, Boston, (1991), p. 480. 
         47. D. Lin-Vien. N. B. Colthup, W. G. Fateley, J. G. Grasselli,  The Handbook of Infrared and Raman Frequencies of Organic Molecules,  Academic Press, Inc., Harcourt Brace Jovanovich, Boston, (1991), p. 187. 
         48. 1,3-butadiene at http://webbook.nist.gov/. 
         49. G. Herzberg,  Molecular Spectra and Molecular Structure II. Infrared and Raman Spectra of Polyatomic Molecules,  Van Nostrand Reinhold Company, New York, N.Y., (1945), pp. 362-369. 
         50. W. I. F. David, R. M. Ibberson, G. A. Jeffrey, J. R. Ruble, “The structure analysis of deuterated benzene and deuterated nitromethane by pulsed-neutron powder diffraction: a comparison with single crystal neutron analysis,” Physica B (1992), 180 &amp; 181, pp. 597-600. 
         51. G. A. Jeffrey, J. R. Ruble, R. K. McMullan, J. A. Pople, “The crystal structure of deuterated benzene,” Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 414, No. 1846, (Nov. 9, 1987), pp. 47-57. 
         52. H. B. Burgi, S. C. Capelli, “Getting more out of crystal-structure analyses,” Helvetica Chimica Acta, Vol. 86, (2003), pp. 1625-1640. 
         53. D. Lin-Vien. N. B. Colthup, W. G. Fateley, J. G. Grasselli,  The Handbook of Infrared and Raman Frequencies of Organic Molecules,  Academic Press, Inc., Harcourt Brace Jovanovich, Boston, (1991), p. 481. 
         54. E. Csakvari, I. Hargittai, “Molecular structure of 2,6-difluorobenzamine and 2-fluorobenzamine from gas-phase electron diffraction,” J. Phys. Chem., Vol. 96, (1992), pp. 5837-5842. 
         55. E. Rosenthal, B. P. Dailey, “Microwave spectrum of bromobenzene, its structure, quadrupole coupling constants, and carbon-bromine bond,” Journal of Chemical Physics, Vol. 43, No. 6, (1965), pp. 2093-2110. 
         56. H. J. M. Bowen,  Tables of Interatomic Distances and Configuration in Molecules and Ions , L. Sutton, Editor, Special Publication No. 11, The Chemical Society, Burlington House, London (1958). 
         57. R. Boese, D. Blaser, M. Nussbaumer, T. M. Krygowski, “Low temperature crystal and molecular structure of nitrobenzene,” Structural Chemistry, Vol. 3, No. 5, (1992), pp. 363-368. 
         58. G. A. Sim, J. M. Robertson, T. H. Goodwin, “The crystal and molecular structure of benzoic acid,” Acta Cryst., Vol. 8, (1955), pp. 157-164. 
         59. D. Lin-Vien. N. B. Colthup, W. G. Fateley, J. G. Grasselli,  The Handbook of Infrared and Raman Frequencies of Organic Molecules,  Academic Press, Inc., Harcourt Brace Jovanovich, Boston, (1991), p. 301. 
         60. D. Lin-Vien. N. B. Colthup, W. G. Fateley, J. G. Grasselli,  The Handbook of Infrared and Raman Frequencies of Organic Molecules,  Academic Press, Inc., Harcourt Brace Jovanovich, Boston, (1991), p. 303. 
         61. D. Lin-Vien. N. B. Colthup, W. G. Fateley, J. G. Grasselli,  The Handbook of Infrared and Raman Frequencies of Organic Molecules,  Academic Press, Inc., Harcourt Brace Jovanovich, Boston, (1991), p. 207. 
         62. S. Martinez-Carrera, “The crystal structure of Imidazole at −150° C.,” Acta. Cryst., Vol. 20, (1966), pp. 783-789. 
         63. D. Lin-Vien. N. B. Colthup, W. G. Fateley, J. G. Grasselli,  The Handbook of Infrared and Raman Frequencies of Organic Molecules,  Academic Press, Inc., Harcourt Brace Jovanovich, Boston, (1991), pp. 296-297. 
         64. S. Arnott, S. D. Dover, A. J. Wonacott, “Least-squares refinement of the crystal and molecular structures of DNA and RNA from X-ray data and standard bond lengths and angles,” Acta. Cryst., Vol. B-25, (1969), pp. 2192-2206. 
         65. H. Sternglanz, C. E. Bugg, “Conformations of N 6 -monosubstituted adenine derivatives crystal structure of N 6 -methyladenine,” Biochimica et Biophysica Acta, Vol. 308, (1973), pp. 1-8. 
         66. B. Chase, N. Herron, E. Holler, “Vibrational spectroscopy of C 60  and C 70  temperature-dependent studies,” J. Phys. Chem., Vol. 96, (1992), pp. 4262-4266. 
         67. D. Lin-Vien. N. B. Colthup, W. G. Fateley, J. G. Grasselli,  The Handbook of Infrared and Raman Frequencies of Organic Molecules,  Academic Press, Inc., Harcourt Brace Jovanovich, Boston, (1991), p. 272. 
         68. J. D. Cox, G. Pilcher,  Thermochemistry of Organometallic Compounds,  Academic Press, New York, (1970), pp. 478-485. 
         69. M. G. Newton, B. S. Campbell, “Preparation and crystal structures of trans-methyl meso-hydrobenzoin phosphite and phosphate,” JACS, Vol. 96, No. 25, (1974), pp. 7790-7797. 
         70. D. Lin-Vien. N. B. Colthup, W. G. Fateley, J. G. Grasselli,  The Handbook of Infrared and Raman Frequencies of Organic Molecules,  Academic Press, Inc., Harcourt Brace Jovanovich, Boston, (1991), p. 271. 
         71. J. C. J. Bart, G. Favini, R. Todeschini, “Conformational analysis of trimethylphoshite and its metal complexes,”  Phosphorous and Sulfur , Gordon and Breach Scientific Publishers, Inc. USA, Vol. 17, (1983), pp. 205-220. 
         72. N. J. Goodwin, W. Henderson, B. K. Nicholson, “Hydrogen bonding in hydroxymethylphosphine chalcogenides,” Inorganica Chimica Acta, Vol. 335, (2002), pp. 113-118. 
         73. M. W. Chase, Jr., C. A. Davies, J. R. Downey, Jr., D. J. Frurip, R. A. McDonald, A. N. Syverud, JANAF Thermochemical Tables, Third Edition, Part II, Cr—Zr, J. Phys. Chem. Ref. Data, Vol. 14, Suppl. 1, (1985), p. 1728. 
         74. D. Lin-Vien. N. B. Colthup, W. G. Fateley, J. G. Grasselli,  The Handbook of Infrared and Raman Frequencies of Organic Molecules,  Academic Press, Inc., Harcourt Brace Jovanovich, Boston, (1991), p. 269. 
       
     
         [0335]    Germanium Organometallic Functional Groups and Molecules 
         [0336]    The branched-chain alkyl germanium molecules, GeC n H 2n-2 , comprise at least one Ge bound by a carbon-germanium single bond comprising a C—Ge group, and the digermanium molecules further comprise a Ge—Ge functional group. Both comprise at least a terminal methyl group (CH 3 ) and may comprise methylene (CH 2 ), methylyne (CH), and C—C functional groups. The methyl and methylene functional groups are equivalent to those of straight-chain alkanes. Six types of C—C bonds can be identified. The n-alkane C—C bond is the same as that of straight-chain alkanes. In addition, the C—C bonds within isopropyl ((CH 3 ) 2 CH) and t-butyl ((CH 3 ) 3 C) groups and the isopropyl to isopropyl, isopropyl to t-butyl, and t-butyl to t-butyl C—C bonds comprise functional groups. 
         [0337]    As in the cases of carbon, silicon, and tin, the bonding in the germanium atom involves four sp 3  hybridized orbitals. For germanium, they are formed from the 4p and 4s electrons of the outer shells. Ge—C bonds form between a Ge4sp 3  HO and a C3sp 3  HO, and Ge—Ge bonds form between between Ge4sp 3  HOs to yield germanes and digermanes, respectively. The geometrical parameters of each Ge—C and Ge—Ge functional group is solved using Eq. (15.51) and the relationships between the prolate spheroidal axes. Then, the sum of the energies of the H 2 -type ellipsoidal MOs is matched to that of the Ge4sp 3  shell as in the case of the corresponding carbon, silicon, and tin molecules. As in the case of the transition metals, the energy of each functional group is determined for the effect of the electron density donation from the each participating C3sp 3  HO and Ge4sp 3  HO to the corresponding MO that maximizes the bond energy. 
         [0338]    The Ge electron configuration is [Ar]4s 2 3d 10 4p 2 , and the orbital arrangement is 
         [0000]    
       
         
           
             
               
                 
                   
                     ↑ 
                     1 
                   
                    
                   
                     
                       ↑ 
                       0 
                     
                     
                       4 
                        
                       p 
                        
                       
                           
                       
                        
                       state 
                     
                   
                    
                   
                     
                         
                     
                     
                       - 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   23.201 
                   ) 
                 
               
             
           
         
       
     
         [0000]    corresponding to the ground state  3 P 0 . The energy of the germanium 4p shell is the negative of the ionization energy of the germanium atom [1] given by 
         [0000]        E (Ge,4 p  shell)=− E (ionization; Ge)=−7.89943 eV   (23.202) 
         [0000]    The energy of germanium is less than the Coulombic energy between the electron and proton of H given by Eq. (1.231), but the atomic orbital may hybridize in order to achieve a bond at an energy minimum. After Eq. (13.422), the Ge4s atomic orbital (AO) combines with the Ge4p AOs to form a single Ge4sp 3  hybridized orbital (HO) with the orbital arrangement 
         [0000]    
       
         
           
             
               
                 
                   
                     ↑ 
                     
                       0 
                       , 
                       0 
                     
                   
                    
                   
                     
                       
                         ↑ 
                         
                           1 
                           , 
                           
                             - 
                             1 
                           
                         
                       
                        
                       
                         ↑ 
                         
                           1 
                           , 
                           0 
                         
                       
                     
                     
                       4 
                        
                       
                         sp 
                         3 
                       
                        
                       
                           
                       
                        
                       state 
                     
                   
                    
                   
                     ↑ 
                     
                       1 
                       , 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   23.203 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where the quantum numbers (l, m l ) are below each electron. The total energy of the state is given by the sum over the four electrons. The sum E T (Ge, 4sp 3 ) of experimental energies [1] of Ge, Ge + , Ge 2+ , and Ge 3+  is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             T 
                           
                            
                           
                             ( 
                             
                               Ge 
                               , 
                               
                                 4 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             45.7131 
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             34.2241 
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             15.93461 
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             7.89943 
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           103.77124 
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.204 
                   ) 
                 
               
             
           
         
       
     
         [0000]    By considering that the central field decreases by an integer for each successive electron of the shell, the radius r 4sp     3    of the Ge4sp 3  shell may be calculated from the Coulombic energy using Eq. (15.13): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           
                             4 
                              
                             
                               sp 
                               3 
                             
                           
                         
                         = 
                           
                          
                         
                           
                             ∑ 
                             
                               n 
                               = 
                               28 
                             
                             31 
                           
                            
                           
                             
                               
                                 ( 
                                 
                                   Z 
                                   - 
                                   n 
                                 
                                 ) 
                               
                                
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               
                                 
                                   πɛ 
                                   0 
                                 
                                  
                                 
                                   ( 
                                   
                                     e 
                                      
                                     
                                         
                                     
                                      
                                     103.77124 
                                      
                                     
                                         
                                     
                                      
                                     eV 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             10 
                              
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 ( 
                                 
                                   e 
                                    
                                   
                                       
                                   
                                    
                                   103.77124 
                                    
                                   
                                       
                                   
                                    
                                   eV 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           1.31113 
                            
                           
                             a 
                             0 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.205 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where Z=32 for germanium. Using Eq. (15.14), the Coulombic energy E Coulomb  (Ge,4sp 3 ) of the outer electron of the Ge4sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             Coulomb 
                           
                            
                           
                             ( 
                             
                               Ge 
                               , 
                               
                                 4 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             
                               r 
                               
                                 4 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             1.31113 
                              
                             
                               a 
                               0 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             10.37712 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.206 
                   ) 
                 
               
             
           
         
       
     
         [0000]    During hybridization, the spin-paired 4s electrons are promoted to Ge4sp 3  shell as unpaired electrons. The energy for the promotion is the magnetic energy given by Eq. (15.15) at the initial radius of the 4s electrons. From Eq. (10.102) with Z=32 and n=30, the radius r 30  of the Ge4s shell is 
         [0000]      r 30 =1.19265a 0    (23.207) 
         [0000]    Using Eqs. (15.15) and (23.207), the unpairing energy is 
         [0000]    
       
         
           
             
               
                 
                   
                     E 
                      
                     
                       ( 
                       magnetic 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         2 
                          
                         
                           πμ 
                           0 
                         
                          
                         
                            
                           2 
                         
                          
                         
                           ℏ 
                           2 
                         
                       
                       
                         
                           
                             m 
                             e 
                             2 
                           
                            
                           
                             ( 
                             
                               r 
                               30 
                             
                             ) 
                           
                         
                         3 
                       
                     
                     = 
                     
                       
                         
                           8 
                            
                           
                             πμ 
                             o 
                           
                            
                           
                             μ 
                             B 
                             2 
                           
                         
                         
                           
                             ( 
                             
                               1.19265 
                                
                               
                                 a 
                                 0 
                               
                             
                             ) 
                           
                           3 
                         
                       
                       = 
                       
                         0.06744 
                          
                         
                             
                         
                          
                         eV 
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.208 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Using Eqs. (23.206) and (23.208), the energy E (Ge,4sp 3 ) of the outer electron of the Ge4sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           E 
                            
                           
                             ( 
                             
                               Ge 
                               , 
                               
                                 4 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               - 
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 r 
                                 
                                   4 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                             
                           
                           + 
                           
                             
                               2 
                                
                               
                                 πμ 
                                 0 
                               
                                
                               
                                  
                                 2 
                               
                                
                               
                                 ℏ 
                                 2 
                               
                             
                             
                               
                                 
                                   m 
                                   e 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     r 
                                     30 
                                   
                                   ) 
                                 
                               
                               3 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               10.37712 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             0.06744 
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             10.30968 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.209 
                   ) 
                 
               
             
           
         
       
     
         [0339]    Next, consider the formation of the Ge-L-bond MO of gernmanium compounds wherein L is a ligand including germanium and carbon and each gemanium atom has a Ge4sp 3  electron with an energy given by Eq. (23.209). The total energy of the state of each germanium atom is given by the sum over the four electrons. The sum E T (Ge Ge-L , 4sp 3 ) of energies of Ge4sp 3  (Eq. (23.209)), Ge + , Ge 2+ , and Ge 3+  is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             T 
                           
                            
                           
                             ( 
                             
                               
                                 Ge 
                                 
                                   Ge 
                                   - 
                                   L 
                                 
                               
                               , 
                               
                                 4 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           - 
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       45.7131 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       34.2241 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       15.93461 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       E 
                                        
                                       
                                         ( 
                                         
                                           Ge 
                                           , 
                                           
                                             4 
                                              
                                             
                                               sp 
                                               3 
                                             
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           - 
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       45.7131 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       34.2241 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       15.93461 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       10.30968 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             106.18149 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.210 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where E(Ge,4sp 3 ) is the sum of the energy of Ge, −7.89943 eV, and the hybridization energy. 
         [0340]    A minimum energy is achieved while matching the potential, kinetic, and orbital energy relationships given in the Hydroxyl Radical (OH) section with the donation of electron density from the participating Ge4sp 3  HO to each Ge-L-bond MO. Consider the case wherein each Ge4sp 3  HO donates an excess of 25% of its electron density to the Ge-L-bond MO to form an energy minimum. By considering this electron redistribution in the germanium molecule as well as the fact that the central field decreases by an integer for each successive electron of the shell, in general terms, the radius r Ge-L4sp     3    of the Ge4sp 3  shell may be calculated from the Coulombic energy using Eq. (15.18): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           
                             Ge 
                             - 
                             
                               L 
                                
                               
                                   
                               
                                
                               4 
                                
                               
                                 sp 
                                 3 
                               
                             
                           
                         
                         = 
                           
                          
                         
                           
                             ( 
                             
                               
                                 
                                   ∑ 
                                   
                                     n 
                                     = 
                                     28 
                                   
                                   31 
                                 
                                  
                                 
                                   ( 
                                   
                                     Z 
                                     - 
                                     n 
                                   
                                   ) 
                                 
                               
                               - 
                               0.25 
                             
                             ) 
                           
                            
                           
                             
                                
                               2 
                             
                             
                               8 
                                
                               π 
                                
                               
                                   
                               
                                
                               
                                 
                                   ɛ 
                                   0 
                                 
                                  
                                 
                                   ( 
                                   
                                     e 
                                      
                                     
                                         
                                     
                                      
                                     106.18149 
                                      
                                     
                                         
                                     
                                      
                                     eV 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             9.75 
                              
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 ( 
                                 
                                   e 
                                    
                                   
                                       
                                   
                                    
                                   106.18149 
                                    
                                   
                                       
                                   
                                    
                                   eV 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           1.24934 
                            
                           
                               
                           
                            
                           
                             a 
                             0 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.211 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Using Eqs. (15.19) and (23.211), the Coulombic energy E Coulomb (Ge Ge-L ,4sp 3 ) of the outer electron of the Ge4sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             Coulomb 
                           
                            
                           
                             ( 
                             
                               
                                 Ge 
                                 
                                   Ge 
                                   - 
                                   L 
                                 
                               
                               , 
                               
                                 4 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             
                               r 
                               
                                 Ge 
                                 - 
                                 
                                   L 
                                    
                                   
                                       
                                   
                                    
                                   4 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             1.24934 
                              
                             
                               a 
                               0 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             10.89041 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.212 
                   ) 
                 
               
             
           
         
       
     
         [0000]    During hybridization, the spin-paired 4s electrons are promoted to Ge4sp 3  shell as unpaired electrons. The energy for the promotion is the magnetic energy given by Eq. (23.208). Using Eqs. (23.208) and (23.212), the energy E (Ge Ge-L ,4sp 3 ) of the outer electron of the Ge4sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           E 
                            
                           
                             ( 
                             
                               
                                 Ge 
                                 
                                   Ge 
                                   - 
                                   L 
                                 
                               
                               , 
                               
                                 4 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               - 
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 r 
                                 
                                   Ge 
                                   - 
                                   
                                     L 
                                      
                                     
                                         
                                     
                                      
                                     4 
                                      
                                     
                                       sp 
                                       3 
                                     
                                   
                                 
                               
                             
                           
                           + 
                           
                             
                               2 
                                
                               
                                   
                               
                                
                               π 
                                
                               
                                   
                               
                                
                               
                                 μ 
                                 0 
                               
                                
                               
                                  
                                 2 
                               
                                
                               
                                 ℏ 
                                 2 
                               
                             
                             
                               
                                 
                                   m 
                                   e 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     r 
                                     30 
                                   
                                   ) 
                                 
                               
                               3 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               10.89041 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             0.06744 
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             10.82297 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.213 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Thus, E T (Ge-L,4sp 3 ), the energy change of each Ge4sp 3  shell with the formation of the Ge-L-bond MO is given by the difference between Eq. (23.213) and Eq. (23.209): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             T 
                           
                            
                           
                             ( 
                             
                               
                                 Ge 
                                 - 
                                 L 
                               
                               , 
                               
                                 4 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             E 
                              
                             
                               ( 
                               
                                 
                                   Ge 
                                   
                                     Ge 
                                     - 
                                     L 
                                   
                                 
                                 , 
                                 
                                   4 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                           - 
                           
                             E 
                              
                             
                               ( 
                               
                                 Ge 
                                 , 
                                 
                                   4 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               10.82297 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           - 
                           
                             ( 
                             
                               
                                 - 
                                 10.30968 
                               
                                
                               
                                   
                               
                                
                               eV 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             0.51329 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.214 
                   ) 
                 
               
             
           
         
       
     
         [0341]    Now, consider the formation of the Ge-L-bond MO of gernmanium compounds wherein L is a ligand including germanium and carbon. For the Ge-L functional groups, hybridization of the 4p and 4s AOs of Ge to form a single Ge4sp 3  HO shell forms an energy minimum, and the sharing of electrons between the Ge4sp 3  HO and L HO to form a MO permits each participating orbital to decrease in radius and energy. The C2sp 3  HO has an energy of E(C,2sp 3 )=−14.63489 eV (Eq. (15.25)) and the Ge4sp 3  HO has an enery of E(Ge,4sp 3 )=−10.30968 eV (Eq. (23.209)). To meet the equipotential condition of the union of the Ge-L H 2 -type-ellipsoidal-MO with these orbitals, the hybridization factor C 2  of Eq. (15.61) for the Ge-L-bond MO given by Eq. (15.77) is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             C 
                             2 
                           
                            
                           
                             ( 
                             
                               Ge 
                                
                               
                                   
                               
                                
                               4 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                                
                               
                                   
                               
                                
                               to 
                                
                               
                                   
                               
                                
                               Ge 
                                
                               
                                   
                               
                                
                               4 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             C 
                             2 
                           
                            
                           
                             ( 
                             
                               C 
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                                
                               
                                   
                               
                                
                               to 
                                
                               
                                   
                               
                                
                               Ge 
                                
                               
                                   
                               
                                
                               4 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             E 
                              
                             
                               ( 
                               
                                 Ge 
                                 , 
                                 
                                   4 
                                    
                                   
                                     sp 
                                     3 
                                   
                                    
                                   HO 
                                 
                               
                               ) 
                             
                           
                           
                             E 
                              
                             
                               ( 
                               
                                 C 
                                 , 
                                 
                                   2 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               10.30968 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           
                             
                               - 
                               14.63489 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         0.70446 
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.215 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Since the energy of the MO is matched to that of the Ge4sp 3  HO, E(AO/HO) in Eq. (15.61) is E(Ge,4sp 3  HO) given by Eq. (23.209). In order to match the energies of the HOs within the molecule, E T (atom-atom,msp 3 .AO) of the Ge-L-bond MO for the ligands carbon or germanium is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       - 
                       0.72457 
                     
                     2 
                   
                   . 
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                      
                     
                       ( 
                       14.151 
                       ) 
                     
                   
                   ) 
                 
               
             
           
         
       
     
         [0342]    The symbols of the functional groups of germanium compounds are given in Table 141. The geometrical (Eqs. (15.1-15.5)), intercept (Eqs. (15.31-15.32) and (15.80-15.87)), and energy (Eqs. (15.61) and (23.28-23.33)) parameters of germanium compounds are given in Tables 142, 143, and 144, respectively. The total energy of each germanium compounds given in Table 145 was calculated as the sum over the integer multiple of each E D (Group) of Table 144 corresponding to functional-group composition of the compound. The bond angle parameters of germanium compounds determined using Eqs. (15.88-15.117) are given in Table 146. The charge-densities of exemplary germanium and digermanium compounds, tetraethylgermanium (Ge(CH 2 CH 3 ) 4 ) and hexaethyldigermanium ((C 2 H 5 ) 3 GeGe(C 2 H 5 ) 3 ) comprising atoms with the outer shell bridged by one or more H 2 -type ellipsoidal MOs or joined with one or more hydrogen MOs are shown in  FIGS. 67  as  68 , respectively. 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 141 
               
             
             
               
                   
               
               
                 The symbols of functional groups of germanium compounds. 
               
             
          
           
               
                   
                 Functional Group 
                 Group Symbol 
               
               
                   
                   
               
               
                   
                 GeC group 
                 Ge—C 
               
               
                   
                 GeGe group 
                 Ge—Ge 
               
               
                   
                 CH 3  group 
                 C—H (CH 3 ) 
               
               
                   
                 CH 2  alkyl group 
                 C—H (CH 2 ) 
               
               
                   
                 CH alkyl 
                 C—H 
               
               
                   
                 CC bond (n-C) 
                 C—C (a) 
               
               
                   
                 CC bond (iso-C) 
                 C—C (b) 
               
               
                   
                 CC bond (tert-C) 
                 C—C (c) 
               
               
                   
                 CC (iso to iso-C) 
                 C—C (d) 
               
               
                   
                 CC (t to t-C) 
                 C—C (e) 
               
               
                   
                 CC (t to iso-C) 
                 C—C (f) 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 142 
               
               
                   
               
               
                 The geometrical bond parameters of germanium compounds and 
               
               
                 experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Ge—C 
                 Ge—Ge 
                 C—H (CH 3 ) 
                 C—H (CH 2 ) 
                 C—H 
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 2.27367 
                 2.27367 
                 1.64920 
                 1.67122 
                 1.67465 
               
               
                 c′ (a 0 ) 
                 1.79654 
                 1.79654 
                 1.04856 
                 1.05553 
                 1.05661 
               
               
                 Bond Length 
                 1.90137 
                 1.90137 
                 1.10974 
                 1.11713 
                 1.11827 
               
               
                 2c′ (Å) 
               
               
                 Exp. Bond 
                 1.945  
                   
                 1.107  
                 1.107  
                 1.122  
               
               
                 Length 
                 ((CH 3 ) 4 Ge) 
                   
                 (C—H 
                 (C—H 
                 (isobutane) 
               
               
                 (Å) 
                 1.945  
                   
                 propane) 
                 propane) 
               
               
                   
                 (CH 3 GeH 3 ) 
                   
                 1.117  
                 1.117  
               
               
                   
                 1.89   
                   
                 (C—H 
                 (C—H 
               
               
                   
                 (CH 3 GeCl 3)   
                   
                 butane) 
                 butane) 
               
               
                 b, c (a 0 ) 
                 1.39357 
                 1.39357 
                 1.27295 
                 1.29569 
                 1.29924 
               
               
                 e 
                 0.79015 
                 0.79015 
                 0.63580 
                 0.63159 
                 0.63095 
               
               
                   
               
             
          
           
               
                   
                 C—C (a) 
                 C—C (b) 
                 C—C (c) 
                 C—C (d) 
                 C—C (e) 
                   
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 C—C (f) Group 
               
               
                   
               
               
                 a (a 0 ) 
                 2.12499 
                 2.12499 
                 2.10725 
                 2.12499 
                 2.10725 
                 2.10725 
               
               
                 c′ (a 0 ) 
                 1.45744 
                 1.45744 
                 1.45164 
                 1.45744 
                 1.45164 
                 1.45164 
               
               
                 Bond Length 
                 1.54280 
                 1.54280 
                 1.53635 
                 1.54280 
                 1.53635 
                 1.53635 
               
               
                 2c′ (Å) 
               
               
                 Exp. Bond 
                 1.532  
                 1.532  
                 1.532  
                 1.532  
                 1.532  
                 1.532  
               
               
                 Length 
                 (propane) 
                 (propane) 
                 (propane) 
                 (propane) 
                 (propane) 
                 (propane) 
               
               
                 (Å) 
                 1.531  
                 1.531  
                 1.531  
                 1.531  
                 1.531  
                 1.531  
               
               
                   
                 (butane) 
                 (butane) 
                 (butane) 
                 (butane) 
                 (butane) 
                 (butane) 
               
               
                 b, c (a 0 ) 
                 1.54616 
                 1.54616 
                 1.52750 
                 1.54616 
                 1.52750 
                 1.52750 
               
               
                 e 
                 0.68600 
                 0.68600 
                 0.68888 
                 0.68600 
                 0.68888 
                 0.68888 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 143 
               
               
                   
               
               
                 The MO to HO intercept geometrical bond parameters of germanium compounds. R, R′, R″ are H or 
               
               
                 alkyl groups. E T  is E T  (atom-atom, msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 Final Total 
                   
                   
               
               
                   
                   
                 E T   
                 E T   
                 E T   
                 E T   
                 Energy 
               
               
                   
                   
                 (eV) 
                 (eV) 
                 (eV) 
                 (eV) 
                 Ge4sp 3   
                 r initial   
                   
               
               
                 Bond 
                 Atom 
                 Bond 1 
                 Bond 2 
                 Bond 3 
                 Bond 4 
                 C2sp 3  (eV) 
                 (a 0 ) 
                 r final  (a 0 ) 
               
               
                   
               
               
                 C—H (CH 3 ) 
                 C 
                 −0.18114 
                 0 
                 0 
                 0 
                 −151.79683 
                 0.91771 
                 0.90664 
               
               
                 (CH 3 ) 3 Ge—CH 3   
                 Ge 
                 −0.18114 
                 −0.18114 
                 −0.18114 
                 −0.18114 
                   
                 1.31113 
                 0.87495 
               
               
                 (CH 3 ) 3 Ge—CH 3   
                 C 
                 −0.18114 
                 0 
                 0 
                 0 
                   
                 0.91771 
                 0.90664 
               
               
                 (CH 3 ) 3 Ge—Ge(CH 3 ) 3   
                 Ge 
                 −0.18114 
                 −0.18114 
                 −0.18114 
                 −0.18114 
                   
                 1.31113 
                 0.87495 
               
               
                 C—H (CH 3 ) 
                 C 
                 −0.92918 
                 0 
                 0 
                 0 
                 −152.54487 
                 0.91771 
                 0.86359 
               
               
                 C—H (CH 2 ) (i) 
                 C 
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                 −153.47406 
                 0.91771 
                 0.81549 
               
               
                 C—H (CH) (i) 
                 C 
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C(a)) 
                 C a   
                 −0.92918 
                 0 
                 0 
                 0 
                 −152.54487 
                 0.91771 
                 0.86359 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                 −153.47406 
                 0.91771 
                 0.81549 
               
               
                 R—H 2 C a C b (H 2 C c —R′)HCH 2 —(C—C (b)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 R—H 2 C a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (c)) 
                 C b   
                 −0.92918 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.71860 
                 0.91771 
                 0.75889 
               
               
                 isoC a C b (H 2 C c —R′)HCH 2 —(C—C (d)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 tertC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (e)) 
                 C b   
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.51399 
                 0.91771 
                 0.76765 
               
               
                 tertC a C b (H 2 C c —R′)HCH 2 —(C—C (f)) 
                 C b   
                 −0.72457 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.19863 
                 0.91771 
                 0.78155 
               
               
                 isoC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (f)) 
                 C b   
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.51399 
                 0.91771 
                 0.76765 
               
               
                   
               
             
          
           
               
                   
                   
                 E(Ge4sp 3 ) 
                   
                   
                   
                   
                   
               
               
                   
                 E Coulomb (C2sp 3 ) 
                 E(C2sp 3 ) 
               
               
                   
                 (eV) 
                 (eV) 
                 θ′ 
                 θ 1   
                 θ 2   
                 d 1   
                 d 2   
               
               
                 Bond 
                 Final 
                 Final 
                 (°) 
                 (°) 
                 (°) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 C—H (CH 3 ) 
                 −15.00689 
                 −14.81603 
                 82.43 
                 97.57 
                 44.91 
                 1.16793 
                 0.11938 
               
               
                 (CH 3 ) 3 Ge—CH 3   
                 −15.55033 
                   
                 91.73 
                 88.27 
                 38.87 
                 1.77020 
                 0.02634 
               
               
                 (CH 3 ) 3 Ge—CH 3   
                 −15.00689 
                 −14.81603 
                 94.20 
                 85.80 
                 40.45 
                 1.73010 
                 0.06644 
               
               
                 (CH 3 ) 3 Ge—Ge(CH 3 ) 3   
                 −15.55033 
                   
                 91.73 
                 88.27 
                 38.87 
                 1.77020 
                 0.02634 
               
               
                 C—H (CH 3 ) 
                 −15.75493 
                 −15.56407 
                 77.49 
                 102.51 
                 41.48 
                 1.23564 
                 0.18708 
               
               
                 C—H (CH 2 ) (i) 
                 −16.68412 
                 −16.49325 
                 68.47 
                 111.53 
                 35.84 
                 1.35486 
                 0.29933 
               
               
                 C—H (CH) (i) 
                 −17.61330 
                 −17.42244 
                 61.10 
                 118.90 
                 31.37 
                 1.42988 
                 0.37326 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 −15.75493 
                 −15.56407 
                 63.82 
                 116.18 
                 30.08 
                 1.83879 
                 0.38106 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 −16.68412 
                 −16.49325 
                 56.41 
                 123.59 
                 26.06 
                 1.90890 
                 0.45117 
               
               
                 R—H 2 C a C b (H 2 C c —R′)HCH 2 —(C—C (b)) 
                 −17.61330 
                 −17.42244 
                 48.30 
                 131.70 
                 21.90 
                 1.97162 
                 0.51388 
               
               
                 R—H 2 C a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (c)) 
                 −17.92866 
                 −17.73779 
                 48.21 
                 131.79 
                 21.74 
                 1.95734 
                 0.50570 
               
               
                 isoC a C b (H 2 C c —R′)HCH 2 —(C—C (d)) 
                 −17.61330 
                 −17.42244 
                 48.30 
                 131.70 
                 21.90 
                 1.97162 
                 0.51388 
               
               
                 tertC a (R′—H 2 C d ) C b (R″—H 2 C c )CH 2 —(C—C (e)) 
                 −17.92866 
                 −17.73779 
                 50.04 
                 129.96 
                 22.66 
                 1.94462 
                 0.49298 
               
               
                 tertC a C b (H 2 C c —R′)HCH 2 —(C—C (f)) 
                 −17.40869 
                 −17.21783 
                 52.78 
                 127.22 
                 24.04 
                 1.92443 
                 0.47279 
               
               
                 isoC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (f)) 
                 −17.92866 
                 −17.73779 
                 50.04 
                 129.96 
                 22.66 
                 1.94462 
                 0.49298 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 144 
               
               
                   
               
               
                 The energy parameters (eV) of functional groups of germanium compounds. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 C—C 
               
               
                   
                 Ge—C 
                 Ge—Ge 
                 CH 3   
                 CH 2   
                 CH 
                 (a) 
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 n 1   
                 1 
                 1 
                 3 
                 2 
                 1 
                 1 
               
               
                 n 2   
                 0 
                 0 
                 2 
                 1 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.5 
                 0.5 
                 0.75 
                 0.75 
                 0.75 
                 0.5 
               
               
                 C 2   
                 0.70446 
                 0.70446 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 2   
                 1 
                 1 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
               
               
                 c 3   
                 0 
                 0 
                 0 
                 1 
                 1 
                 0 
               
               
                 c 4   
                 2 
                 2 
                 1 
                 1 
                 1 
                 2 
               
               
                 c 5   
                 0 
                 0 
                 3 
                 2 
                 1 
                 0 
               
               
                 C 1o   
                 0.5 
                 0.5 
                 0.75 
                 0.75 
                 0.75 
                 0.5 
               
               
                 C 2o   
                 0.70446 
                 0.70446 
                 1 
                 1 
                 1 
                 1 
               
               
                 V e  (eV) 
                 −32.46926 
                 −32.46926 
                 −107.32728 
                 −70.41425 
                 −35.12015 
                 −28.79214 
               
               
                 V p  (eV) 
                 7.57336 
                 7.57336 
                 38.92728 
                 25.78002 
                 12.87680 
                 9.33352 
               
               
                 T (eV) 
                 7.14028 
                 7.14028 
                 32.53914 
                 21.06675 
                 10.48582 
                 6.77464 
               
               
                 V m  (eV) 
                 −3.57014 
                 −3.57014 
                 −16.26957 
                 −10.53337 
                 −5.24291 
                 −3.38732 
               
               
                 E (AO/HO) (eV) 
                 −10.30968 
                 −10.30968 
                 −15.56407 
                 −15.56407 
                 −14.63489 
                 −15.56407 
               
               
                 ΔE H     2     MO  (AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 E T  (AO/HO) (eV) 
                 −10.30968 
                 −10.30968 
                 −15.56407 
                 −15.56407 
                 −14.63489 
                 −15.56407 
               
               
                 E T  (H 2 MO) (eV) 
                 −31.63544 
                 −31.63544 
                 −67.69451 
                 −49.66493 
                 −31.63533 
                 −31.63537 
               
               
                 E T  (atom-atom, 
                 −0.36229 
                 −0.36229 
                 0 
                 0 
                 0 
                 −1.85836 
               
               
                 msp 3 .AO) (eV) 
               
               
                 E T  (MO) (eV) 
                 −31.99766 
                 −31.99766 
                 −67.69450 
                 −49.66493 
                 −31.63537 
                 −33.49373 
               
               
                 ω (10 15  rad/s) 
                 14.9144 
                 14.9144 
                 24.9286 
                 24.2751 
                 24.1759 
                 9.43699 
               
               
                 E K  (eV) 
                 9.81690 
                 9.81690 
                 16.40846 
                 15.97831 
                 15.91299 
                 6.21159 
               
               
                 Ē D  (eV) 
                 −0.19834 
                 −0.19834 
                 −0.25352 
                 −0.25017 
                 −0.24966 
                 −0.16515 
               
               
                 Ē Kvib  (eV) 
                 0.15312 [66] 
                 0.06335 [14] 
                 0.35532 
                 0.35532 
                 0.35532 
                 0.12312 [6] 
               
               
                   
                   
                   
                 Eq. 
                 Eq. 
                 Eq. 
               
               
                   
                   
                   
                 (13.458) 
                 (13.458) 
                 (13.458) 
               
               
                 Ē osc  (eV) 
                 −0.12178 
                 −0.16666 
                 −0.22757 
                 −0.14502 
                 −0.07200 
                 −0.10359 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                 E T  (Group) (eV) 
                 −32.11943 
                 −32.16432 
                 −67.92207 
                 −49.80996 
                 −31.70737 
                 −33.59732 
               
               
                 E initial  (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
               
               
                 E initial  (c 5  AO/HO) (eV) 
                 0 
                 0 
                 −13.59844 
                 −13.59844 
                 −13.59844 
                 0 
               
               
                 E D  (Group) (eV) 
                 2.84965 
                 2.89454 
                 12.49186 
                 7.83016 
                 3.32601 
                 4.32754 
               
               
                   
               
             
          
           
               
                   
                   
                 C—C 
                 C—C 
                 C—C 
                 C—C 
                 C—C 
               
               
                   
                   
                 (b) 
                 (c) 
                 (d) 
                 (e) 
                 (f) 
               
               
                   
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
                   
               
               
                   
                 n 1   
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                   
                 n 2   
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                   
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                   
                 C 1   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
               
               
                   
                 C 2   
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                   
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                   
                 c 2   
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
               
               
                   
                 c 3   
                 0 
                 0 
                 1 
                 1 
                 0 
               
               
                   
                 c 4   
                 2 
                 2 
                 2 
                 2 
                 2 
               
               
                   
                 c 5   
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                   
                 C 1o   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
               
               
                   
                 C 2o   
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                   
                 V e  (eV) 
                 −28.79214 
                 −29.10112 
                 −28.79214 
                 −29.10112 
                 −29.10112 
               
               
                   
                 V p  (eV) 
                 9.33352 
                 9.37273 
                 9.33352 
                 9.37273 
                 9.37273 
               
               
                   
                 T (eV) 
                 6.77464 
                 6.90500 
                 6.77464 
                 6.90500 
                 6.90500 
               
               
                   
                 V m  (eV) 
                 −3.38732 
                 −3.45250 
                 −3.38732 
                 −3.45250 
                 −3.45250 
               
               
                   
                 E (AO/HO) (eV) 
                 −15.56407 
                 −15.35946 
                 −15.56407 
                 −15.35946 
                 −15.35946 
               
               
                   
                 ΔE H     2     MO  (AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                   
                 E T  (AO/HO) (eV) 
                 −15.56407 
                 −15.35946 
                 −15.56407 
                 −15.35946 
                 −15.35946 
               
               
                   
                 E T  (H 2 MO) (eV) 
                 −31.63537 
                 −31.63535 
                 −31.63537 
                 −31.63535 
                 −31.63535 
               
               
                   
                 E T  (atom-atom, 
                 −1.85836 
                 −1.44915 
                 −1.85836 
                 −1.44915 
                 −1.44915 
               
               
                   
                 msp 3 .AO) (eV) 
               
               
                   
                 E T  (MO) (eV) 
                 −33.49373 
                 −33.08452 
                 −33.49373 
                 −33.08452 
                 −33.08452 
               
               
                   
                 ω (10 15  rad/s) 
                 9.43699 
                 15.4846 
                 9.43699 
                 9.55643 
                 9.55643 
               
               
                   
                 E K  (eV) 
                 6.21159 
                 10.19220 
                 6.21159 
                 6.29021 
                 6.29021 
               
               
                   
                 Ē D  (eV) 
                 −0.16515 
                 −0.20896 
                 −0.16515 
                 −0.16416 
                 −0.16416 
               
               
                   
                 Ē Kvib  (eV) 
                 0.17978 [7] 
                 0.09944 [8] 
                 0.12312 [6] 
                 0.12312 [6] 
                 0.12312 [6] 
               
               
                   
                 Ē osc  (eV) 
                 −0.07526 
                 −0.15924 
                 −0.10359 
                 −0.10260 
                 −0.10260 
               
               
                   
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                   
                 E T  (Group) (eV) 
                 −33.49373 
                 −33.24376 
                 −33.59732 
                 −33.18712 
                 −33.18712 
               
               
                   
                 E initial  (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
               
               
                   
                 E initial  (c 5  AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                   
                 E D  (Group) (eV) 
                 4.29921 
                 3.97398 
                 4.17951 
                 3.62128 
                 3.91734 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 145 
               
             
             
               
                   
               
               
                 The total bond energies of gaseous-state germanium compounds calculated using the functional 
               
               
                 group composition (separate functional groups designated in the first row) and the energies of 
               
               
                 Table 144 compared to the gaseous-state experimental values [67] except where indicated. 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                   
                   
                   
                   
                   
                 C—C 
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Ge—C 
                 Ge—Ge 
                 CH 3   
                 CH 2   
                 CH 
                 (a) 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 C 8 H 20 Ge 
                 Tetraethylgermanium 
                 4 
                 0 
                 4 
                 4 
                 0 
                 4 
                 109.99686 
                 110.18166 
                 0.00168 
               
               
                 C 12 H 28 Ge 
                 Tetra-n-propylgermanium 
                 4 
                 0 
                 4 
                 8 
                 0 
                 8 
                 158.62766 
                 158.63092 
                 0.00002 
               
               
                 C 12 H 30 Ge 2   
                 Hexaethyldigermanium 
                 6 
                 1 
                 6 
                 6 
                 0 
                 6 
                 167.88982 
                 167.89836 
                 0.00005 
               
               
                   
               
               
                   a Crystal. 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 146 
               
               
                   
               
               
                 The bond angle parameters of germanium compounds and experimental values [3]. In the 
               
               
                 calculation of θ v , the parameters from the preceding angle were used. E T  is E T  (atom-atom, 
               
               
                 msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                 2c′ 
                   
                 Atom 1 
                   
                 Atom 2 
                   
                   
               
               
                   
                 2c′ 
                 2c′ 
                 Terminal 
                   
                 Hybridization 
                   
                 Hybridization 
               
               
                 Atoms of 
                 Bond 1 
                 Bond 2 
                 Atoms 
                 E Coulombic   
                 Designation 
                 E Coulombic   
                 Designation 
                 c 2   
                 c 2   
               
               
                 Angle 
                 (a 0 ) 
                 (a 0 ) 
                 (a 0 ) 
                 Atom 1 
                 (Table 7) 
                 Atom 2 
                 (Table 7) 
                 Atom 1 
                 Atom 2 
               
               
                   
               
               
                 Methyl 
                 2.09711 
                 2.09711 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
                 1 
               
               
                 ∠HC a H 
               
               
                 ∠H a C a Ge 
               
               
                 ∠C a GeC b   
                 3.59307 
                 3.59307 
                 5.7446 
                 −15.55033 
                 5 
                 −15.55033 
                 5 
                 0.87495 
                 0.87495 
               
               
                 Methylene 
                 2.11106 
                 2.11106 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
                 1 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
               
               
                 ∠C a C b H 
               
               
                 Methyl 
                 2.09711 
                 2.09711 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
                 1 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
               
               
                 ∠C a C b H 
               
               
                 ∠C b C a C c   
                 2.91547 
                 2.91547 
                 4.7958 
                 −16.68412 
                 26 
                 −16.68412 
                 26  
                 0.81549 
                 0.81549 
               
               
                 iso C a   
                   
                   
                   
                 C b   
                   
                 C c   
               
               
                 ∠C b C a H 
                 2.91547 
                 2.11323 
                 4.1633 
                 −15.55033 
                 5 
                 −14.82575 
                 1 
                 0.87495 
                 0.91771 
               
               
                 iso C a   
                   
                   
                   
                 C a   
                   
                 C b   
               
               
                 ∠C a C b H 
                 2.91547 
                 2.09711 
                 4.1633 
                 −15.55033 
                 5 
                 −14.82575 
                 1 
                 0.87495 
                 0.91771 
               
               
                 iso C a   
                   
                   
                   
                 C b   
                   
                 C a   
               
               
                 ∠C b C a C b   
                 2.90327 
                 2.90327 
                 4.7958 
                 −16.68412 
                 26 
                 −16.68412 
                 26  
                 0.81549 
                 0.81549 
               
               
                 tert C a   
                   
                   
                   
                 C b   
                   
                 C b   
               
               
                 ∠C b C a C d   
               
               
                   
               
             
          
           
               
                 Atoms of 
                   
                   
                   
                   
                 E T   
                 θ v   
                 θ 1   
                 θ 2   
                 Cal. θ 
                 Exp. θ 
               
               
                 Angle 
                 C 1   
                 C 2   
                 c 1   
                 c 2 ′ 
                 (eV) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
               
               
                   
               
               
                 Methyl 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 109.50 
               
               
                 ∠HC a H 
               
               
                 ∠H a C a Ge 
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
                 108 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (tetramethyl germanium) 
               
               
                 ∠C a GeC b   
                 1 
                 1 
                 1 
                 0.87495 
                 −1.85836 
                   
                   
                   
                 106.14 
                 109.5 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (tetramethyl germanium) 
               
               
                 Methylene 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 108.44 
                   107 (propane) 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
                   
                   
                   
                   
                   
                 69.51 
                   
                   
                 110.49 
                   112 (propane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 113.8 (butane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 110.8 (isobutane) 
               
               
                 ∠C a C b H 
                   
                   
                   
                   
                   
                 69.51 
                   
                   
                 110.49 
                 111.0 (butane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 111.4 (isobutane) 
               
               
                 Methyl 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 109.50 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                 ∠C a C b H 
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                 ∠C b C a C c   
                 1 
                 1 
                 1 
                 0.81549 
                 −1.85836 
                   
                   
                   
                 110.67 
                 110.8 (isobutane) 
               
               
                 iso C a   
               
               
                 ∠C b C a H 
                 0.75 
                 1 
                 0.75 
                 1.04887 
                 0 
                   
                   
                   
                 110.76 
               
               
                 iso C a   
               
               
                 ∠C a C b H 
                 0.75 
                 1 
                 0.75 
                 1.04887 
                 0 
                   
                   
                   
                 111.27 
                 111.4 (isobutane) 
               
               
                 iso C a   
               
               
                 ∠C b C a C b   
                 1 
                 1 
                 1 
                 0.81549 
                 −1.85836 
                   
                   
                   
                 111.37 
                 110.8 (isobutane) 
               
               
                 tert C a   
               
               
                 ∠C b C a C d   
                   
                   
                   
                   
                   
                 72.50 
                   
                   
                 107.50 
               
               
                   
               
             
          
         
       
     
         [0343]    Tin Functional Groups and Molecules 
         [0344]    As in the cases of carbon and tin, the bonding in the tin atom involves four sp 3  hybridized orbitals formed from the 5 p and 5s electrons of the outer shells. Sn—X X=halide, oxide, Sn—H, and Sn—Sn bonds form between Sn5sp 3  HOs and between a halide or oxide AO, a H1s AO, and a Sn5sp 3  HO, respectively to yield tin halides and oxides, stannanes, and distannes, respectively. The geometrical parameters of each Sn—X X=halide, oxide , Sn—H , and Sn—Sn functional group is solved from the force balance equation of the electrons of the corresponding σ-MO and the relationships between the prolate spheroidal axes. Then, the sum of the energies of the H 2 -type ellipsoidal MOs is matched to that of the Sn5sp 3  shell as in the case of the corresponding carbon and tin molecules. As in the case of the transition metals, the energy of each functional group is determined for the effect of the electron density donation from the each participating Sn5sp 3  HO and AO to the corresponding MO that maximizes the bond energy. 
         [0345]    The branched-chain alkyl stannanes and distannes, Sn m C n H 2(m+n)+2 , comprise at least a terminal methyl group (CH 3 ) and at least one Sn bound by a carbon-tin single bond comprising a C—Sn group, and may comprise methylene (CH 2 ), methylyne (CH), C—C, SnH n=1,2,3 , and Sn—Sn functional groups. The methyl and methylene functional groups are equivalent to those of straight-chain alkanes. Six types of C—C bonds can be identified. The n-alkane C—C bond is the same as that of straight-chain alkanes. In addition, the C—C bonds within isopropyl ((CH 3 ) 2 CH) and t-butyl ((CH 3 ) 3 C) groups and the isopropyl to isopropyl, isopropyl to t-butyl, and t-butyl to t-butyl C—C bonds comprise functional groups. 
         [0346]    The Sn electron configuration is [Kr]5s 2  4d 10 5 p 2 , and the orbital arrangement is 
         [0000]    
       
         
           
             
               
                 
                   
                     ↑ 
                     1 
                   
                    
                   
                     
                       ↑ 
                       0 
                     
                     
                       5 
                        
                       p 
                        
                       
                           
                       
                        
                       state 
                     
                   
                    
                   
                     
                         
                     
                     
                       - 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   23.216 
                   ) 
                 
               
             
           
         
       
     
         [0000]    corresponding to the ground state  3 P 0 . The energy of the carbon 5p shell is the negative of the ionization energy of the tin atom [1] given by 
         [0000]        E (Sn,5  p  shell)=− E (ionization; Sn)=−7.34392 eV   (23.217) 
         [0000]    The energy of tin is less than the Coulombic energy between the electron and proton of H given by Eq. (1.231), but the atomic orbital may hybridize in order to achieve a bond at an energy minimum. After Eq. (13.422), the Sn5s atomic orbital (AO) combines with the Sn5 p AOs to form a single Sn5sp 3  hybridized orbital (HO) with the orbital arrangement 
         [0000]    
       
         
           
             
               
                 
                   
                     ↑ 
                     
                       0 
                       , 
                       0 
                     
                   
                    
                   
                     
                       
                         ↑ 
                         
                           1 
                           , 
                           
                             - 
                             1 
                           
                         
                       
                        
                       
                         ↑ 
                         
                           1 
                           , 
                           0 
                         
                       
                     
                     
                       5 
                        
                       
                         sp 
                         3 
                       
                        
                       
                           
                       
                        
                       state 
                     
                   
                    
                   
                     ↑ 
                     
                       1 
                       , 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   23.218 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where the quantum numbers (l, m l ) are below each electron. The total energy of the state is given by the sum over the four electrons. The sum E T (Sn,4sp 3 ) of experimental energies [1] of Sn, Sn + , Sn 2+ , and Sn 3+  is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             T 
                           
                            
                           
                             ( 
                             
                               Sn 
                               , 
                               
                                 5 
                                  
                                 
                                     
                                 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             40.73502 
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             30.50260 
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             14.6322 
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             7.3492 
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           93.21374 
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.219 
                   ) 
                 
               
             
           
         
       
     
         [0000]    By considering that the central field decreases by an integer for each successive electron of the shell, the radius r 5sp     3    of the Sn5sp 3  shell may be calculated from the Coulombic energy using Eq. (15.13): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           
                             5 
                              
                             
                               sp 
                               3 
                             
                           
                         
                         = 
                           
                          
                         
                           
                             ∑ 
                             
                               n 
                               = 
                               46 
                             
                             49 
                           
                            
                           
                             
                               
                                 ( 
                                 
                                   Z 
                                   - 
                                   n 
                                 
                                 ) 
                               
                                
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               
                                 
                                   πɛ 
                                   0 
                                 
                                  
                                 
                                   ( 
                                   
                                     e 
                                      
                                     
                                         
                                     
                                      
                                     93.21374 
                                      
                                     
                                         
                                     
                                      
                                     eV 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             10 
                              
                             
                                 
                             
                              
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 ( 
                                 
                                   e 
                                    
                                   
                                       
                                   
                                    
                                   93.21374 
                                    
                                   
                                       
                                   
                                    
                                   eV 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           1.45964 
                            
                           
                             a 
                             0 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.220 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where Z=50 for tin. Using Eq. (15.14), the Coulombic energy E Coulomb  (Sn,5sp 3 ) of the outer electron of the Sn5sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             Coulomb 
                           
                            
                           
                             ( 
                             
                               Sn 
                               , 
                               
                                 5 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             
                               r 
                               
                                 5 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             1.45964 
                              
                             
                               a 
                               0 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             9.321374 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.221 
                   ) 
                 
               
             
           
         
       
     
         [0000]    During hybridization, the spin-paired 5s electrons are promoted to Sn5sp 3  shell as unpaired electrons. The energy for the promotion is the magnetic energy given by Eq. (15.15) at the initial radius of the 5s electrons. From Eq. (10.255) with Z=50, the radius r 48  of Sn5s shell is 
         [0000]      r 48 =1.33816a 0    (23.222) 
         [0000]    Using Eqs. (15.15) and (23.206), the unpairing energy is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           E 
                            
                           
                             ( 
                             magnetic 
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             2 
                              
                             π 
                              
                             
                                 
                             
                              
                             
                               μ 
                               0 
                             
                              
                             
                                
                               2 
                             
                              
                             
                               ℏ 
                               2 
                             
                           
                           
                             
                               
                                 m 
                                 e 
                                 2 
                               
                                
                               
                                 ( 
                                 
                                   r 
                                   48 
                                 
                                 ) 
                               
                             
                             3 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             8 
                              
                             
                               πμ 
                               o 
                             
                              
                             
                               μ 
                               B 
                               2 
                             
                           
                           
                             
                               ( 
                               
                                 1.33816 
                                  
                                 
                                   a 
                                   0 
                                 
                               
                               ) 
                             
                             3 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           0.04775 
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.223 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Using Eqs. (23.203) and (23.207), the energy E (Sn,5sp 3 ) of the outer electron of the Sn5sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           E 
                            
                           
                             ( 
                             
                               Sn 
                               , 
                               
                                 5 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               - 
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 r 
                                 
                                   5 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                             
                           
                           + 
                           
                             
                               2 
                                
                               
                                 πμ 
                                 0 
                               
                                
                               
                                  
                                 2 
                               
                                
                               
                                 ℏ 
                                 2 
                               
                             
                             
                               
                                 
                                   m 
                                   e 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     r 
                                     48 
                                   
                                   ) 
                                 
                               
                               3 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               9.321374 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             0.04775 
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             9.27363 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.244 
                   ) 
                 
               
             
           
         
       
     
         [0347]    Next, consider the formation of the Sn-L-bond MO of tin compounds wherein L is a ligand including tin and each tin atom has a Sn5sp 3  electron with an energy given by Eq. (23.224). The total energy of the state of each tin atom is given by the sum over the four electrons. The sum E T (Sn Sn-L ,5sp 3 ) of energies of Sn5sp 3  (Eq. (23.224)), Sn + , Sn 2+ , and Sn 3+  is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             T 
                           
                            
                           
                             ( 
                             
                               
                                 Sn 
                                 
                                   Sn 
                                   - 
                                   L 
                                 
                               
                               , 
                               
                                 5 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           - 
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       40.73502 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       30.50260 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       14.6322 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       E 
                                        
                                       
                                         ( 
                                         
                                           Sn 
                                           , 
                                           
                                             5 
                                              
                                             
                                               sp 
                                               3 
                                             
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           - 
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       40.73502 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       30.50260 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       14.6322 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       9.27363 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             95.14345 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.225 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where E (Sn,5sp 3 ) is the sum of the energy of Sn, −7.34392 eV, and the hybridization energy. 
         [0348]    A minimum energy is achieved while matching the potential, kinetic, and orbital energy relationships given in the Hydroxyl Radical (OH) section with the donation of electron density from the participating Sn5sp 3  HO to each Sn-L-bond MO. As in the case of acetylene given in the Acetylene Molecule section, the energy of each Sn-L functional group is determined for the effect of the charge donation. For example, as in the case of the Si—Si-bond MO given in the Alkyl Silanes and Disilanes section, the sharing of electrons between two Sn5sp 3  HOs to form a Sn—Sn-bond MO permits each participating orbital to decrease in size and energy. In order to further satisfy the potential, kinetic, and orbital energy relationships, each Sn5sp 3  HO donates an excess of 25% of its electron density to the Sn—Sn-bond MO to form an energy minimum. By considering this electron redistribution in the distannane molecule as well as the fact that the central field decreases by an integer for each successive electron of the shell, in general terms, the radius r Sn-L5sp     3    of the Sn5sp 3  shell may be calculated from the Coulombic energy using Eq. (15.18): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           
                             Sn 
                             - 
                             
                               L 
                                
                               
                                   
                               
                                
                               5 
                                
                               
                                 sp 
                                 3 
                               
                             
                           
                         
                         = 
                           
                          
                         
                           
                             ( 
                             
                               
                                 
                                   ∑ 
                                   
                                     n 
                                     = 
                                     46 
                                   
                                   49 
                                 
                                  
                                 
                                   ( 
                                   
                                     Z 
                                     - 
                                     n 
                                   
                                   ) 
                                 
                               
                               - 
                               0.25 
                             
                             ) 
                           
                            
                           
                             
                                
                               2 
                             
                             
                               8 
                                
                               
                                 
                                   πɛ 
                                   0 
                                 
                                  
                                 
                                   ( 
                                   
                                     e 
                                      
                                     
                                         
                                     
                                      
                                     95.14345 
                                      
                                     
                                         
                                     
                                      
                                     eV 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             9.75 
                              
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 ( 
                                 
                                   e 
                                    
                                   
                                       
                                   
                                    
                                   95.14345 
                                    
                                   
                                       
                                   
                                    
                                   eV 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           1.39428 
                            
                           
                             a 
                             0 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.226 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Using Eqs. (15.19) and (23.210), the Coulombic energy E Coulomb (Sn sn-L ,5sp 3 ) of the outer electron of the Sn5sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             Coulomb 
                           
                            
                           
                             ( 
                             
                               
                                 Sn 
                                 
                                   Sn 
                                   - 
                                   L 
                                 
                               
                               , 
                               
                                 5 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             
                               r 
                               
                                 Sn 
                                 - 
                                 
                                   L 
                                    
                                   
                                       
                                   
                                    
                                   5 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             1.39428 
                              
                             
                               a 
                               0 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             9.75830 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.227 
                   ) 
                 
               
             
           
         
       
     
         [0000]    During hybridization, the spin-paired 5s electrons are promoted to Sn5sp 3  shell as unpaired electrons. The energy for the promotion is the magnetic energy given by Eq. (23.223). Using Eqs. (23.223) and (23.227), the energy E(Sn Sn-L , 5sp 3 ) of the outer electron of the Si3sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           E 
                            
                           
                             ( 
                             
                               
                                 Sn 
                                 
                                   Sn 
                                   - 
                                   L 
                                 
                               
                               , 
                               
                                 5 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               - 
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 r 
                                 
                                   Sn 
                                   - 
                                   
                                     L 
                                      
                                     
                                         
                                     
                                      
                                     5 
                                      
                                     
                                       sp 
                                       3 
                                     
                                   
                                 
                               
                             
                           
                           + 
                           
                             
                               2 
                                
                               
                                 πμ 
                                 0 
                               
                                
                               
                                  
                                 2 
                               
                                
                               
                                 ℏ 
                                 2 
                               
                             
                             
                               
                                 
                                   m 
                                   e 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     r 
                                     48 
                                   
                                   ) 
                                 
                               
                               3 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               9.75830 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             0.04775 
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             9.71056 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.228 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Thus, E T (Sn-L,5sp 3 ), the energy change of each Sn5sp 3  shell with the formation of the Sn-L-bond MO is given by the difference between Eq. (23.228) and Eq. (23.224): 
         [0000]        E   T (Sn-L,5sp 3 )= E (Sn sn-L ,5sp 3 )− E (Sn,5sp 3 )=−0.43693 eV   (23.229) 
         [0349]    Next, consider the formation of the Si-L-bond MO of additional functional groups wherein each tin atom contributes a Sn5sp 3  electron having the sum E T (Sn Sn-L ,5Sp 3 ) of energies of Sn5sp 3  (Eq. (23.224)), Se + , Sn 2+ , and Sn 3+  given by Eq. (23.209). Each Sn-L-bond MO of each functional group Si-L forms with the sharing of electrons between a Sn5sp 3  HO and a AO or HO of L, and the donation of electron density from the Sn5sp 3  HO to the Sn-L-bond MO permits the participating orbitals to decrease in size and energy. In order to further satisfy the potential, kinetic, and orbital energy relationships while forming an energy minimum, the permitted values of the excess fractional charge of its electron density that the Sn5sp 3  HO donates to the Si-L-bond MO given by Eq. (15.18) is s (0.25); s=1,2,3,4 and linear combinations thereof. By considering this electron redistribution in the tin molecule as well as the fact that the central field decreases by an integer for each successive electron of the shell, the radius r Sn-L5sp     3    of the Sn5sp 3  shell may be calculated from the Coulombic energy using Eq. (15.18): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           
                             Sn 
                             - 
                             
                               L 
                                
                               
                                   
                               
                                
                               5 
                                
                               
                                 sp 
                                 3 
                               
                             
                           
                         
                         = 
                           
                          
                         
                           
                             ( 
                             
                               
                                 
                                   ∑ 
                                   
                                     n 
                                     = 
                                     46 
                                   
                                   49 
                                 
                                  
                                 
                                   ( 
                                   
                                     Z 
                                     - 
                                     n 
                                   
                                   ) 
                                 
                               
                               - 
                               
                                 s 
                                  
                                 
                                   ( 
                                   0.25 
                                   ) 
                                 
                               
                             
                             ) 
                           
                            
                           
                             
                                
                               2 
                             
                             
                               8 
                                
                               
                                 
                                   πɛ 
                                   0 
                                 
                                  
                                 
                                   ( 
                                   
                                     e 
                                      
                                     
                                         
                                     
                                      
                                     95.14345 
                                      
                                     
                                         
                                     
                                      
                                     eV 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               ( 
                               
                                 10 
                                 - 
                                 
                                   s 
                                    
                                   
                                     ( 
                                     0.25 
                                     ) 
                                   
                                 
                               
                               ) 
                             
                              
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 ( 
                                 
                                   e 
                                    
                                   
                                       
                                   
                                    
                                   95.14345 
                                    
                                   
                                       
                                   
                                    
                                   eV 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.230 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Using Eqs. (15.19) and (23.230), the Coulombic energy E Coulomb (Sn sn-L ,5sp 3 ) of the outer electron of the Sn5sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             Coulomb 
                           
                            
                           
                             ( 
                             
                               
                                 Sn 
                                 
                                   Sn 
                                   - 
                                   L 
                                 
                               
                               , 
                               
                                 5 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             
                               r 
                               
                                 Sn 
                                 - 
                                 
                                   L 
                                    
                                   
                                       
                                   
                                    
                                   5 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             
                               
                                 
                                   ( 
                                   
                                     10 
                                     - 
                                     
                                       s 
                                        
                                       
                                         ( 
                                         0.25 
                                         ) 
                                       
                                     
                                   
                                   ) 
                                 
                                  
                                 
                                    
                                   2 
                                 
                               
                               
                                 8 
                                  
                                 
                                   
                                     πɛ 
                                     0 
                                   
                                    
                                   
                                     ( 
                                     
                                       e 
                                        
                                       
                                           
                                       
                                        
                                       95.14345 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             95.14345 
                              
                             
                                 
                             
                              
                             eV 
                           
                           
                             ( 
                             
                               10 
                               - 
                               
                                 s 
                                  
                                 
                                   ( 
                                   0.25 
                                   ) 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.231 
                   ) 
                 
               
             
           
         
       
     
         [0000]    During hybridization, the spin-paired 5s electrons are promoted to Sn5sp 3  shell as unpaired electrons. The energy for the promotion is the magnetic energy given by Eq. (23.223). Using Eqs. (23.223) and (23.231), the energy E(Sn sn-L ,5sp 3 ) of the outer electron of the Si3sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           E 
                            
                           
                             ( 
                             
                               
                                 Sn 
                                 
                                   Sn 
                                   - 
                                   L 
                                 
                               
                               , 
                               
                                 5 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               - 
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 r 
                                 
                                   Sn 
                                   - 
                                   
                                     L 
                                      
                                     
                                         
                                     
                                      
                                     5 
                                      
                                     
                                       sp 
                                       3 
                                     
                                   
                                 
                               
                             
                           
                           + 
                           
                             
                               2 
                                
                               
                                 πμ 
                                 0 
                               
                                
                               
                                  
                                 2 
                               
                                
                               
                                 ℏ 
                                 2 
                               
                             
                             
                               
                                 
                                   m 
                                   e 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     r 
                                     48 
                                   
                                   ) 
                                 
                               
                               3 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               95.14345 
                                
                               
                                   
                               
                                
                               eV 
                             
                             
                               ( 
                               
                                 10 
                                 - 
                                 
                                   s 
                                    
                                   
                                     ( 
                                     0.25 
                                     ) 
                                   
                                 
                               
                               ) 
                             
                           
                           + 
                           
                             0.04775 
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.232 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Thus, E T (Sn-L,5sp 3 ), the energy change of each Sn5sp 3  shell with the formation of the Sn-L-bond MO is given by the difference between Eq. (23.232) and Eq. (23.224): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             T 
                           
                            
                           
                             ( 
                             
                               
                                 Sn 
                                 - 
                                 L 
                               
                               , 
                               
                                 5 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             E 
                              
                             
                               ( 
                               
                                 
                                   Sn 
                                   
                                     Sn 
                                     - 
                                     L 
                                   
                                 
                                 , 
                                 
                                   5 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                           - 
                           
                             E 
                              
                             
                               ( 
                               
                                 Sn 
                                 , 
                                 
                                   5 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               
                                 95.14345 
                                 
                                   ( 
                                   
                                     10 
                                     - 
                                     
                                       s 
                                        
                                       
                                         ( 
                                         0.25 
                                         ) 
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                              
                             eV 
                           
                           + 
                           
                             0.04775 
                              
                             
                                 
                             
                              
                             eV 
                           
                           - 
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           ( 
                           
                             
                               - 
                               9.27363 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.233 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Using Eq. (15.28) for the case that the energy matching and energy minimum conditions of the MOs in the tin molecule are met by a linear combination of values of s (s 1  and s 2 ) in Eqs. (23.230-23.233), the energy E(Sn Sn-L ,5sp 3 ) of the outer electron of the Si3sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     E 
                      
                     
                       ( 
                       
                         
                           Sn 
                           
                             Sn 
                             - 
                             L 
                           
                         
                         , 
                         
                           5 
                            
                           
                             sp 
                             3 
                           
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           
                             
                               
                                 95.14345 
                                  
                                 
                                     
                                 
                                  
                                 eV 
                               
                               
                                 ( 
                                 
                                   10 
                                   - 
                                   
                                     
                                       s 
                                       1 
                                     
                                      
                                     
                                       ( 
                                       0.25 
                                       ) 
                                     
                                   
                                 
                                 ) 
                               
                             
                             + 
                             
                               
                                 95.14345 
                                  
                                 
                                     
                                 
                                  
                                 eV 
                               
                               
                                 ( 
                                 
                                   10 
                                   - 
                                   
                                     
                                       s 
                                       2 
                                     
                                      
                                     
                                       ( 
                                       0.25 
                                       ) 
                                     
                                   
                                 
                                 ) 
                               
                             
                             + 
                           
                         
                       
                       
                         
                           
                             2 
                              
                             
                               ( 
                               
                                 0.04775 
                                  
                                 
                                     
                                 
                                  
                                 eV 
                               
                               ) 
                             
                           
                         
                       
                     
                     2 
                   
                 
               
               
                 
                   ( 
                   23.234 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Using Eqs. (15.13) and (23.234), the radius corresponding to Eq. (23.234) is: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           
                             5 
                              
                             
                               sp 
                               3 
                             
                           
                         
                         = 
                           
                          
                         
                           
                              
                             2 
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             
                               E 
                                
                               
                                 ( 
                                 
                                   
                                     Sn 
                                     
                                       Sn 
                                       - 
                                       L 
                                     
                                   
                                   , 
                                   
                                     5 
                                      
                                     
                                       sp 
                                       3 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                              
                             2 
                           
                           
                             8 
                              
                             
                               
                                 πɛ 
                                 0 
                               
                               ( 
                               
                                 e 
                                 ( 
                                 
                                   
                                     
                                       
                                         
                                           
                                             
                                               95.14345 
                                                
                                               
                                                   
                                               
                                                
                                               eV 
                                             
                                             
                                               ( 
                                               
                                                 10 
                                                 - 
                                                 
                                                   
                                                     s 
                                                     1 
                                                   
                                                    
                                                   
                                                     ( 
                                                     0.25 
                                                     ) 
                                                   
                                                 
                                               
                                               ) 
                                             
                                           
                                           + 
                                           
                                             
                                               95.14345 
                                                
                                               
                                                   
                                               
                                                
                                               eV 
                                             
                                             
                                               ( 
                                               
                                                 10 
                                                 - 
                                                 
                                                   
                                                     s 
                                                     2 
                                                   
                                                    
                                                   
                                                     ( 
                                                     0.25 
                                                     ) 
                                                   
                                                 
                                               
                                               ) 
                                             
                                           
                                           + 
                                         
                                       
                                     
                                     
                                       
                                         
                                           2 
                                            
                                           
                                             ( 
                                             
                                               0.04775 
                                                
                                               
                                                   
                                               
                                                
                                               eV 
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                   
                                   2 
                                 
                                 ) 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.235 
                   ) 
                 
               
             
           
         
       
     
         [0000]    E T (Sn-L,5sp 3 ), the energy change of each Sn5sp 3  shell with the formation of the Sn-L-bond MO is given by the difference between Eq. (23.235) and Eq. (23.224): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             T 
                           
                            
                           
                             ( 
                             
                               
                                 Sn 
                                 - 
                                 L 
                               
                               , 
                               
                                 5 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             E 
                              
                             
                               ( 
                               
                                 
                                   Sn 
                                   
                                     Sn 
                                     - 
                                     L 
                                   
                                 
                                 , 
                                 
                                   5 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                           - 
                           
                             E 
                              
                             
                               ( 
                               
                                 Sn 
                                 , 
                                 
                                   5 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               
                                 
                                   
                                     
                                       
                                         95.14345 
                                          
                                         
                                             
                                         
                                          
                                         eV 
                                       
                                       
                                         ( 
                                         
                                           10 
                                           - 
                                           
                                             
                                               s 
                                               1 
                                             
                                              
                                             
                                               ( 
                                               0.25 
                                               ) 
                                             
                                           
                                         
                                         ) 
                                       
                                     
                                     + 
                                     
                                       
                                         95.14345 
                                          
                                         
                                             
                                         
                                          
                                         eV 
                                       
                                       
                                         ( 
                                         
                                           10 
                                           - 
                                           
                                             
                                               s 
                                               2 
                                             
                                              
                                             
                                               ( 
                                               0.25 
                                               ) 
                                             
                                           
                                         
                                         ) 
                                       
                                     
                                     + 
                                   
                                 
                               
                               
                                 
                                   
                                     2 
                                      
                                     
                                       ( 
                                       
                                         0.04775 
                                          
                                         
                                             
                                         
                                          
                                         eV 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                             2 
                           
                           - 
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           ( 
                           
                             
                               - 
                               9.27363 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.236 
                   ) 
                 
               
             
           
         
       
     
         [0350]    E T (Sn-L,5sp 3 ) is also given by Eq. (15.29). Bonding parameters for Sn-L-bond MO of tin functional groups due to charge donation from the HO to the MO are given in Table 147. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 147 
               
             
             
               
                   
               
               
                 The values of r Sn5sp   3 , E Coulomb (Sn Sn-L ,5sp 3 ), and E(Sn Sn-L ,5sp 3 ) and the resulting 
               
               
                 E T (Sn-L,5sp 3 ) of the MO due to charge donation from the HO to the MO. 
               
             
          
           
               
                 MO 
                   
                   
                   
                 E Coulomb (Sn Sn-L ,5sp 3 ) 
                 E(Sn Sn-L ,5sp 3 ) 
                   
               
               
                 Bond 
                   
                   
                 r Sn5sp   3 (a 0 ) 
                 (eV) 
                 (eV) 
                 E T (Sn-L,5sp 3 ) 
               
               
                 Type 
                 s1 
                 s2 
                 Final 
                 Final 
                 Final 
                 (eV) 
               
               
                   
               
             
          
           
               
                 0 
                 0 
                 0 
                 1.45964 
                 −9.321374 
                 −9.27363 
                 0 
               
               
                 I 
                 1 
                 0 
                 1.39428 
                 −9.75830 
                 −9.71056 
                 −0.43693 
               
               
                 II 
                 2 
                 0 
                 1.35853 
                 −10.01510 
                 −9.96735 
                 −0.69373 
               
               
                 III 
                 3 
                 0 
                 1.32278 
                 −10.28578 
                 −10.23803 
                 −0.96440 
               
               
                 IV 
                 4 
                 0 
                 1.28703 
                 −10.57149 
                 −10.52375 
                 −1.25012 
               
               
                 I + II 
                 1 
                 2 
                 1.37617 
                 −9.88670 
                 −9.83895 
                 −0.56533 
               
               
                 II + III 
                 2 
                 3 
                 1.34042 
                 −10.15044 
                 −10.10269 
                 −0.82906 
               
               
                   
               
             
          
         
       
     
         [0351]    The semimajor axis a solution given by Eq. (23.41) of the force balance equation, Eq. (23.39), for the σ-MO of the Sn-L-bond MO of SnL n  is given in Table 149 with the force-equation parameters Z=50, n e , and L corresponding to the orbital and spin angular momentum terms of the 4s HO shell. The semimajor axis a of organometallic compounds, stannanes and distannes, are solved using Eq. (15.51). 
         [0352]    For the Sn-L functional groups, hybridization of the 5p and 5s AOs of Sn to form a single Sn5sp 3  HO shell forms an energy minimum, and the sharing of electrons between the Sn5sp 3  HO and L AO to form a MO permits each participating orbital to decrease in radius and energy. The Cl AO has an energy of E(Cl)=−12.96764 eV, the Br AO has an energy of E(Br)=−11.8138 eV, the I AO has an energy of E(I)=−10.45126 eV, the O AO has an energy of E(O)=−13.61805 eV, the C2sp 3  HO has an energy of E(C,2sp 3 )=−14.63489 eV (Eq. (15.25)), 13.605804 eV is the magnitude of the Coulombic energy between the electron and proton of H (Eq. (1.231)), the Coulomb energy of the Sn5sp 3  HO is E Coulomb (Sn,5sp 3 HO)=−9.32137 eV (Eq. (23.205)), and the Sn5sp 3  HO has an energy of E(Sn,5sp 3 HO)=−9.27363 eV (Eq. (23.208)). To meet the equipotential condition of the union of the Sn-L H 2 -type-ellipsoidal-MO with these orbitals, the hybridization factor(s), at least one of c 2  and C 2  of Eq. (15.61) for the Sn-L-bond MO given by Eq. (15.77) is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             c 
                             2 
                           
                            
                           
                             ( 
                             
                               ClAO 
                                
                               
                                   
                               
                                
                               to 
                                
                               
                                   
                               
                                
                               Sn 
                                
                               
                                   
                               
                                
                               5 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             C 
                             2 
                           
                            
                           
                             ( 
                             
                               ClAO 
                                
                               
                                   
                               
                                
                               to 
                                
                               
                                   
                               
                                
                               Sn 
                                
                               
                                   
                               
                                
                               5 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             E 
                              
                             
                               ( 
                               
                                 Sn 
                                 , 
                                 
                                   5 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                           
                             E 
                              
                             
                               ( 
                               ClAO 
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               9.27363 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           
                             
                               - 
                               12.96764 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         0.71514 
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.237 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             C 
                             2 
                           
                            
                           
                             ( 
                             
                               BrAO 
                                
                               
                                   
                               
                                
                               to 
                                
                               
                                   
                               
                                
                               Sn 
                                
                               
                                   
                               
                                
                               5 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             E 
                              
                             
                               ( 
                               
                                 Sn 
                                 , 
                                 
                                   5 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                           
                             E 
                              
                             
                               ( 
                               BrAO 
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               9.27363 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           
                             
                               - 
                               11.8138 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         0.78498 
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.238 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             c 
                             2 
                           
                            
                           
                             ( 
                             
                               IAO 
                                
                               
                                   
                               
                                
                               to 
                                
                               
                                   
                               
                                
                               Sn 
                                
                               
                                   
                               
                                
                               5 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             E 
                              
                             
                               ( 
                               
                                 Sn 
                                 , 
                                 
                                   Sn 
                                    
                                   
                                       
                                   
                                    
                                   5 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                           
                             E 
                              
                             
                               ( 
                               IAO 
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               9.27363 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           
                             
                               - 
                               10.45126 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         0.88732 
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.239 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             c 
                             2 
                           
                            
                           
                             ( 
                             
                               O 
                                
                               
                                   
                               
                                
                               to 
                                
                               
                                   
                               
                                
                               Sn 
                                
                               
                                   
                               
                                
                               5 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             C 
                             2 
                           
                            
                           
                             ( 
                             
                               O 
                                
                               
                                   
                               
                                
                               to 
                                
                               
                                   
                               
                                
                               Sn 
                                
                               
                                   
                               
                                
                               5 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             E 
                              
                             
                               ( 
                               
                                 Sn 
                                 , 
                                 
                                   5 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                           
                             E 
                              
                             
                               ( 
                               O 
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               9.27363 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           
                             
                               - 
                               13.61805 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         0.68098 
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.240 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             c 
                             2 
                           
                            
                           
                             ( 
                             
                               HAO 
                                
                               
                                   
                               
                                
                               to 
                                
                               
                                   
                               
                                
                               Sn 
                                
                               
                                   
                               
                                
                               5 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               E 
                               Coulomb 
                             
                              
                             
                               ( 
                               
                                 Sn 
                                 , 
                                 
                                   5 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                           
                             E 
                              
                             
                               ( 
                               H 
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               9.32137 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           
                             
                               - 
                               13.605804 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         0.68510 
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.241 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             C 
                             2 
                           
                            
                           
                             ( 
                             
                               C 
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                 sp 
                                 2 
                               
                                
                               HO 
                                
                               
                                   
                               
                                
                               to 
                                
                               
                                   
                               
                                
                               Sn 
                                
                               
                                   
                               
                                
                               5 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             E 
                              
                             
                               ( 
                               
                                 Sn 
                                 , 
                                 
                                   5 
                                    
                                   
                                     sp 
                                     3 
                                   
                                    
                                   HO 
                                 
                               
                               ) 
                             
                           
                           
                             E 
                              
                             
                               ( 
                               
                                 C 
                                 , 
                                 
                                   2 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             c 
                             2 
                           
                            
                           
                             ( 
                             
                               C 
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               
                                 - 
                                 9.27363 
                               
                                
                               
                                   
                               
                                
                               eV 
                             
                             
                               
                                 - 
                                 14.63489 
                               
                                
                               
                                   
                               
                                
                               eV 
                             
                           
                            
                           
                             ( 
                             0.91771 
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         0.58152 
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.242 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             c 
                             2 
                           
                            
                           
                             ( 
                             
                               Sn 
                                
                               
                                   
                               
                                
                               5 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                                
                               
                                   
                               
                                
                               to 
                                
                               
                                   
                               
                                
                               Sn 
                                
                               
                                   
                               
                                
                               5 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               E 
                               Coulomb 
                             
                              
                             
                               ( 
                               
                                 Sn 
                                 , 
                                 
                                   5 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                           
                             E 
                              
                             
                               ( 
                               H 
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               9.32137 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           
                             
                               - 
                               13.605804 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         0.68510 
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.243 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where Eq. (15.71) was used in Eqs. (23.241) and (23.243) and Eqs. (15.76), (15.79), and (13.430) were used in Eq. (23.242). Since the energy of the MO is matched to that of the Sn5sp 3  HO, E(AO/HO) in Eq. (15.61) is E(Sn,5sp 3 HO) given by Eq. (23.224) for single bonds and twice this value for double bonds. E T (atom-atom, msp 3 .AO) of the Sn-L-bond MO is determined by considering that the bond involves up to an electron transfer from the tin atom to the ligand atom to form partial ionic character in the bond as in the case of the zwitterions such as H 2 B + —F −  given in the Halido Boranes section. For the tin compounds, E T (atom-atom,msp 3 .AO) is that which forms an energy minimum for the hybridization and other bond parameter. The general values of Table 147 are given by Eqs. (23.233) and (23.226), and the specific values for the tin functional groups are given in Table 151. 
         [0353]    The symbols of the functional groups of tin compounds are given in Table 148. The geometrical (Eqs. (15.1-15.5) and (23.41)), intercept (Eqs. (15.31-15.32) and (15.80-15.87)), and energy (Eqs. (15.61) and (23.28-23.33)) parameters of tin compounds are given in Tables 149, 150, and 151, respectively. The total energy of each tin compounds given in Table 152 was calculated as the sum over the integer multiple of each E D (Group) of Table 151 corresponding to functional-group composition of the compound. The bond angle parameters of tin compounds determined using Eqs. (15.88-15.117) are given in Table 153. The E T (atom-atom, msp 3 .AO) term for SnCl 4  was calculated using Eqs. (23.230-23.277) with s=1 for the energies of E(Sn,5sp 3 ). The charge-densities of exemplary tin coordinate and organometallic compounds, tin tetrachloride (SnCl 4 ) and hexaphenyldistannane ((C 6 H 5 ) 3 SnSn(C 6 H 5 ) 3 ) comprising the concentric shells of atoms with the outer shell bridged by one or more H 2 -type ellipsoidal MOs or joined with one or more hydrogen MOs are shown in  FIGS. 69 and 70 , respectively. 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 148 
               
             
             
               
                   
               
               
                 The symbols of functional groups of tin compounds. 
               
             
          
           
               
                   
                 Functional Group 
                 Group Symbol 
               
               
                   
                   
               
               
                   
                 SnCl group 
                 Sn—Cl 
               
               
                   
                 SnBr group 
                 Sn—Br 
               
               
                   
                 SnI group 
                 Sn—I 
               
               
                   
                 SnO group 
                 Sn—O 
               
               
                   
                 SnH group 
                 Sn—H 
               
               
                   
                 SnC group 
                 Sn—C 
               
               
                   
                 SnSn group 
                 Sn—Sn 
               
               
                   
                 CH 3  group 
                 C—H (CH 3 ) 
               
               
                   
                 CH 2  alkyl group 
                 C—H (CH 2 ) (i) 
               
               
                   
                 CH alkyl 
                 C—H (i) 
               
               
                   
                 CC bond (n-C) 
                 C—C (a) 
               
               
                   
                 CC bond (iso-C) 
                 C—C (b) 
               
               
                   
                 CC bond (tert-C) 
                 C—C (c) 
               
               
                   
                 CC (iso to iso-C) 
                 C—C (d) 
               
               
                   
                 CC (t to t-C) 
                 C—C (e) 
               
               
                   
                 CC (t to iso-C) 
                 C—C (f) 
               
               
                   
                 CC double bond 
                 C═C 
               
               
                   
                 C vinyl single bond to —C(C)═C 
                 C—C (i) 
               
               
                   
                 C vinyl single bond to —C(H)═C 
                 C—C (ii) 
               
               
                   
                 C vinyl single bond to —C(C)═CH 2   
                 C—C (iii) 
               
               
                   
                 CH 2  alkenyl group 
                 C—H (CH 2 ) (ii) 
               
               
                   
                 CC (aromatic bond) 
                 C 3e ═C 
               
               
                   
                 CH (aromatic) 
                 CH (ii) 
               
               
                   
                 C a —C b  (CH 3  to aromatic bond) 
                 C—C (iv) 
               
               
                   
                 C—C(O) 
                 C—C(O) 
               
               
                   
                 C═O (aryl carboxylic acid) 
                 C═O 
               
               
                   
                 (O)C—O 
                 C—O 
               
               
                   
                 OH group 
                 OH 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 149A 
               
               
                   
               
               
                 The geometrical bond parameters of tin compounds and experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Sn—Cl 
                 Sn—Br 
                 Sn—I 
                 Sn—O 
                 Sn—H 
                 Sn—C 
                 Sn—Sn 
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 n e   
                 3     
                 5     
                 5     
                 2     
                 2     
                   
                 6     
               
               
                   
               
               
                 L 
                 
                   
                     
                       
                         
                           3 
                           4 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         3 
                          
                         
                           
                             3 
                             4 
                           
                         
                       
                     
                   
                 
                 0     
                 
                   
                     
                       
                         2 
                          
                         
                           
                             3 
                             4 
                           
                         
                       
                     
                   
                 
                 0     
                   
                 0     
               
               
                   
               
               
                 a (a 0 ) 
                 2.51732 
                 3.55196 
                 3.50000 
                 2.03464 
                 2.00000 
                 2.44449 
                 4.00000 
               
               
                 c′ (a 0 ) 
                 2.16643 
                 2.45626 
                 2.64575 
                 1.72853 
                 1.63299 
                 2.05027 
                 2.79011 
               
               
                 Bond Length 
                 2.2928  
                 2.59959 
                 2.80014 
                 1.82940 
                 1.72829 
                 2.16991 
                 2.95293 
               
               
                 2c′ (Å) 
               
               
                 Exp. Bond 
                 2.280  
                 2.495 [68] 
                 2.7081 [69] 
                 1.8325  
                 1.711  
                 2.144  
                 2.79 [70] 
               
               
                 Length 
                 (SnCl 4 ) 
                 ((C 6 H 5 ) 3 SnBr) 
                 ((C 6 H 5 ) 3 SnI) 
                 (SnO) 
                 (SnH 4 ) 
                 (Sn(CH 3 ) 4 ) 
                 ((CH 3 ) 3 SnSn(CH 3 ) 3 ) 
               
               
                 (Å) 
               
               
                 b, c (a 0 ) 
                 1.28199 
                 2.56578 
                 2.29129 
                 1.07329 
                 1.15470 
                 1.33114 
                 2.86623 
               
               
                 e 
                 0.86061 
                 0.69152 
                 0.75593 
                 0.84955 
                 0.81650 
                 0.83873 
                 0.69753 
               
               
                   
               
               
                   
                 C—H (CH 3 ) 
                 C—H (CH 2 ) (i) 
                 C—H (i) 
                 C—C (a) 
                 C—C (b) 
                 C—C (c) 
                 C—C (d) 
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 n e   
               
               
                 L 
               
               
                 a (a 0 ) 
                 1.64920 
                 1.67122 
                 1.67465 
                 2.12499 
                 2.12499 
                 2.10725 
                 2.12499 
               
               
                 c′ (a 0 ) 
                 1.04856 
                 1.05553 
                 1.05661 
                 1.45744 
                 1.45744 
                 1.45164 
                 1.45744 
               
               
                 Bond Length 
                 1.10974 
                 1.11713 
                 1.11827 
                 1.54280 
                 1.54280 
                 1.53635 
                 1.54280 
               
               
                 2c′ (Å) 
               
               
                   
               
               
                   
                 1.107  
                 1.107  
                   
                 1.532  
                 1.532  
                 1.532  
                 1.532  
               
               
                 Exp. Bond 
                 (C—H propane) 
                 (C—H propane) 
                   
                 (propane) 
                 (propane) 
                 (propane) 
                 (propane) 
               
               
                 Length 
                 1.117  
                 1.117  
                 1.122  
                 1.531  
                 1.531  
                 1.531  
                 1.531  
               
               
                 (Å) 
                 (C—H butane) 
                 (C—H butane) 
                 (isobutane) 
                 (butane) 
                 (butane) 
                 (butane) 
                 (butane) 
               
               
                   
               
               
                 b,c (a 0 ) 
                 1.27295 
                 1.29569 
                 1.29924 
                 1.54616 
                 1.54616 
                 1.52750 
                 1.54616 
               
               
                 e 
                 0.63580 
                 0.63159 
                 0.63095 
                 0.68600 
                 0.68600 
                 0.68888 
                 0.68600 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 149B 
               
               
                   
               
               
                 The geometrical bond parameters of tin compounds and experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                 C—H (CH 2 ) 
               
               
                   
                 C—C (e) 
                 C—C (f) 
                 C═C 
                 C—C (i) 
                 C—C (ii) 
                 C—C (iii) 
                 (ii) 
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 2.10725 
                 2.10725 
                 1.47228 
                 2.04740 
                 2.04740 
                 2.04740 
                 1.64010 
               
               
                 c′ (a 0 ) 
                 1.45164 
                 1.45164 
                 1.26661 
                 1.43087 
                 1.43087 
                 1.43087 
                 1.04566 
               
               
                 Bond Length 
                 1.53635 
                 1.53635 
                 1.34052 
                 1.51437 
                 1.51437 
                 1.51437 
                 1.10668 
               
               
                 2c′ (Å) 
               
               
                 Exp. Bond 
                 1.532  
                 1.532  
                 1.342  
                   
                 1.508  
                 1.508  
                 1.10   
               
               
                 Length 
                 (propane) 
                 (propane) 
                 (2-methylpropene) 
                   
                 (2-butene) 
                 (2- 
                 (2- 
               
               
                 (Å) 
                 1.531  
                 1.531  
                 1.346  
                   
                   
                 methylpropene) 
                 methylpropene) 
               
               
                   
                 (butane) 
                 (butane) 
                 (2-butene) 
                   
                   
                   
                 1.108 (avg.) 
               
               
                   
                   
                   
                 1.349  
                   
                   
                   
                 (1,3-butadiene) 
               
               
                   
                   
                   
                 (1,3-butadiene) 
               
               
                 b, c (a 0 ) 
                 1.52750 
                 1.52750 
                 0.75055 
                 1.46439 
                 1.46439 
                 1.46439 
                 1.26354 
               
               
                 e 
                 0.68888 
                 0.68888 
                 0.86030 
                 0.69887 
                 0.69887 
                 0.69887 
                 0.63756 
               
               
                   
               
             
          
           
               
                   
                 C 3e ═C 
                 CH (ii) 
                 C—C (iv) 
                 C—C(O) 
                 C═O 
                 C—O 
                 OH 
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 1.47348 
                 1.60061 
                 2.06004 
                 1.95111 
                 1.29907 
                 1.73490 
                 1.26430 
               
               
                 c′ (a 0 ) 
                 1.31468 
                 1.03299 
                 1.43528 
                 1.39682 
                 1.13977 
                 1.31716 
                 0.91808 
               
               
                 Bond Length 
                 1.39140 
                 1.09327 
                 1.51904 
                 1.47833 
                 1.20628 
                 1.39402 
                  0.971651 
               
               
                 2c′ (Å) 
               
               
                 Exp. Bond 
                 1.399  
                 1.101  
                 1.524  
                 1.48 [71] 
                 1.214  
                 1.393  
                 0.972  
               
               
                 Length 
                 (benzene) 
                 (benzene) 
                 (toluene) 
                 (benzoic acid) 
                 (acetic acid) 
                 (methyl 
                 (formic acid) 
               
               
                 (Å) 
                   
                   
                   
                   
                   
                 formate) 
               
               
                 b, c (a 0 ) 
                 0.66540 
                 1.22265 
                 1.47774 
                 1.36225 
                 0.62331 
                 1.12915 
                 0.86925 
               
               
                 e 
                 0.89223 
                 0.64537 
                 0.69673 
                 0.71591 
                 0.87737 
                 0.75921 
                 0.72615 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 150 
               
               
                   
               
               
                 The MO to HO intercept geometrical bond parameters of tin compounds. R, R′, R″ are H or 
               
               
                 alkyl groups. E T  is E T  (atom-atom, msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 Final 
                   
                   
               
               
                   
                   
                   
                   
                   
                   
                 Total 
               
               
                   
                   
                   
                   
                   
                   
                 Energy 
               
               
                   
                   
                 E T   
                 E T   
                 E T   
                 E T   
                 Sn5sp 3   
               
               
                   
                   
                 (eV) 
                 (eV) 
                 (eV) 
                 (eV) 
                 C2sp 3   
                 r initial   
                 r final   
               
               
                 Bond 
                 Atom 
                 Bond 1 
                 Bond 2 
                 Bond 3 
                 Bond 4 
                 (eV) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 Sn—Cl (SnCl 4 ) 
                 Sn 
                 −0.69373 
                 −0.69373 
                 −0.69373 
                 −0.69373 
                   
                 1.45964 
                 1.12479 
               
               
                 Sn—Cl (SnCl 4 ) 
                 Cl 
                 −0.69373 
                 0 
                 0 
                 0 
                   
                 1.05158 
                 0.99593 
               
               
                 Sn—Br (SnBr 4 ) 
                 Sn 
                 −1.25012 
                 −1.25012 
                 −1.25012 
                 −1.25012 
                   
                 1.45964 
                 0.95000 
               
               
                 Sn—Br (SnBr 4 ) 
                 Br 
                 −1.25012 
                 0 
                 0 
                 0 
                   
                 1.15169 
                 1.04148 
               
               
                 Sn—I (SnI 4 ) 
                 Sn 
                 −0.62506 
                 −0.62506 
                 −0.62506 
                 −0.62506 
                   
                 1.45964 
                 1.15093 
               
               
                 Sn—I (SnI 4 ) 
                 I 
                 −0.62506 
                 0 
                 0 
                 0 
                   
                 1.30183 
                 1.22837 
               
               
                 Sn—O (SnO) 
                 Sn 
                 −0.56533 
                 0 
                 0 
                 0 
                   
                 1.45964 
                 1.37617 
               
               
                 Sn—O (SnO) 
                 O 
                 −0.56533 
                 0 
                 0 
                 0 
                   
                 1.00000 
                 0.95928 
               
               
                 Sn—H (SnH 4 ) 
                 Sn 
                 −0.82906 
                 −0.82906 
                 −0.82906 
                 −0.82906 
                   
                 1.45964 
                 1.07661 
               
               
                 Sn—(CH 3 ) 4   
                 Sn 
                 0 
                 0 
                 0 
                 0 
                   
                 1.45964 
                 0.91771 
               
               
                 Sn—(CH 3 ) 4   
                 C 
                 0 
                 0 
                 0 
                 0 
                   
                 0.91771 
                 0.91771 
               
               
                 (CH 3 ) 3 Sn—Sn(CH 3 ) 3   
                 Sn 
                 −0.21846 
                 0 
                 0 
                 0 
                   
                 1.45964 
                 1.42621 
               
               
                 C—H (CH 3 ) 
                 C 
                 −0.92918 
                 0 
                 0 
                 0 
                 −152.54487 
                 0.91771 
                 0.86359 
               
               
                 C—H (CH 2 ) (i) 
                 C 
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                 −153.47406 
                 0.91771 
                 0.81549 
               
               
                 C—H (CH) (i) 
                 C 
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 C a   
                 −0.92918 
                 0 
                 0 
                 0 
                 −152.54487 
                 0.91771 
                 0.86359 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                 −153.47406 
                 0.91771 
                 0.81549 
               
               
                 R—H 2 C a C b (H 2 C c —R′)HCH 2 —(C—C (b)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 R—H 2 C a (R′—H 2 C d )C b   
                 C b   
                 −0.92918 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.71860 
                 0.91771 
                 0.75889 
               
               
                 (R″—H 2 C c )CH 2 —(C—C (c)) 
               
               
                 isoC a C b (H 2 C c —R′)HCH 2 —(C—C (d)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 tertC a (R′—H 2 C d )C b   
                 C b   
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.51399 
                 0.91771 
                 0.76765 
               
               
                 (R″—H 2 C c )CH 2 —(C—C (e)) 
               
               
                 tertC a C b (H 2 C c —R′)HCH 2 —(C—C (f)) 
                 C b   
                 −0.72457 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.19863 
                 0.91771 
                 0.78155 
               
               
                 isoC a (R′—H 2 C d )C b   
                 C b   
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.51399 
                 0.91771 
                 0.76765 
               
               
                 (R″—H 2 C c )CH 2 —(C—C (f)) 
               
               
                 C c (H)C a ═C a (H)C d   
                 C a   
                 −1.13380 
                 −0.92918 
                 0 
                 0 
                 −153.67867 
                 0.91771 
                 0.80561 
               
               
                 C c (H)C a ═C b H 2   
                 C b   
                 −1.13380 
                 0 
                 0 
                 0 
                 −152.74949 
                 0.91771 
                 0.85252 
               
               
                 C c (C d )C a ═C b H,C e   
                 C a   
                 −1.13380 
                 −0.72457 
                 −0.72457 
                 0 
                 −154.19863 
                 0.91771 
                 0.78155 
               
               
                 R 1 C b H 2 —C a (C)═C 
                 C a   
                 −1.13380 
                 −0.72457 
                 −0.72457 
                 0 
                 −154.19863 
                 0.91771 
                 0.78155 
               
               
                 (C—C (i)) 
               
               
                 R 1 C b H 2 —C a (C)═C 
                 C b   
                 −0.72457 
                 −0.92918 
                 0 
                 0 
                 −153.26945 
                 0.91771 
                 0.82562 
               
               
                 (C—C (i)) 
               
               
                 R 1 C b H 2 —C a (C)═CH 2   
               
               
                 (C—C (iii)) 
               
               
                 R 1 C b H 2 —C a (H)═C 
                 C a   
                 −1.13380 
                 −0.92918 
                 0 
                 0 
                 −153.67866 
                 0.91771 
                 0.80561 
               
               
                 (C—C (ii)) 
               
               
                 R 1 C b H 2 —C a (H)═C 
                 C b   
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                 −153.47405 
                 0.91771 
                 0.81549 
               
               
                 (C—C (i)) 
               
               
                 C—H (CH 2 ) (ii) 
                 C 
                 −1.13380 
                 0 
                 0 
                 0 
                 −152.74949 
                 0.91771 
                 0.85252 
               
               
                 C 3e ═(Sn)C a   3e ═C 
                 C a   
                 −0.85035 
                 −0.85035 
                 0 
                 0 
                 −153.31638 
                 0.91771 
                 0.82327 
               
               
                 C—H (CH) (ii) 
                 C 
                 −0.85035 
                 −0.85035 
                 −0.56690 
                 0 
                 −153.88327 
                 0.91771 
                 0.79597 
               
               
                 C 3e ═HC b   3e ═C 
                 C b   
                 −0.85035 
                 −0.85035 
                 −0.56690 
                 0 
                 −153.88327 
                 0.91771 
                 0.79597 
               
               
                 C—H (C a H 3 ) 
                 C a   
                 −0.56690 
                 0 
                 0 
                 0 
                 −152.18259 
                 0.91771 
                 0.88392 
               
               
                 C—H (C c H) 
                 C c   
                 −0.85035 
                 −0.85035 
                 −0.56690 
                 0 
                 −153.88327 
                 0.91771 
                 0.79597 
               
               
                 C 3e ═HC c   3e ═C 
                 C c   
                 −0.85035 
                 −0.85035 
                 −0.56690 
                 0 
                 −153.88327 
                 0.91771 
                 0.79597 
               
               
                 C 3e ═(H 3 C a )C b   3e ═C 
                 C b   
               
               
                 (C 3e ═) 2 C b —C a H 3   
                 C a   
                 −0.56690 
                 0 
                 0 
                 0 
                 −152.18259 
                 0.91771 
                 0.88392 
               
               
                 (C 3e ═) 2 C b —C a H 3   
                 C b   
                 −0.56690 
                 −0.85035 
                 −0.85035 
                 0 
                 −153.88328 
                 0.91771 
                 0.79597 
               
               
                 C 3e ═HC b   3e ═C 
                 C b   
                 −0.85035 
                 −0.85035 
                 −0.56690 
                 0 
                 −153.88327 
                 0.91771 
                 0.79597 
               
               
                 C 3e ═(HOOC a )C b   3e ═C c (H) 
                 C c   
               
               
                 C 3e ═(Cl)C a   3e ═C b (H) 
                 C b   
               
               
                 C 3e ═(H 2 N)C a   3e ═C b (H) 
                 C b   
               
               
                 C b C a (O)O—H 
                 O 
                 −0.92918 
                 0 
                 0 
                 0 
                   
                 1.00000 
                 0.86359 
               
               
                 C b C a (O)—OH 
                 O 
                 −0.92918 
                 0 
                 0 
                 0 
                   
                 1.00000 
                 0.86359 
               
               
                 C b C a (O)—OH 
                 C a   
                 −0.92918 
                 −1.34946 
                 −0.64574 
                 0 
                 −154.54007 
                 0.91771 
                 0.76652 
               
               
                 C b C a (OH)═O 
                 O 
                 −1.34946 
                 0 
                 0 
                 0 
                   
                 1.00000 
                 0.84115 
               
               
                 C b C a (OH)═O 
                 C a   
                 −1.34946 
                 −0.64574 
                 −0.92918 
                 0 
                 −154.54007 
                 0.91771 
                 0.76652 
               
               
                 C b —C a (O)OH 
                 C a   
                 −0.64574 
                 −1.34946 
                 −0.92918 
                 0 
                 −154.54007 
                 0.91771 
                 0.76652 
               
               
                 C b —C a (O)OH 
                 C b   
                 −0.64574 
                 −0.85035 
                 −0.85035 
                 0 
                 −153.96212 
                 0.91771 
                 0.79232 
               
               
                   
               
             
          
           
               
                   
                   
                 E(Sn5sp 3 ) 
                   
                   
                   
                   
                   
               
               
                   
                 E Coulomb (C2sp 3 ) 
                 E(C2sp 3 ) 
               
               
                   
                 (eV) 
                 (eV) 
                 θ′ 
                 θ 1   
                 θ 2   
                 d 1   
                 d 2   
               
               
                 Bond 
                 Final 
                 Final 
                 (°) 
                 (°) 
                 (°) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 Sn—Cl (SnCl 4 ) 
                 −12.09627 
                   
                 119.18 
                 60.82 
                 50.00 
                 1.61807 
                 0.54836 
               
               
                 Sn—Cl (SnCl 4 ) 
                 −13.66137 
                   
                 113.59 
                 66.41 
                 45.39 
                 1.76780 
                 0.39862 
               
               
                 Sn—Br (SnBr 4 ) 
                 −14.32185 
               
               
                 Sn—Br (SnBr 4 ) 
                 −13.06392 
               
               
                 Sn—I (SnI 4 ) 
                 −11.82161 
                   
                 66.35 
                 113.65 
                 27.39 
                 3.10753 
                 0.46178 
               
               
                 Sn—I (SnI 4 ) 
                 −11.07632 
                   
                 72.99 
                 107.01 
                 30.84 
                 3.00509 
                 0.35933 
               
               
                 Sn—O (SnO) 
                 −9.88670 
                   
                 133.85 
                 46.15 
                 67.61 
                 0.77508 
                 0.41569 
               
               
                 Sn—O (SnO) 
                 −14.18339 
                   
                 118.84 
                 61.16 
                 51.53 
                 1.26580 
                 0.46831 
               
               
                 Sn—H (SnH 4 ) 
                 −12.63763 
                   
                 117.80 
                 62.20 
                 55.57 
                 1.13092 
                 0.50208 
               
               
                 Sn—(CH 3 ) 4   
                 −14.82575 
                   
                 104.51 
                 75.49 
                 41.87 
                 1.82034 
                 0.22992 
               
               
                 Sn—(CH 3 ) 4   
                 −14.82575 
                 −14.63489 
                 104.51 
                 75.49 
                 41.87 
                 1.82034 
                 0.22992 
               
               
                 (CH 3 ) 3 Sn—Sn(CH 3 ) 3   
                 −9.53983 
                   
                 50.89 
                 129.11 
                 22.71 
                 3.68987 
                 0.89976 
               
               
                 C—H (CH 3 ) 
                 −15.75493 
                 −15.56407 
                 77.49 
                 102.51 
                 41.48 
                 1.23564 
                 0.18708 
               
               
                 C—H (CH 2 ) (i) 
                 −16.68412 
                 −16.49325 
                 68.47 
                 111.53 
                 35.84 
                 1.35486 
                 0.29933 
               
               
                 C—H (CH) (i) 
                 −17.61330 
                 −17.42244 
                 61.10 
                 118.90 
                 31.37 
                 1.42988 
                 0.37326 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 −15.75493 
                 −15.56407 
                 63.82 
                 116.18 
                 30.08 
                 1.83879 
                 0.38106 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 −16.68412 
                 −16.49325 
                 56.41 
                 123.59 
                 26.06 
                 1.90890 
                 0.45117 
               
               
                 R—H 2 C a C b (H 2 C c —R′)HCH 2 —(C—C (b)) 
                 −17.61330 
                 −17.42244 
                 48.30 
                 131.70 
                 21.90 
                 1.97162 
                 0.51388 
               
               
                 R—H 2 C a (R′—H 2 C d )C b (R″—H 2 C c ) 
                 −17.92866 
                 −17.73779 
                 48.21 
                 131.79 
                 21.74 
                 1.95734 
                 0.50570 
               
               
                 CH 2 —(C—C (c)) 
               
               
                 isoC a C b (H 2 C c —R′)HCH 2 —(C—C (d)) 
                 −17.61330 
                 −17.42244 
                 48.30 
                 131.70 
                 21.90 
                 1.97162 
                 0.51388 
               
               
                 tertC a (R′—H 2 C d )C b (R″—H 2 C c ) 
                 −17.92866 
                 −17.73779 
                 50.04 
                 129.96 
                 22.66 
                 1.94462 
                 0.49298 
               
               
                 CH 2 —(C—C (e)) 
               
               
                 tertC a C b (H 2 C c —R′)HCH 2 —(C—C (f)) 
                 −17.40869 
                 −17.21783 
                 52.78 
                 127.22 
                 24.04 
                 1.92443 
                 0.47279 
               
               
                 isoC a (R′—H 2 C d )C b (R″—H 2 C c ) 
                 −17.92866 
                 −17.73779 
                 50.04 
                 129.96 
                 22.66 
                 1.94462 
                 0.49298 
               
               
                 CH 2 —(C—C (f)) 
               
               
                 C c (H)C a ═C a (H)C d   
                 −16.88873 
                 −16.69786 
                 127.61 
                 52.39 
                 58.24 
                 0.77492 
                 0.49168 
               
               
                 C c (H)C a ═C b H 2   
                 −15.95955 
                 −15.76868 
                 129.84 
                 50.16 
                 60.70 
                 0.72040 
                 0.54620 
               
               
                 C c (C d )C a ═C b H,C e   
                 −17.40869 
                 −17.21783 
                 126.39 
                 53.61 
                 56.95 
                 0.80289 
                 0.46371 
               
               
                 R 1 C b H 2 —C a (C)═C 
                 −17.40869 
                 −17.21783 
                 60.88 
                 119.12 
                 27.79 
                 1.81127 
                 0.38039 
               
               
                 (C—C (i)) 
               
               
                 R 1 C b H 2 —C a (C)═C 
                 −16.47951 
                 −16.28864 
                 67.40 
                 112.60 
                 31.36 
                 1.74821 
                 0.31734 
               
               
                 (C—C (i)) 
               
               
                 R 1 C b H 2 —C a (C)═CH 2   
               
               
                 (C—C (iii)) 
               
               
                 R 1 C b H 2 —C a (H)═C 
                 −16.88873 
                 −16.69786 
                 64.57 
                 115.43 
                 29.79 
                 1.77684 
                 0.34596 
               
               
                 (C—C (ii)) 
               
               
                 R 1 C b H 2 —C a (H)═C 
                 −16.68411 
                 −16.49325 
                 65.99 
                 114.01 
                 30.58 
                 1.76270 
                 0.33183 
               
               
                 (C—C (i)) 
               
               
                 C—H (CH 2 ) (ii) 
                 −15.95955 
                 −15.76868 
                 77.15 
                 102.85 
                 41.13 
                 1.23531 
                 0.18965 
               
               
                 C 3e ═(Sn)C a   3e ═C 
                 −16.52644 
                 −16.33558 
                 135.37 
                 44.63 
                 60.36 
                 0.72875 
                 0.58594 
               
               
                 C—H (CH) (ii) 
                 −17.09334 
                 −16.90248 
                 74.42 
                 105.58 
                 38.84 
                 1.24678 
                 0.21379 
               
               
                 C 3e ═HC b   3e ═C 
                 −17.09334 
                 −16.90248 
                 134.24 
                 45.76 
                 58.98 
                 0.75935 
                 0.55533 
               
               
                 C—H (C a H 3 ) 
                 −15.39265 
                 −15.20178 
                 79.89 
                 101.11 
                 43.13 
                 1.20367 
                 0.15511 
               
               
                 C—H (C c H) 
                 −17.09334 
                 −16.90248 
                 74.42 
                 105.58 
                 38.84 
                 1.24678 
                 0.21379 
               
               
                 C 3e ═HC c   3e ═C 
                 −17.09334 
                 −16.90248 
                 134.24 
                 45.76 
                 58.98 
                 0.75935 
                 0.55533 
               
               
                 C 3e ═(H 3 C a )C b   3e ═C 
               
               
                 (C 3e ═) 2 C b —C a H 3   
                 −15.39265 
                 −15.20178 
                 73.38 
                 106.62 
                 34.97 
                 1.68807 
                 0.25279 
               
               
                 (C 3e ═) 2 C b —C a H 3   
                 −17.09334 
                 −16.90247 
                 61.56 
                 118.44 
                 28.27 
                 1.81430 
                 0.37901 
               
               
                 C 3e ═HC b   3e ═C 
                 −17.09334 
                 −16.90248 
                 134.24 
                 45.76 
                 58.98 
                 0.75935 
                 0.55533 
               
               
                 C 3e ═(HOOC a )C b   3e ═C c (H) 
               
               
                 C 3e ═(Cl)C a   3e ═C b (H) 
               
               
                 C 3e ═(H 2 N)C a   3e ═C b (H) 
               
               
                 C b C a (O)O—H 
                 −15.75493 
                   
                 115.09 
                 64.91 
                 64.12 
                 0.55182 
                 0.36625 
               
               
                 C b C a (O)—OH 
                 −15.75493 
                   
                 101.32 
                 78.68 
                 48.58 
                 1.14765 
                 0.16950 
               
               
                 C b C a (O)—OH 
                 −17.75013 
                 −17.55927 
                 93.11 
                 86.89 
                 42.68 
                 1.27551 
                 0.04165 
               
               
                 C b C a (OH)═O 
                 −16.17521 
                   
                 137.27 
                 42.73 
                 66.31 
                 0.52193 
                 0.61784 
               
               
                 C b C a (OH)═O 
                 −17.75013 
                 −17.55927 
                 134.03 
                 45.97 
                 62.14 
                 0.60699 
                 0.53278 
               
               
                 C b —C a (O)OH 
                 −17.75013 
                 −17.55927 
                 70.34 
                 109.66 
                 32.00 
                 1.65466 
                 0.25784 
               
               
                 C b —C a (O)OH 
                 −17.17218 
                 −16.98131 
                 73.74 
                 106.26 
                 33.94 
                 1.61863 
                 0.22181 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 151A 
               
               
                   
               
               
                 The energy parameters (eV) of functional groups of tin. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Sn—Cl 
                 Sn—Br 
                 Sn—I 
                 Sn—O 
                 Sn—H 
                 Sn—C 
                 Sn—Sn 
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 n 1   
                 1 
                 1 
                 1 
                 2 
                 1 
                 1 
                 1 
               
               
                 n 2   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.375 
                 0.375 
                 0.25 
                 0.5 
                 0.375 
                 0.5 
                 0.375 
               
               
                 C 2   
                 0.71514 
                 0.78498 
                 1 
                 0.68098 
                 1 
                 0.58152 
                 0.68510 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 2   
                 0.71514 
                 1 
                 0.88732 
                 0.68098 
                 0.68510 
                 1 
                 1 
               
               
                 c 3   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 c 4   
                 1 
                 1 
                 1 
                 2 
                 1 
                 2 
                 2 
               
               
                 c 5   
                 1 
                 1 
                 1 
                 2 
                 1 
                 0 
                 0 
               
               
                 C 1o   
                 0.375 
                 0.375 
                 0.25 
                 0.5 
                 0.375 
                 0.5 
                 0.375 
               
               
                 C 2o   
                 0.71514 
                 0.78498 
                 1 
                 0.68098 
                 1 
                 0.58152 
                 0.68510 
               
               
                 V e  (eV) 
                 −23.27710 
                 −18.85259 
                 −18.00852 
                 −53.79650 
                 −26.17110 
                 −32.30127 
                 −16.82311 
               
               
                 V p  (eV) 
                 6.28029 
                 5.53925 
                 5.14251 
                 15.74264 
                 8.33182 
                 6.63612 
                 4.87644 
               
               
                 T (eV) 
                 4.62339 
                 2.65383 
                 2.57265 
                 13.22015 
                 6.54278 
                 6.60696 
                 2.10289 
               
               
                 V m  (eV) 
                 −2.31169 
                 −1.32691 
                 −1.28632 
                 −6.61007 
                 −3.27139 
                 −3.30348 
                 −1.05144 
               
               
                 E(AO/HO) (eV) 
                 −9.27363 
                 −9.27363 
                 −9.27363 
                 −18.54725 
                 −9.27363 
                 −9.27363 
                 −9.27363 
               
               
                 ΔE H   2 MO (AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 E T  (AO/HO) (eV) 
                 −9.27363 
                 −9.27363 
                 −9.27363 
                 −18.54725 
                 −9.27363 
                 −9.27363 
                 −9.27363 
               
               
                 E T  (H 2 MO) (eV) 
                 −23.95874 
                 −21.26006 
                 −20.85331 
                 −49.99104 
                 −23.84152 
                 −31.63530 
                 −20.16886 
               
               
                 E T  (atom-atom, 
                 −1.38745 
                 −2.50024 
                 −1.25012 
                 −1.13065 
                 −1.65813 
                 0 
                 −0.43693 
               
               
                 msp 3 .AO) (eV) 
               
               
                 E T  (MO) (eV) 
                 −25.34619 
                 −23.76030 
                 −22.10343 
                 −51.12170 
                 −25.49965 
                 −31.63537 
                 −20.60579 
               
               
                 ω(10 15  rad/s) 
                 14.7492 
                 5.45759 
                 3.15684 
                 21.6951 
                 8.95067 
                 14.5150 
                 2.61932 
               
               
                 E K  (eV) 
                 9.70820 
                 3.59228 
                 2.07789 
                 14.28009 
                 5.89149 
                 9.55403 
                 1.72408 
               
               
                 Ē D  (eV) 
                 −0.15624 
                 −0.08909 
                 −0.06303 
                 −0.19109 
                 −0.12245 
                 −0.19345 
                 −0.05353 
               
               
                 Ē Kvib  (eV) 
                 0.04353 [14] 
                 0.03065 [14] 
                 0.02467 [14] 
                 0.10193 [14] 
                 0.22937 [72] 
                 0.14754 [72] 
                 0.02343 [73] 
               
               
                 Ē osc  (eV) 
                 −0.13447 
                 −0.07377 
                 −0.05070 
                 −0.14013 
                 −0.00776 
                 −0.11968 
                 −0.04181 
               
               
                 E mag  (eV) 
                 0.03679 
                 0.03679 
                 0.03679 
                 0.03679 
                 0.03679 
                 0.14803 
                 0.03679 
               
               
                 E T  (Group) (eV) 
                 −25.48066 
                 −23.83407 
                 −22.15413 
                 −51.40195 
                 −25.50741 
                 −31.75505 
                 −20.64760 
               
               
                 E initial  (c 4  AO/HO) (eV) 
                 −9.27363 
                 −9.27363 
                 −9.27363 
                 −9.27363 
                 −9.27363 
                 −14.63489 
                 −9.27363 
               
               
                 E initial  (c 5  AO/HO) (eV) 
                 −12.96764 
                 −11.8138 
                 −10.45126 
                 −13.61806 
                 −13.59844 
                 0 
                 0 
               
               
                 E D  (Group) (eV) 
                 3.23939 
                 2.74664 
                 2.42924 
                 5.61858 
                 2.63534 
                 2.48527 
                 2.10034 
               
               
                   
               
               
                   
                   
                   
                   
                 C—C 
                 C—C 
                 C—C 
                 C—C 
               
               
                   
                 CH 3   
                 CH 2  (i) 
                 CH (i) 
                 (a) 
                 (b) 
                 (c) 
                 (d) 
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 n 1   
                 3 
                 2 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 n 2   
                 2 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.75 
                 0.75 
                 0.75 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
               
               
                 C 2   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 2   
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
               
               
                 c 3   
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
               
               
                 c 4   
                 1 
                 1 
                 1 
                 2 
                 2 
                 2 
                 2 
               
               
                 c 5   
                 3 
                 2 
                 1 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1o   
                 0.75 
                 0.75 
                 0.75 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
               
               
                 C 2o   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 V e  (eV) 
                 −107.32728 
                 −70.41425 
                 −35.12015 
                 −28.79214 
                 −28.79214 
                 −29.10112 
                 −28.79214 
               
               
                 V p  (eV) 
                 38.92728 
                 25.78002 
                 12.87680 
                 9.33352 
                 9.33352 
                 9.37273 
                 9.33352 
               
               
                 T (eV) 
                 32.53914 
                 21.06675 
                 10.48582 
                 6.77464 
                 6.77464 
                 6.90500 
                 6.77464 
               
               
                 V m  (eV) 
                 −16.26957 
                 −10.53337 
                 −5.24291 
                 −3.38732 
                 −3.38732 
                 −3.45250 
                 −3.38732 
               
               
                 E(AO/HO) (eV) 
                 −15.56407 
                 −15.56407 
                 −14.63489 
                 −15.56407 
                 −15.56407 
                 −15.35946 
                 −15.56407 
               
               
                 ΔE H   2  MO (AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 E T  (AO/HO) (eV) 
                 −15.56407 
                 −15.56407 
                 −14.63489 
                 −15.56407 
                 −15.56407 
                 −15.35946 
                 −15.56407 
               
               
                 E T  (H 2 MO) (eV) 
                 −67.69451 
                 −49.66493 
                 −31.63533 
                 −31.63537 
                 −31.63537 
                 −31.63535 
                 −31.63537 
               
               
                 E T  (atom-atom, 
                 0 
                 0 
                 0 
                 −1.85836 
                 −1.85836 
                 −1.44915 
                 −1.85836 
               
               
                 msp 3 .AO) (eV) 
               
               
                 E T  (MO) (eV) 
                 −67.69450 
                 −49.66493 
                 −31.63537 
                 −33.49373 
                 −33.49373 
                 −33.08452 
                 −33.49373 
               
               
                 ω(10 15  rad/s) 
                 24.9286 
                 24.2751 
                 24.1759 
                 9.43699 
                 9.43699 
                 15.4846 
                 9.43699 
               
               
                 E K  (eV) 
                 16.40846 
                 15.97831 
                 15.91299 
                 6.21159 
                 6.21159 
                 10.19220 
                 6.21159 
               
               
                 Ē D  (eV) 
                 −0.25352 
                 −0.25017 
                 −0.24966 
                 −0.16515 
                 −0.16515 
                 −0.20896 
                 −0.16515 
               
               
                 Ē Kvib  (eV) 
                 0.35532 
                 0.35532 
                 0.35532 
                 0.12312 [6]  
                 0.17978 [7]  
                 0.09944 [8]  
                 0.12312 [6]  
               
               
                   
                 Eq. 
                 Eq. 
                 Eq. 
               
               
                   
                 (13.458) 
                 (13.458) 
                 (13.458) 
               
               
                 Ē osc  (eV) 
                 −0.22757 
                 −0.14502 
                 −0.07200 
                 −0.10359 
                 −0.07526 
                 −0.15924 
                 −0.10359 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                 E T  (Group) (eV) 
                 −67.92207 
                 −49.80996 
                 −31.70737 
                 −33.59732 
                 −33.49373 
                 −33.24376 
                 −33.59732 
               
               
                 E initial  (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
               
               
                 E initial  (c 5  AO/HO) (eV) 
                 −13.59844 
                 −13.59844 
                 −13.59844 
                 0 
                 0 
                 0 
                 0 
               
               
                 E D  (Group) (eV) 
                 12.49186 
                 7.83016 
                 3.32601 
                 4.32754 
                 4.29921 
                 3.97398 
                 4.17951 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 151B 
               
               
                   
               
               
                 The energy parameters (eV) of functional groups of tin compounds. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 C—C 
                   
                   
                   
                 C—C 
                 C—C 
                   
               
               
                   
                 (e) 
                 C—C (f) 
                 C═C 
                 C—C (i) 
                 (ii) 
                 (iii) 
                 CH 2  (ii) 
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 f 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 n 1   
                 1 
                 1 
                 2 
                 1 
                 1 
                 1 
                 2 
               
               
                 n 2   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.75 
               
               
                 C 2   
                 1 
                 1 
                 0.91771 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 2   
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
               
               
                 c 3   
                 1 
                 0 
                 0 
                 1 
                 0 
                 1 
                 1 
               
               
                 c 4   
                 2 
                 2 
                 4 
                 2 
                 2 
                 2 
                 1 
               
               
                 c 5   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 2 
               
               
                 C 1o   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.75 
               
               
                 C 2o   
                 1 
                 1 
                 0.91771 
                 1 
                 1 
                 1 
                 1 
               
               
                 V e  (eV) 
                 −29.10112 
                 −29.10112 
                 −102.08992 
                 −30.19634 
                 −30.19634 
                 −30.19634 
                 −72.03287 
               
               
                 V p  (eV) 
                 9.37273 
                 9.37273 
                 21.48386 
                 9.50874 
                 9.50874 
                 9.50874 
                 26.02344 
               
               
                 T (eV) 
                 6.90500 
                 6.90500 
                 34.67062 
                 7.37432 
                 7.37432 
                 7.37432 
                 21.95990 
               
               
                 V m  (eV) 
                 −3.45250 
                 −3.45250 
                 −17.33531 
                 −3.68716 
                 −3.68716 
                 −3.68716 
                 −10.97995 
               
               
                 E (AO/HO) (eV) 
                 −15.35946 
                 −15.35946 
                 0 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
               
               
                 ΔE H     2     MO  (AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 E T  (AO/HO) (eV) 
                 −15.35946 
                 −15.35946 
                 0 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
               
               
                 E T  (H 2 MO) (eV) 
                 −31.63535 
                 −31.63535 
                 −63.27075 
                 −31.63534 
                 −31.63534 
                 −31.63534 
                 −49.66437 
               
               
                 E T  (atom-atom, 
                 −1.44915 
                 −1.44915 
                 −2.26759 
                 −1.44915 
                 −1.85836 
                 −1.44915 
                 0 
               
               
                 msp 3 .AO) (eV) 
               
               
                 E T  (MO) (eV) 
                 −33.08452 
                 −33.08452 
                 −65.53833 
                 −33.08452 
                 −33.49373 
                 −33.08452 
                 −49.66493 
               
               
                 ω (10 15  rad/s) 
                 9.55643 
                 9.55643 
                 43.0680 
                 9.97851 
                 16.4962 
                 9.97851 
                 25.2077 
               
               
                 E K  (eV) 
                 6.29021 
                 6.29021 
                 28.34813 
                 6.56803 
                 10.85807 
                 6.56803 
                 16.59214 
               
               
                 Ē D  (eV) 
                 −0.16416 
                 −0.16416 
                 −0.34517 
                 −0.16774 
                 −0.21834 
                 −0.16774 
                 −0.25493 
               
               
                 Ē Kvib  (eV) 
                 0.12312 [6] 
                 0.12312 [6] 
                 0.17897 [74] 
                 0.15895 [75] 
                 0.09931 [76] 
                 0.09931 [76] 
                 0.35532 
               
               
                   
                   
                   
                   
                   
                   
                   
                 Eq. 
               
               
                   
                   
                   
                   
                   
                   
                   
                 (13.458) 
               
               
                 Ē osc  (eV) 
                 −0.10260 
                 −0.10260 
                 −0.25568 
                 −0.08827 
                 −0.16869 
                 −0.11809 
                 −0.07727 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                 E T  (Group) (eV) 
                 −33.18712 
                 −33.18712 
                 −66.04969 
                 −33.17279 
                 −33.66242 
                 −33.20260 
                 −49.81948 
               
               
                 E initial  (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
               
               
                 E initial  (c 5  AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 −13.59844 
               
               
                 E D  (Group) (eV) 
                 3.62128 
                 3.91734 
                 7.51014 
                 3.75498 
                 4.39264 
                 3.78480 
                 7.83968 
               
               
                   
               
             
          
           
               
                   
                   
                   
                 C—C 
                   
                   
                   
                   
               
               
                   
                 C 3e ═C 
                 CH (ii) 
                 (iv) 
                 C—C(O) 
                 C═O 
                 C—O 
                 OH 
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 f 1   
                 0.75 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 n 1   
                 2 
                 1 
                 1 
                 1 
                 2 
                 1 
                 1 
               
               
                 n 2   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.5 
                 0.75 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.75 
               
               
                 C 2   
                 0.85252 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 0.75 
               
               
                 c 2   
                 0.85252 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.85395 
                 0.85395 
                 1 
               
               
                 c 3   
                 0 
                 1 
                 0 
                 0 
                 2 
                 0 
                 1 
               
               
                 c 4   
                 3 
                 1 
                 2 
                 2 
                 4 
                 2 
                 1 
               
               
                 c 5   
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
               
               
                 C 1o   
                 0.5 
                 0.75 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.75 
               
               
                 C 2o   
                 0.85252 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 V e  (eV) 
                 −101.12679 
                 −37.10024 
                 −29.95792 
                 −32.15216 
                 −111.25473 
                 −35.08488 
                 −40.92709 
               
               
                 V p  (eV) 
                 20.69825 
                 13.17125 
                 9.47952 
                 9.74055 
                 23.87467 
                 10.32968 
                 14.81988 
               
               
                 T (eV) 
                 34.31559 
                 11.58941 
                 7.27120 
                 8.23945 
                 42.82081 
                 10.11150 
                 16.18567 
               
               
                 V m  (eV) 
                 −17.15779 
                 −5.79470 
                 −3.63560 
                 −4.11973 
                 −21.41040 
                 −5.05575 
                 −8.09284 
               
               
                 E (AO/HO) (eV) 
                 0 
                 −14.63489 
                 −15.35946 
                 −14.63489 
                 0 
                 −14.63489 
                 −13.6181 
               
               
                 ΔE H     2     MO  (AO/HO) (eV) 
                 0 
                 −1.13379 
                 −0.56690 
                 −1.29147 
                 −2.69893 
                 −2.69893 
                 0 
               
               
                 E T  (AO/HO) (eV) 
                 0 
                 −13.50110 
                 −14.79257 
                 −13.34342 
                 2.69893 
                 −11.93596 
                 −13.6181 
               
               
                 E T  (H 2 MO) (eV) 
                 −63.27075 
                 −31.63539 
                 −31.63537 
                 −31.63530 
                 −63.27074 
                 −31.63541 
                 −31.63247 
               
               
                 E T  (atom-atom, 
                 −2.26759 
                 −0.56690 
                 −1.13379 
                 −1.29147 
                 −2.69893 
                 −1.85836 
                 0 
               
               
                 msp 3 .AO) (eV) 
               
               
                 E T  (MO) (eV) 
                 −65.53833 
                 −32.20226 
                 −32.76916 
                 −32.92684 
                 −65.96966 
                 −33.49373 
                 −31.63537 
               
               
                 ω (10 15  rad/s) 
                 49.7272 
                 26.4826 
                 16.2731 
                 10.7262 
                 59.4034 
                 24.3637 
                 44.1776 
               
               
                 E K  (eV) 
                 32.73133 
                 17.43132 
                 10.71127 
                 7.06019 
                 39.10034 
                 16.03660 
                 29.07844 
               
               
                 Ē D  (eV) 
                 −0.35806 
                 −0.26130 
                 −0.21217 
                 −0.17309 
                 −0.40804 
                 −0.26535 
                 −0.33749 
               
               
                 Ē Kvib  (eV) 
                 0.19649 [30] 
                 0.35532 
                 0.14940 [43] 
                 0.10502 [77] 
                 0.21077 [78] 
                 0.14010 [79] 
                 0.46311 [80-81] 
               
               
                   
                   
                 Eq. 
               
               
                   
                   
                 (13.458) 
               
               
                 Ē osc  (eV) 
                 −0.25982 
                 −0.08364 
                 −0.13747 
                 −0.12058 
                 −0.30266 
                 −0.19530 
                 −0.10594 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.11441 
                 0.14803 
                 0.11441 
               
               
                 E T  (Group) (eV) 
                 −49.54347 
                 −32.28590 
                 −32.90663 
                 −33.04742 
                 −66.57498 
                 −33.68903 
                 −31.74130 
               
               
                 E initial  (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −13.6181 
               
               
                 E intial  (c 5  AO/HO) (eV) 
                 0 
                 −13.59844 
                 0 
                 0 
                 0 
                 0 
                 −13.59844 
               
               
                 E D  (Group) (eV) 
                 5.63881 
                 3.90454 
                 3.63685 
                 3.77764 
                 7.80660 
                 4.41925 
                 4.41035 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 152 
               
               
                   
               
               
                 The total bond energies of gaseous-state tin compounds calculated using the functional 
               
               
                 group composition (separate functional groups designated in the first row) and the energies of Tables 151 
               
               
                 A and B compared to the gaseous-state experimental values except where indicated. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 CH 2   
                 CH 
                 C—C 
                 C—C 
                 C—C 
                   
                 C—C 
                 CH 2   
               
               
                 Formula 
                 Name 
                 SnCl 
                 SnBi 
                 SnI 
                 SnO 
                 SnH 
                 SnC 
                 SnSn 
                 CH 3   
                 (i) 
                 (i) 
                 (a) 
                 (b) 
                 (c) 
                 C═C 
                 (ii) 
                 (ii) 
               
               
                   
               
               
                 SnCl 4   
                 Tin tetrachloride 
                 4 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 CH 3 Cl 3 Sn 
                 Methyltin trichloride 
                 3 
                 0 
                 0 
                 0 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 2 H 6 Cl 2 Sn 
                 Dimethyltin dichloride 
                 2 
                 0 
                 0 
                 0 
                 0 
                 2 
                 0 
                 2 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 3 H 9 ClSn 
                 Trimethylin Chloride 
                 1 
                 0 
                 0 
                 0 
                 0 
                 3 
                 0 
                 3 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 SnBr 4   
                 Tin tetrabromide 
                 0 
                 4 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 3 H 9 BrSn 
                 Trimethyltin bromide 
                 0 
                 1 
                 0 
                 0 
                 0 
                 3 
                 0 
                 3 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 12 H 10 Br 2 Sn 
                 Diphenyltin dibromide 
                 0 
                 2 
                 0 
                 0 
                 0 
                 2 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 12 H 27 BrSn 
                 Tri-n-butyltin bromide 
                 0 
                 1 
                 0 
                 0 
                 0 
                 3 
                 0 
                 3 
                 9 
                 0 
                 9 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 18 H 15 BrSn 
                 Triphenyltin bromide 
                 0 
                 1 
                 0 
                 0 
                 0 
                 3 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 SnI 4   
                 Tin tetraiodide 
                 0 
                 0 
                 4 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 3 H 9 ISn 
                 Trimethyltin iodide 
                 0 
                 0 
                 1 
                 0 
                 0 
                 3 
                 0 
                 3 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 18 H 15 SnI 
                 Triphenyltin iodide 
                 0 
                 0 
                 1 
                 0 
                 0 
                 3 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 SnO 
                 Tin oxide 
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 SnH 4   
                 Stannane 
                 0 
                 0 
                 0 
                 0 
                 4 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 2 H 8 Sn 
                 Dimethylstannane 
                 0 
                 0 
                 0 
                 0 
                 2 
                 2 
                 0 
                 2 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 3 H 10 Sn 
                 Trimethylstannane 
                 0 
                 0 
                 0 
                 0 
                 1 
                 3 
                 0 
                 3 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 4 H 12 Sn 
                 Diethylstannane 
                 0 
                 0 
                 0 
                 0 
                 2 
                 2 
                 0 
                 2 
                 2 
                 0 
                 2 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 4 H 12 Sn 
                 Tetramethyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 4 
                 0 
                 4 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 5 H 12 Sn 
                 Trimethylvinyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 4 
                 0 
                 3 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 0 
                 1 
               
               
                 C 5 H 14 Sn 
                 Trimethylethyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 4 
                 0 
                 4 
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 6 H 16 Sn 
                 Trimethylisopropyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 4 
                 0 
                 5 
                 0 
                 1 
                 0 
                 2 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 8 H 12 Sn 
                 Tetravinyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 4 
                 0 
                 0 
                 0 
                 4 
                 0 
                 0 
                 0 
                 4 
                 0 
                 4 
               
               
                 C 6 H 18 Sn 2   
                 Hexamethyldistannane 
                 0 
                 0 
                 0 
                 0 
                 0 
                 6 
                 1 
                 6 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 7 H 18 Sn 
                 Trimethyl-t-butyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 4 
                 0 
                 6 
                 0 
                 0 
                 0 
                 0 
                 3 
                 0 
                 0 
                 0 
               
               
                 C 9 H 14 Sn 
                 Trimethylphenyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 4 
                 0 
                 3 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 8 H 18 Sn 
                 Triethylvinyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 4 
                 0 
                 3 
                 3 
                 1 
                 3 
                 0 
                 0 
                 1 
                 0 
                 1 
               
               
                 C 8 H 20 Sn 
                 Tetraethyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 4 
                 0 
                 4 
                 4 
                 0 
                 4 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 10 H 16 Sn 
                 Trimethylbenzyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 4 
                 0 
                 3 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 10 H 14 O 2 Sn 
                 Trimethyltin benzoate 
                 0 
                 0 
                 0 
                 0 
                 0 
                 4 
                 0 
                 3 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 10 H 20 Sn 
                 Tetra-allyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 4 
                 0 
                 0 
                 4 
                 4 
                 0 
                 0 
                 0 
                 4 
                 0 
                 4 
               
               
                 C 12 H 28 Sn 
                 Tetra-n-propyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 4 
                 0 
                 4 
                 8 
                 0 
                 8 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 12 H 28 Sn 
                 Tetraisopropyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 4 
                 0 
                 8 
                 0 
                 4 
                 0 
                 4 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 12 H 30 Sn 2   
                 Hexaethyldistannane 
                 0 
                 0 
                 0 
                 0 
                 0 
                 6 
                 1 
                 6 
                 6 
                 0 
                 6 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 19 H 18 Sn 
                 Triphenylmethyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 4 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 20 H 20 Sn 
                 Triphenylethyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 4 
                 0 
                 1 
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 16 H 36 Sn 
                 Tetra-n-butyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 4 
                 0 
                 4 
                 12 
                 0 
                 12 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 16 H 36 Sn 
                 Tetraisobutyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 4 
                 0 
                 8 
                 4 
                 4 
                 0 
                 12 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 21 H 24 Sn 2   
                 Triphenyl- 
                 0 
                 0 
                 0 
                 0 
                 0 
                 6 
                 1 
                 3 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                   
                 trimethyldistannane 
               
               
                 C 24 H 20 Sn 
                 Tetraphenyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 4 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 24 H 44 Sn 
                 Tetracyclohexyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 4 
                 0 
                 0 
                 20 
                 4 
                 24 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 36 H 30 Sn 2   
                 Hexaphenyldistannane 
                 0 
                 0 
                 0 
                 0 
                 0 
                 6 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                   
                 CH 
                 C—C 
                   
                   
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 C 3e ═C 
                 (ii) 
                 (iv) 
                 C—C(O) 
                 C═O 
                 C—O 
                 OH 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 SnCl 4   
                 Tin tetrachloride 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 12.95756 
                 13.03704 [82] 
                 0.00610 
               
               
                 CH 3 Cl 3 Sn 
                 Methyltin trichioride 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 24.69530 
                 25.69118 a  [83]  
                 0.03876 
               
               
                 C 2 H 6 Cl 2 Sn 
                 Dimethyltin dichloride 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 36.43304 
                 37.12369 [84] 
                 0.01860 
               
               
                 C 3 H 9 ClSn 
                 Trimethylin Chloride 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 48.17077 
                 49.00689 [84] 
                 0.01706 
               
               
                 SnBr 4   
                 Tin tetrabromide 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 10.98655 
                 11.01994 [82] 
                 0.00303 
               
               
                 C 3 H 9 BrSn 
                 Trimethyltin bromide 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 47.67802 
                 48.35363 [84] 
                 0.01397 
               
               
                 C 12 H 10 Br 2 Sn 
                 Diphenyltin dibromide 
                 12 
                 10 
                 0 
                 0 
                 0 
                 0 
                 0 
                 117.17489 
                 117.36647 a  [83]  
                 0.00163 
               
               
                 C 12 H 27 BrSn 
                 Tri-n-butyltin bromide 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 157.09732 
                 157.26555 a  [83]  
                 0.00107 
               
               
                 C 18 H 15 BrSn 
                 Triphenyltin bromide 
                 18 
                 15 
                 0 
                 0 
                 0 
                 0 
                 0 
                 170.26905 
                 169.91511 a  [83]  
                 −0.00208 
               
               
                 SnI 4   
                 Tin tetraiodide 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 9.71697 
                  9.73306 [85] 
                 0.00165 
               
               
                 C 3 H 9 ISn 
                 Trimethyltin iodide 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 47.36062 
                 47.69852 [84] 
                 0.00708 
               
               
                 C 18 H 15 SnI 
                 Triphenyltin iodide 
                 18 
                 15 
                 0 
                 0 
                 0 
                 0 
                 0 
                 169.95165 
                 167.87948 a  [84]  
                 −0.01234 
               
               
                 SnO 
                 Tin oxide 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 5.61858 
                  5.54770 [82] 
                 −0.01278 
               
               
                 SnH 4   
                 Stannane 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 10.54137 
                 10.47181 [82] 
                 −0.00664 
               
               
                 C 2 H 8 Sn 
                 Dimethylstannane 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 35.22494 
                 35.14201 [84] 
                 −0.00236 
               
               
                 C 3 H 10 Sn 
                 Trimethylstannane 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 47.56673 
                 47.77353 [84] 
                 0.00433 
               
               
                 C 4 H 12 Sn 
                 Diethylstannane 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 59.54034 
                 59.50337 [84] 
                 −0.00062 
               
               
                 C 4 H 12 Sn 
                 Tetramethyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 59.90851 
                 60.13973 [82] 
                 0.00384 
               
               
                 C 5 H 12 Sn 
                 Trimethylvinyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 66.09248 
                 66.43260 [84] 
                 0.00526 
               
               
                 C 5 H 14 Sn 
                 Trimethylethyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 72.06621 
                 72.19922 [83] 
                 0.00184 
               
               
                 C 6 H 16 Sn 
                 Trimethylisopropyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 84.32480 
                 84.32346 [83] 
                 −0.00002 
               
               
                 C 8 H 12 Sn 
                 Tetravinyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 84.64438 
                 86.53803 a  [83]  
                 0.02188 
               
               
                 C 6 H 18 Sn 2   
                 Hexamethyldistannane 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 91.96311 
                 91.75569 [83] 
                 −0.00226 
               
               
                 C 7 H 18 Sn 
                 Trimethyl-t-butyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 96.81417 
                 96.47805 [82] 
                 −0.00348 
               
               
                 C 9 H 14 Sn 
                 Trimethylphenyltin 
                 6 
                 5 
                 0 
                 0 
                 0 
                 0 
                 0 
                 100.77219 
                 100.42716 [83]  
                 −0.00344 
               
               
                 C 8 H 18 Sn 
                 Triethylvinyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 102.56558 
                 102.83906 a  [83]  
                 −0.00266 
               
               
                 C 8 H 20 Sn 
                 Tetraethyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 108.53931 
                 108.43751 [83]  
                 −0.00094 
               
               
                 C 10 H 16 Sn 
                 Trimethylbenzyltin 
                 6 
                 5 
                 1 
                 0 
                 0 
                 0 
                 0 
                 112.23920 
                 112.61211 [83]  
                 0.00331 
               
               
                 C 10 H 14 O 2 Sn 
                 Trimethyltin benzoate 
                 6 
                 4 
                 0 
                 1 
                 1 
                 1 
                 1 
                 117.28149 
                 119.31199 a  [83]  
                 0.01702 
               
               
                 C 10 H 20 Sn 
                 Tetra-allyltin 
                 0 
                 0 
                 4 
                 0 
                 0 
                 0 
                 0 
                 133.53558 
                 139.20655 a  [83]  
                 0.04074 
               
               
                 C 12 H 28 Sn 
                 Tetra-n-propyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 157.17011 
                 157.01253 [83]  
                 −0.00100 
               
               
                 C 12 H 28 Sn 
                 Tetraisopropyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 157.57367 
                 156.9952 [83] 
                 −0.00366 
               
               
                 C 12 H 30 Sn 2   
                 Hexaethyldistannane 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 164.90931 
                 164.76131 a  [83]  
                 −0.00090 
               
               
                 C 19 H 18 Sn 
                 Triphenylmethyltin 
                 18 
                 15 
                 0 
                 0 
                 0 
                 0 
                 0 
                 182.49954 
                 180.97881 a  [84]  
                 −0.00840 
               
               
                 C 20 H 20 Sn 
                 Triphenylethyltin 
                 18 
                 15 
                 0 
                 0 
                 0 
                 0 
                 0 
                 194.65724 
                 192.92526 a  [84]  
                 −0.00898 
               
               
                 C 16 H 36 Sn 
                 Tetra-n-butyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 205.80091 
                 205.60055 [83]  
                 −0.00097 
               
               
                 C 16 H 36 Sn 
                 Tetraisobutyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 206.09115 
                 206.73234 [83]  
                 0.003.10 
               
               
                 C 21 H 24 Sn 2   
                 Triphenyl- 
                 18 
                 15 
                 0 
                 0 
                 0 
                 0 
                 0 
                 214.55414 
                 212.72973 a  [84]  
                 −0.00858 
               
               
                   
                 trimethyldistannane 
               
               
                 C 24 H 20 Sn 
                 Tetraphenyltin 
                 24 
                 20 
                 0 
                 0 
                 0 
                 0 
                 0 
                 223.36322 
                 221.61425 [83] 
                 −0.00789 
               
               
                 C 24 H 44 Sn 
                 Tetracyclohexyltin 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 283.70927 
                 284.57603 [83] 
                 0.00305 
               
               
                 C 36 H 30 Sn 2   
                 Hexaphenyldistannane 
                 36 
                 30 
                 0 
                 0 
                 0 
                 0 
                 0 
                 337.14517 
                 333.27041 [83] 
                 −0.01163 
               
               
                   
               
               
                   a Crystal. 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 153 
               
               
                   
               
               
                 The bond angle parameters of tin compounds and experimental values [3]. In the calculation of θ v , the parameters from 
               
               
                 the preceding angle were used. E T  is E T  (atom-atom, msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                 2c′ 
                   
                 Atom 1 
                   
                 Atom 2 
                   
                   
               
               
                   
                 2c′ 
                 2c′ 
                 Terminal 
                   
                 Hybridization 
                   
                 Hybridization 
               
               
                   
                 Bond 1 
                 Bond 2 
                 Atoms 
                 E Coulombic   
                 Designation 
                 E Coulombic   
                 Designation 
                 c 2   
                 c 2   
               
               
                 Atoms of Angle 
                 (a 0 ) 
                 (a 0 ) 
                 (a 0 ) 
                 Atom 1 
                 (Table 7) 
                 Atom 2 
                 (Table 7) 
                 Atom 1 
                 Atom 2 
               
               
                   
               
               
                 ∠ClSnCl 
                 4.33286 
                 4.33286 
                 6.9892 
                 −12.96764 
                 Cl 
                 −12.96764 
                 Cl 
                 0.71514 
                 0.71514 
               
               
                   
                   
                   
                   
                 Cl 
                   
                 Cl 
               
               
                 ∠HSnH 
                 3.26599 
                 3.26599 
                 5.3417 
                  −9.32137 
                 (Eq. 23.221) 
                 H 
                 H 
                 0.68510 
                 1 
               
               
                   
                   
                   
                   
                 Sn 
               
               
                 ∠CSnC 
                 4.10053 
                 4.10053 
                 6.7082 
                 −14.82575 
                 1 
                 −14.82575 
                 1 
                 0.91771 
                 0.91771 
               
               
                 Methyl 
                 2.09711 
                 2.09711 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
                 1 
               
               
                 ∠HC a H 
               
               
                 ∠HC a Sn 
               
               
                 ∠C a C b C c   
               
               
                 Methylene 
                 2.11106 
                 2.11106 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
                 1 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
               
               
                 ∠C a C b H 
               
               
                 Methyl 
                 2.09711 
                 2.09711 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
                 1 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
               
               
                 ∠C a C b H 
               
               
                 ∠C b C a C c   
                 2.91547 
                 2.91547 
                 4.7958 
                 −16.68412 
                 26 
                 −16.68412 
                 26 
                 0.81549 
                 0.81549 
               
               
                 iso C a   
                   
                   
                   
                 C b   
                   
                 C c   
               
               
                 ∠C b C a H 
                 2.91547 
                 2.11323 
                 4.1633 
                 −15.55033 
                 5 
                 −14.82575 
                 1 
                 0.87495 
                 0.91771 
               
               
                 iso C a   
                   
                   
                   
                 C a   
                   
                 C b   
               
               
                 ∠C a C b H 
                 2.91547 
                 2.09711 
                 4.1633 
                 −15.55033 
                 5 
                 −14.82575 
                 1 
                 0.87495 
                 0.91771 
               
               
                 iso C a   
                   
                   
                   
                 C b   
                   
                 C a   
               
               
                 ∠C b C a C b   
                 2.90327 
                 2.90327 
                 4.7958 
                 −16.68412 
                 26 
                 −16.68412 
                 26 
                 0.81549 
                 0.81549 
               
               
                 tert C a   
                   
                   
                   
                 C b   
                   
                 C b   
               
               
                 ∠C b C a C d   
               
               
                 ∠HC a C c   
                 2.11323 
                 2.86175 
                 4.2895 
                 −15.95954 
                 10 
                 −14.82575 
                 1 
                 0.85252 
                 0.91771 
               
               
                 (C c (H)C a ═C b ) 
                   
                   
                   
                 C a   
                   
                 C c   
               
               
                 ∠C c C a C c   
                 2.86175 
                 2.86175 
                 4.7958 
                 −16.68411 
                 25 
                 −16.68411 
                 25 
                 0.81549 
                 0.81549 
               
               
                 (C c (C c )C a ═C b ) 
                   
                   
                   
                 C c   
                   
                 C c   
               
               
                 ∠C b C a C c   
                 2.53321 
                 2.86175 
                 4.7539 
                 −16.88873 
                 30 
                 −16.68411 
                 25 
                 0.80561 
                 0.81549 
               
               
                 (C b ═C a C c ) 
                   
                   
                   
                 C b   
                   
                 C c   
               
               
                 ∠HC a C b   
               
               
                 ∠HC a H 
                 2.04578 
                 2.04578 
                 3.4756 
                 −15.95955 
                 10 
                 H 
                 H 
                 0.85252 
                 1 
               
               
                 (H 2 C a ═C b C c ) 
               
               
                 ∠C b C a H 
               
               
                 (H 2 C a ═C b C c ) 
               
               
                 ∠CCC 
                 2.62936 
                 2.62936 
                 4.5585 
                 −17.17218 
                 38 
                 −17.17218 
                 38 
                 0.79232 
                 0.79232 
               
               
                 (aromatic) 
               
               
                 ∠CCH 
               
               
                 (aromatic) 
               
               
                 ∠C a O b H 
                 2.63431 
                 1.83616 
                 3.6405 
                 −14.82575 
                 1 
                 −14.82575 
                 1 
                 1 
                 0.91771 
               
               
                 ∠C b C a O a   
                 2.82796 
                 2.27954 
                 4.4721 
                 −17.17218 
                 38 
                 −13.61806 
                 O 
                 0.79232 
                 0.85395 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (Eq. (15.133)) 
               
               
                 ∠C b C a O b   
                 2.82796 
                 2.63431 
                 4.6690 
                 −16.40067 
                 20 
                 −13.61806 
                 O 
                 0.82959 
                 0.85395 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (Eq. (15.133)) 
               
               
                 ∠O a C a O b   
                 2.27954 
                 2.63431 
                 4.3818 
                 −16.17521 
                 13 
                 −15.75493 
                 7 
                 0.84115 
                 0.86359 
               
               
                   
                   
                   
                   
                 O a   
                   
                 O b   
               
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                 E T   
                 θ v   
                 θ 1   
                 θ 2   
                 Cal. θ 
                 Exp. θ 
               
               
                 Atoms of Angle 
                 C 1   
                 C 2   
                 c 1   
                 c 2 ′ 
                 (eV) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
               
               
                   
               
               
                 ∠ClSnCl 
                 0.75 
                 0.71514 
                 1 
                 0.71514 
                 −0.87386 
                   
                   
                   
                 107.52 
                 109.5 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (tin 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 tetrachloride) 
               
               
                 ∠HSnH 
                 0.75 
                 1 
                 1 
                 0.68510 
                 −1.65813 
                   
                   
                   
                 109.72 
                 109.5 
               
               
                   
                   
                   
                   
                   
                 (Eq. 23.236) 
                   
                   
                   
                   
                 (stannane) 
               
               
                 ∠CSnC 
                 1 
                 1 
                 1 
                 0.91771 
                 0 
                   
                   
                   
                 109.76 
                 109.5 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (tetramethyltin) 
               
               
                 Methyl 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 109.50 
               
               
                 ∠HC a H 
               
               
                 ∠HC a Sn 
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                 ∠C a C b C c   
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                 Methylene 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 108.44 
                 107 
               
               
                 ∠HC a H 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (propane) 
               
               
                 ∠C a C b C c   
                   
                   
                   
                   
                   
                 69.51 
                   
                   
                 110.49 
                 112 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (propane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 113.8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (butane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 110.8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C a C b H 
                   
                   
                   
                   
                   
                 69.51 
                   
                   
                 110.49 
                 111.0 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (butane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 111.4 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 Methyl 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 109.50 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                 ∠C a C b H 
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                 ∠C b C a C c   
                 1 
                 1 
                 1 
                 0.81549 
                 −1.85836 
                   
                   
                   
                 110.67 
                 110.8 
               
               
                 iso C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C b C a H 
                 0.75 
                 1 
                 0.75 
                 1.04887 
                 0 
                   
                   
                   
                 110.76 
               
               
                 iso C a   
               
               
                 ∠C a C b H 
                 0.75 
                 1 
                 0.75 
                 1.04887 
                 0 
                   
                   
                   
                 111.27 
                 111.4 
               
               
                 iso C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C b C a C b   
                 1 
                 1 
                 1 
                 0.81549 
                 −1.85836 
                   
                   
                   
                 111.37 
                 110.8 
               
               
                 tert C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C b C a C d   
                   
                   
                   
                   
                   
                 72.50 
                   
                   
                 107.50 
               
               
                 ∠HC a C c   
                 0.75 
                 1 
                 0.75 
                 1.07647 
                 0 
                   
                   
                   
                 118.36 
               
               
                 (C c (H)C a ═ 
               
               
                 ∠C c C a C c   
                 1 
                 1 
                 1 
                 0.81549 
                 −1.85836 
                   
                   
                   
                 113.84 
               
               
                 (C c (C c )C a ═ 
               
               
                 ∠C b C a C c   
                 1 
                 1 
                 1 
                 0.81055 
                 −1.85836 
                   
                   
                   
                 123.46 
                 124.4 
               
               
                 (C b ═C a C c ) 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (1,3,5- 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 hexatriene 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 CbCcCc) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 121.7 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (1,3,5- 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 hexatriene 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 CaCbCc) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 124.4 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (1,3-butadiene 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 CCC) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 125.3 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (2-butene 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 CbCaCc) 
               
               
                 ∠HC a C b   
                   
                   
                   
                   
                   
                   
                 118.36 
                 123.46 
                 118.19 
               
               
                 ∠HC a H 
                 1 
                 1 
                 0.75 
                 1.17300 
                 0 
                   
                   
                   
                 116.31 
                 118.5 
               
               
                 (H 2 C a ═C b C 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (2- 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 methylpropene) 
               
               
                 ∠C b C a H 
                   
                   
                   
                   
                   
                   
                 116.31 
                   
                 121.85 
                 121 
               
               
                 (H 2 C a ═C b C 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (2- 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 methylpropene) 
               
               
                 ∠CCC 
                 1 
                 1 
                 1 
                 0.79232 
                 −1.85836 
                   
                   
                   
                 120.19 
                 120 [34-36] 
               
               
                 (aromatic) 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (benzene) 
               
               
                 ∠CCH 
                   
                   
                   
                   
                   
                   
                 120.19 
                   
                 119.91 
                 120 [34-36] 
               
               
                 (aromatic) 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (benzene) 
               
               
                 ∠C a O b H 
                 0.75 
                 1 
                 0.75 
                 0.91771 
                 0 
                   
                   
                   
                 107.71 
               
               
                 ∠C b C a O a   
                 1 
                 1 
                 1 
                 0.82313 
                 −1.65376 
                   
                   
                   
                 121.86 
                 122 [55] 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (benzoic acid) 
               
               
                 ∠C b C a O b   
                 1 
                 1 
                 1 
                 0.84177 
                 −1.65376 
                   
                   
                   
                 117.43 
                 118 [55] 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (benzoic acid) 
               
               
                 ∠O a C a O b   
                 1 
                 1 
                 1 
                 0.85237 
                 −1.44915 
                   
                   
                   
                 126.03 
                 122 [55] 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (benzoic acid) 
               
               
                   
               
             
          
         
       
     
         [0354]    Lead Organometallic Functional Groups and Molecules 
         [0355]    The branched-chain alkyl lead molecules, PbC n H 2n-2 , comprise at least one Pb bound by a carbon-lead single bond comprising a C—Pb group, at least a terminal methyl group (CH 3 ), and may comprise methylene (CH 2 ), methylyne (CH), and C—C functional groups. The methyl and methylene functional groups are equivalent to those of straight-chain alkanes. Six types of C—C bonds can be identified. The n-alkane C—C bond is the same as that of straight-chain alkanes. In addition, the C—C bonds within isopropyl ((CH 3 ) 2 CH) and t-butyl ((CH 3 ) 3 C) groups and the isopropyl to isopropyl, isopropyl to t-butyl, and t-butyl to t-butyl C—C bonds comprise functional groups. 
         [0356]    As in the cases of carbon, silicon, tin, and germanium, the bonding in the lead atom involves four sp 3  hybridized orbitals. For lead, they are formed from the 6p and 6s electrons of the outer shells. Pb—C bonds form between a Pb6sp 3  HO and a C3sp 3  HO to yield alkyl leads. The geometrical parameters of the Pb—C functional group is solved using Eq. (15.51) and the relationships between the prolate spheroidal axes. Then, the sum of the energies of the H 2 -type ellipsoidal MOs is matched to that of the Pb6sp 3  shell as in the case of the corresponding carbon, silicon, tin, germanium molecules. As in the case of the transition metals, the energy of each functional group is determined for the effect of the electron density donation from the each participating C3sp 3  HO and Pb6sp 3  HO to the corresponding MO that maximizes the bond energy. 
         [0357]    The Pb electron configuration is [Xe]6s 2 4f 14 5d 10 6p 2 , and the orbital arrangement is 
         [0000]    
       
         
           
             
               
                 
                   
                     ↑ 
                     1 
                   
                    
                   
                     
                       ↑ 
                       0 
                     
                     
                       6 
                        
                       p 
                        
                       
                           
                       
                        
                       state 
                     
                   
                    
                   
                     
                         
                     
                     
                       - 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   23.244 
                   ) 
                 
               
             
           
         
       
     
         [0000]    corresponding to the ground state  3 P 0 . The energy of the lead 6p shell is the negative of the ionization energy of the lead atom [1] given by 
         [0000]        E (Pb,6 p  shell)=− E (ionization; Pb)=−7.41663 eV   (23.245) 
         [0000]    The energy of lead is less than the Coulombic energy between the electron and proton of H given by Eq. (1.231), but the atomic orbital may hybridize in order to achieve a bond at an energy minimum. After Eq. (13.422), the Pb6s atomic orbital (AO) combines with the Pb6p AOs to form a single Pb6sp 3  hybridized orbital (HO) with the orbital arrangement 
         [0000]    
       
         
           
             
               
                 
                   
                     ↑ 
                     
                       0 
                       , 
                       0 
                     
                   
                    
                   
                     
                       
                         ↑ 
                         
                           1 
                           , 
                           
                             - 
                             1 
                           
                         
                       
                        
                       
                         ↑ 
                         
                           1 
                           , 
                           0 
                         
                       
                     
                     
                       6 
                        
                       
                         sp 
                         3 
                       
                        
                       
                           
                       
                        
                       state 
                     
                   
                    
                   
                     ↑ 
                     
                       1 
                       , 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   23.246 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where the quantum numbers (l, m l ) are below each electron. The total energy of the state is given by the sum over the four electrons. The sum E T (Pb,6sp 3 ) of experimental energies [1] of Pb, Pb + , Pb 2+ , and Pb 3+  is 
         [0000]        E   T (Pb,6 sp   3 )=42.32 eV+31.9373 eV+15.03248 eV+7.41663 eV=96.70641 eV   (23.247) 
         [0000]    By considering that the central field decreases by an integer for each successive electron of the shell, the radius r 6sp     3    of the Pb6sp 3  shell may be calculated from the Coulombic energy using Eq. (15.13): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           
                             6 
                              
                             
                               sp 
                               3 
                             
                           
                         
                         = 
                           
                          
                         
                           
                             ∑ 
                             
                               n 
                               = 
                               78 
                             
                             81 
                           
                            
                           
                             
                               
                                 ( 
                                 
                                   Z 
                                   - 
                                   n 
                                 
                                 ) 
                               
                                
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               
                                 
                                   πɛ 
                                   0 
                                 
                                  
                                 
                                   ( 
                                   
                                     e 
                                      
                                     
                                         
                                     
                                      
                                     96.70641 
                                      
                                     
                                         
                                     
                                      
                                     eV 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             10 
                              
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 ( 
                                 
                                   e 
                                    
                                   
                                       
                                   
                                    
                                   96.70641 
                                    
                                   
                                       
                                   
                                    
                                   eV 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           1.40692 
                            
                           
                             a 
                             0 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.248 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where Z=82 for lead. Using Eq. (15.14), the Coulombic energy E Coulomb (Pb,6sp 3 ) of the outer electron of the Pb6sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             Coulomb 
                           
                            
                           
                             ( 
                             
                               Pb 
                               , 
                               
                                 6 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             
                               r 
                               
                                 6 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             1.40692 
                              
                             
                               a 
                               
                                 0 
                                  
                                 
                                     
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             9.67064 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.249 
                   ) 
                 
               
             
           
         
       
     
         [0000]    During hybridization, the spin-paired 6s electrons are promoted to Pb6sp 3  shell as unpaired electrons. The energy for the promotion is the magnetic energy given by Eq. (15.15) at the initial radius of the 6s electrons. From Eq. (10.102) with Z=82 and n=80, the radius r 80  of the Pb6s shell is 
         [0000]      r 80 =1.27805a 0    (23.250) 
         [0000]    Using Eqs. (15.15) and (23.250), the unpairing energy is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           E 
                            
                           
                             ( 
                             magnetic 
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             2 
                              
                             
                               πμ 
                               0 
                             
                              
                             
                                
                               2 
                             
                              
                             
                               ℏ 
                               2 
                             
                           
                           
                             
                               
                                 m 
                                 e 
                                 2 
                               
                                
                               
                                 ( 
                                 
                                   r 
                                   80 
                                 
                                 ) 
                               
                             
                             3 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             8 
                              
                             
                               πμ 
                               o 
                             
                              
                             
                               μ 
                               B 
                               2 
                             
                           
                           
                             
                               ( 
                               
                                 1.27805 
                                  
                                 
                                   a 
                                   0 
                                 
                               
                               ) 
                             
                             3 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           0.05481 
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.251 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Using Eqs. (23.249) and (23.251), the energy E(Pb,6sp 3 ) of the outer electron of the Pb6sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           E 
                            
                           
                             ( 
                             
                               Pb 
                               , 
                               
                                 6 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               - 
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 r 
                                 
                                   6 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                             
                           
                           + 
                           
                             
                               2 
                                
                               
                                 πμ 
                                 0 
                               
                                
                               
                                  
                                 2 
                               
                                
                               
                                 ℏ 
                                 2 
                               
                             
                             
                               
                                 
                                   m 
                                   e 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     r 
                                     80 
                                   
                                   ) 
                                 
                               
                               
                                 3 
                                  
                                 
                                     
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               9.67064 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             0.05481 
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             9.61584 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.252 
                   ) 
                 
               
             
           
         
       
     
         [0358]    Next, consider the formation of the Pb-L-bond MO of lead compounds wherein L is a ligand including carbon and each lead atom has a Pb6sp 3  electron with an energy given by Eq. (23.252). The total energy of the state of each lead atom is given by the sum over the four electrons. The sum E T (Pb Pb-L ,6Sp 3 ) of energies of Pb6sp 3  (Eq. (23.252)), Pb + , Pb 2+ , and Pb 3+  is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             T 
                           
                            
                           
                             ( 
                             
                               
                                 Pb 
                                 
                                   Pb 
                                   - 
                                   L 
                                 
                               
                               , 
                               
                                 6 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           - 
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       42.32 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       31.9373 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       15.03248 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       E 
                                        
                                       
                                         ( 
                                         
                                           Pb 
                                           , 
                                           
                                             6 
                                              
                                             
                                               sp 
                                               3 
                                             
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           - 
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       42.32 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       31.9373 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       15.03248 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       9.61584 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             98.90562 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.253 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where E(Pb,6sp 3 ) is the sum of the energy of Pb, −7.41663 eV, and the hybridization energy. 
         [0359]    A minimum energy is achieved while matching the potential, kinetic, and orbital energy relationships given in the Hydroxyl Radical (OH) section with the donation of electron density from the participating Pb6sp 3  HO to each Pb-L-bond MO. Consider the case wherein each Pb6sp 3  HO donates an excess of 25% of its electron density to the Pb-L-bond MO to form an energy minimum. By considering this electron redistribution in the lead molecule as well as the fact that the central field decreases by an integer for each successive electron of the shell, in general terms, the radius r Pb-L6sp     3    of the Pb6sp 3  shell may be calculated from the Coulombic energy using Eq. (15.18): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           
                             Pb 
                             - 
                             
                               L 
                                
                               
                                   
                               
                                
                               6 
                                
                               
                                 sp 
                                 3 
                               
                             
                           
                         
                         = 
                           
                          
                         
                           
                             ( 
                             
                               
                                 
                                   ∑ 
                                   
                                     n 
                                     = 
                                     78 
                                   
                                   81 
                                 
                                  
                                 
                                   ( 
                                   
                                     Z 
                                     - 
                                     n 
                                   
                                   ) 
                                 
                               
                               - 
                               0.25 
                             
                             ) 
                           
                            
                           
                             
                                
                               
                                 2 
                                  
                                 
                                     
                                 
                               
                             
                             
                               8 
                                
                               
                                 
                                   πɛ 
                                   0 
                                 
                                  
                                 
                                   ( 
                                   
                                     e 
                                      
                                     
                                         
                                     
                                      
                                     98.90562 
                                      
                                     
                                         
                                     
                                      
                                     eV 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             9.75 
                              
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 ( 
                                 
                                   e 
                                    
                                   
                                       
                                   
                                    
                                   98.90562 
                                    
                                   
                                       
                                   
                                    
                                   eV 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           1.34124 
                            
                           
                               
                           
                            
                           
                             a 
                             0 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.254 
                   ) 
                 
               
             
           
         
       
     
         [0360]    Using Eqs. (15.19) and (23.254), the Coulombic energy E Coulomb (Pb pb-L ,6sp 3 ) of the outer electron of the Pb6sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             Coulomb 
                           
                            
                           
                             ( 
                             
                               
                                 Pb 
                                 
                                   Pb 
                                   - 
                                   L 
                                 
                               
                               , 
                               
                                 6 
                                  
                                 
                                   sp 
                                   
                                     3 
                                      
                                     
                                         
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             π 
                              
                             
                                 
                             
                              
                             
                               ɛ 
                               0 
                             
                              
                             
                               r 
                               
                                 Pb 
                                 - 
                                 
                                   L 
                                    
                                   
                                       
                                   
                                    
                                   6 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             1.34124 
                              
                             
                               a 
                               0 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             10.14417 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.255 
                   ) 
                 
               
             
           
         
       
     
         [0000]    During hybridization, the spin-paired 6s electrons are promoted to Pb6sp 3  shell as unpaired electrons. The energy for the promotion is the magnetic energy given by Eq. (23.251). Using Eqs. (23.251) and (23.255), the energy E (Pb Ph-L ,6sp 3 ) of the outer electron of the Pb6sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           E 
                            
                           
                             ( 
                             
                               
                                 Pb 
                                 
                                   Pb 
                                   - 
                                   L 
                                 
                               
                               , 
                               
                                 6 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               - 
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 r 
                                 
                                   Pb 
                                   - 
                                   
                                     L 
                                      
                                     
                                         
                                     
                                      
                                     6 
                                      
                                     
                                       sp 
                                       3 
                                     
                                   
                                 
                               
                             
                           
                           + 
                           
                             
                               2 
                                
                               
                                 πμ 
                                 0 
                               
                                
                               
                                  
                                 2 
                               
                                
                               
                                 ℏ 
                                 2 
                               
                             
                             
                               
                                 
                                   m 
                                   e 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     r 
                                     80 
                                   
                                   ) 
                                 
                               
                               3 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               10.14417 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             0.05481 
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             10.08936 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.256 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Thus, E T (Pb-L,6sp 3 ), the energy change of each Pb6sp 3  shell with the formation of the Pb-L-bond MO is given by the difference between Eq. (23.256) and Eq. (23.252): 
         [0000]        E   T (Pb-L,6sp 3 )= E (Pb Pb-L ,6sp 3 )− E (Pb,6sp 3 )=−10.08936 eV−(−9.61584 eV)=−0.47352 eV   (23.257) 
         [0361]    Next, consider the formation of the Pb—C-bond MO by bonding with a carbon having a C2sp 3  electron with an energy given by Eq. (14.146). The total energy of the state is given by the sum over the four electrons. The sum E T (C ethane ,2sp 3 ) of calculated energies of C2sp 3 , C + , C 2+ , and C 3+  from Eqs. (10.123), (10.113-10.114), (10.68), and (10.48), respectively, is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             T 
                           
                            
                           
                             ( 
                             
                               
                                 C 
                                 ethane 
                               
                               , 
                               
                                 2 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           - 
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       64.3921 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       48.3125 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       24.2762 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       E 
                                        
                                       
                                         ( 
                                         
                                           C 
                                           , 
                                           
                                             2 
                                              
                                             
                                               sp 
                                               3 
                                             
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           - 
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       64.3921 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       48.3125 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       24.2762 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       14.63489 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             151.61569 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.258 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where E(C,2sp 3 ) is the sum of the energy of C, −11.27671 eV, and the hybridization energy. 
         [0362]    The sharing of electrons between the Pb6sp 3  Ho and C2sp 3  HOs to form a Pb—C-bond MO permits each participating hybridized orbital to decrease in radius and energy. A minimum energy is achieved while satisfying the potential, kinetic, and orbital energy relationships, when the Pb6sp 3  HO donates, and the C2sp 3  HO receives, excess electron density equivalent to an electron within the Pb—C-bond MO. By considering this electron redistribution in the alkyl lead molecule as well as the fact that the central field decreases by an integer for each successive electron of the shell, the radius r Pb-C2sp     3    of the C2sp 3  shell of the Pb—C-bond MO may be calculated from the Coulombic energy using Eqs. (15.18) and (23.258): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           
                             Pb 
                             - 
                             
                               C 
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                 sp 
                                 3 
                               
                             
                           
                         
                         = 
                           
                          
                         
                           
                             ( 
                             
                               
                                 
                                   ∑ 
                                   
                                     n 
                                     = 
                                     2 
                                   
                                   5 
                                 
                                  
                                 
                                   ( 
                                   
                                     Z 
                                     - 
                                     n 
                                   
                                   ) 
                                 
                               
                               + 
                               1 
                             
                             ) 
                           
                            
                           
                             
                                
                               2 
                             
                             
                               8 
                                
                               
                                 
                                   πɛ 
                                   0 
                                 
                                  
                                 
                                   ( 
                                   
                                     e 
                                      
                                     
                                         
                                     
                                      
                                     151.61569 
                                      
                                     
                                         
                                     
                                      
                                     eV 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             11 
                              
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 ( 
                                 
                                   e 
                                    
                                   
                                       
                                   
                                    
                                   151.61569 
                                    
                                   
                                       
                                   
                                    
                                   eV 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           0.98713 
                            
                           
                             a 
                             0 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.259 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Using Eqs. (15.19) and (23.259), the Coulombic energy E Coulomb (C Pb—C ,2sp 3 ) of the outer electron of the C2sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             
                               Coulomb 
                                
                               
                                   
                               
                             
                           
                            
                           
                             ( 
                             
                               
                                 C 
                                 
                                   Pb 
                                   - 
                                   C 
                                 
                               
                               , 
                               
                                 2 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             
                               r 
                               
                                 Pb 
                                 - 
                                 
                                   C 
                                    
                                   
                                       
                                   
                                    
                                   2 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             0.98713 
                              
                             
                               a 
                               0 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             13.78324 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.260 
                   ) 
                 
               
             
           
         
       
     
         [0363]    During hybridization, the spin-paired 2s electrons are promoted to C2sp 3  shell as unpaired electrons. The energy for the promotion is the magnetic energy given by Eq. (14.145). Using Eqs. (14.145) and (23.260), the energy E(C Pb—C ,2sp 3 ) of the outer electron of the C2sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           E 
                            
                           
                             ( 
                             
                               
                                 C 
                                 
                                   Pb 
                                   - 
                                   C 
                                 
                               
                               , 
                               
                                 2 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               - 
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 r 
                                 
                                   Pb 
                                   - 
                                   
                                     C 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                      
                                     
                                       sp 
                                       3 
                                     
                                   
                                 
                               
                             
                           
                           + 
                           
                             
                               2 
                                
                               
                                 πμ 
                                 0 
                               
                                
                               
                                  
                                 2 
                               
                                
                               
                                 ℏ 
                                 2 
                               
                             
                             
                               
                                 
                                   m 
                                   e 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     r 
                                     3 
                                   
                                   ) 
                                 
                               
                               
                                 3 
                                  
                                 
                                     
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               13.78324 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             0.19086 
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             13.59238 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.261 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Thus, E T (Pb—C,2sp 3 ), the energy change of each C2sp 3  shell with the formation of the Pb—C-bond MO is given by the difference between Eq. (23.261) and Eq. (14.146): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             T 
                           
                            
                           
                             ( 
                             
                               
                                 Pb 
                                 - 
                                 C 
                               
                               , 
                               
                                 2 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             E 
                              
                             
                               ( 
                               
                                 
                                   C 
                                   
                                     Pb 
                                     - 
                                     C 
                                   
                                 
                                 , 
                                 
                                   2 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                           - 
                           
                             E 
                              
                             
                               ( 
                               
                                 C 
                                 , 
                                 
                                   2 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               13.59238 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           - 
                           
                             ( 
                             
                               
                                 - 
                                 14.63489 
                               
                                
                               
                                   
                               
                                
                               eV 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           1.04251 
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.262 
                   ) 
                 
               
             
           
         
       
     
         [0364]    Now, consider the formation of the Pb-L-bond MO of lead compounds wherein L is a ligand including carbon. For the Pb-L functional groups, hybridization of the 6p and 6s AOs of Pb to form a single Pb6sp 3  HO shell forms an energy minimum, and the sharing of electrons between the Pb6sp 3  HO and L HO to form a MO permits each participating orbital to decrease in radius and energy. The C2sp 3  HO has an energy of E(C,2sp 3 )=−14.63489 eV (Eq. (15.25)) and the Pb6sp 3  HO has an energy of E(Pb,6sp 3 )=−9.61584 eV (Eq. (23.252)). To meet the equipotential condition of the union of the Pb-L H 2 -type-ellipsoidal-MO with these orbitals, the hybridization factors c 2  and C 2  of Eq. (15.61) for the Pb-L-bond MO given by Eq. (15.77) are 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             c 
                             2 
                           
                            
                           
                             ( 
                             
                               C 
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                                
                               
                                   
                               
                                
                               to 
                                
                               
                                   
                               
                                
                               Pb 
                                
                               
                                   
                               
                                
                               6 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             C 
                             2 
                           
                            
                           
                             ( 
                             
                               C 
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                                
                               
                                   
                               
                                
                               to 
                                
                               
                                   
                               
                                
                               Pb 
                                
                               
                                   
                               
                                
                               6 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             E 
                              
                             
                               ( 
                               
                                 Pb 
                                 , 
                                 
                                   6 
                                    
                                   
                                     sp 
                                     3 
                                   
                                    
                                   HO 
                                 
                               
                               ) 
                             
                           
                           
                             E 
                              
                             
                               ( 
                               
                                 C 
                                 , 
                                 
                                   2 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               9.61584 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           
                             
                               - 
                               14.63489 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         0.65705 
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.263 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Since the energy of the MO is matched to that of the Pb6sp 3  HO, E (AO/HO) in Eq. (15.61) is E(Pb,6sp 3 HO) given by Eq. (23.252). In order to match the energies of the carbon and lead HOs within the molecule, E T (atom-atom,msp 3 .AO) of the Pb-L-bond MO for the ligand carbon is one half E T (Pb C,2sp 3 ) (Eq. (23.262)). 
         [0365]    The symbols of the functional groups of lead compounds are given in Table 154. The geometrical (Eqs. (15.1-15.5)), intercept (Eqs. (15.31-15.32) and (15.80-15.87)), and energy (Eqs. (15.61) and (23.28-23.33)) parameters of lead compounds are given in Tables 155, 156, and 157, respectively. The total energy of each lead compounds given in Table 158 was calculated as the sum over the integer multiple of each E D (Group) of Table 157 corresponding to functional-group composition of the compound. The bond angle parameters of lead compounds determined using Eqs. (15.88-15.117) are given in Table 159. The charge-densities of exemplary lead compound, tetraethyl lead (Pb(CH 2 CH 3 ) 4 ) comprising atoms with the outer shell bridged by one or more H 2 -type ellipsoidal MOs or joined with one or more hydrogen MOs are shown in  FIG. 71 . 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 154 
               
             
             
               
                   
               
               
                 The symbols of functional groups of lead compounds. 
               
             
          
           
               
                   
                 Functional Group 
                 Group Symbol 
               
               
                   
                   
               
               
                   
                 PbC group 
                 Pb—C 
               
               
                   
                 CH 3  group 
                 C—H (CH 3 ) 
               
               
                   
                 CH 2  alkyl group 
                 C—H (CH 2 ) 
               
               
                   
                 CH alkyl 
                 C—H 
               
               
                   
                 CC bond (n-C) 
                 C—C (a) 
               
               
                   
                 CC bond (iso-C) 
                 C—C (b) 
               
               
                   
                 CC bond (tert-C) 
                 C—C (c) 
               
               
                   
                 CC (iso to iso-C) 
                 C—C (d) 
               
               
                   
                 CC (t to t-C) 
                 C—C (e) 
               
               
                   
                 CC (t to iso-C) 
                 C—C (f) 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 155 
               
             
             
               
                   
               
               
                 The geometrical bond parameters of lead compounds and experimental values [3]. 
               
             
          
           
               
                 Param- 
                 Pb—C 
                 C—H(CH 3 ) 
                 C—H(CH           
                 C—H 
                 C—C (a) 
                 C—C (b) 
                 C—C (c) 
                 C—C (d) 
                 C—C (e) 
                 C—C (f) 
               
               
                 eter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 2.21873 
                 1.64920 
                 1.67122 
                 1.67465 
                 2.12499 
                 2.12499 
                 2.10725 
                 2.12499 
                 2.10725 
                 2.10725 
               
               
                 c′ (a 0 ) 
                 2.12189 
                 1.04856 
                 1.05553 
                 1.05661 
                 1.45744 
                 1.45744 
                 1.45164 
                 1.45744 
                 1.45164 
                 1.45164 
               
               
                 Bond 
                 2.24571 
                 1.10974 
                 1.11713 
                 1.11827 
                 1.54280 
                 1.54280 
                 1.53635 
                 1.54280 
                 1.53635 
                 1.53635 
               
               
                 Length 
               
               
                 2c′ (Å) 
               
               
                 Exp. 
                 2.238 
                 1.107 
                 1.107 
                 1.122 
                 1.532 
                 1.532 
                 1.532 
                 1.532 
                 1.532 
                 1.532 
               
               
                 Bond 
                 ((CH 3 ) 4 Pb) 
                 (C—H 
                 (C—H 
                 (isobutane) 
                 (propane) 
                 (propane) 
                 (propane) 
                 (propane) 
                 (propane) 
                 (propane) 
               
               
                 Length 
                   
                 propane) 
                 propane) 
                   
                 1.531 
                 1.531 
                 1.531 
                 1.531 
                 1.531 
                 1.531 
               
               
                 (Å) 
                   
                 1.117 
                 1.117 
                   
                 (butane) 
                 (butane) 
                 (butane) 
                 (butane) 
                 (butane) 
                 (butane) 
               
               
                   
                   
                 (C—H 
                 (C—H 
               
               
                   
                   
                 butane) 
                 butane) 
               
               
                 b, c (a 0 ) 
                 0.64834 
                 1.27295 
                 1.29569 
                 1.29924 
                 1.54616 
                 1.54616 
                 1.52750 
                 1.54616 
                 1.52750 
                 1.52750 
               
               
                 e 
                 0.95635 
                 0.63580 
                 0.63159 
                 0.63095 
                 0.68600 
                 0.68600 
                 0.68888 
                 0.68600 
                 0.68888 
                 0.68888 
               
               
                   
               
               
                             indicates data missing or illegible when filed 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 156 
               
               
                   
               
               
                 The MO to HO intercept geometrical bond parameters of lead compounds. R, R′, R″ are H or alkyl groups. E T  is E T   
               
               
                 (atom-atom, msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 Final Total Energy 
                   
                   
               
               
                   
                   
                 E T   
                 E T   
                 E T   
                 E T   
                 Pb6sp 3   
               
               
                   
                   
                 (eV) 
                 (eV) 
                 (eV) 
                 (eV) 
                 C2sp 3   
                 r initial   
                 r final   
               
               
                 Bond 
                 Atom 
                 Bond 1 
                 Bond 2 
                 Bond 3 
                 Bond 4 
                 (eV) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 C—H(CH 3 ) 
                 C 
                 0.26063 
                 0 
                 0 
                 0 
                 −151.35506 
                 0.91771 
                 0.93414 
               
               
                 (CH 3 ) 3 Pb—CH 3   
                 Pb 
                 0.26063 
                 0.26063 
                 0.26063 
                 0.26063 
                   
                 1.40692 
                 0.98713 
               
               
                 (CH 3 ) 3 Pb—CH 3   
                 C 
                 0.26063 
                 0 
                 0 
                 0 
                   
                 0.91771 
                 0.93414 
               
               
                 C—H(CH 3 ) 
                 C 
                 −0.92918 
                 0 
                 0 
                 0 
                 −152.54487 
                 0.91771 
                 0.86359 
               
               
                 C—H(CH 2 ) (i) 
                 C 
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                 −153.47406 
                 0.91771 
                 0.81549 
               
               
                 C—H(CH) (i) 
                 C 
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 C a   
                 −0.92918 
                 0 
                 0 
                 0 
                 −152.54487 
                 0.91771 
                 0.86359 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                 −153.47406 
                 0.91771 
                 0.81549 
               
               
                 R—H 2 C a C b (H 2 C c —R′)HCH 2 —(C—C (b)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 R—H 2 C a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (c)) 
                 C b   
                 −0.92918 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.71860 
                 0.91771 
                 0.75889 
               
               
                 isoC a C b (H 2 C c —R′)HCH 2 —(C—C (d)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 tertC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (e)) 
                 C b   
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.51399 
                 0.91771 
                 0.76765 
               
               
                 tertC a C b (H 2 C c —R′)HCH 2 —(C—C (f)) 
                 C b   
                 −0.72457 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.19863 
                 0.91771 
                 0.78155 
               
               
                 isoC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (f)) 
                 C b   
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.51399 
                 0.91771 
                 0.76765 
               
               
                   
               
             
          
           
               
                   
                 E Coulomb  (C2sp 3 ) 
                 E (Pb6sp 3 ) 
                   
                   
                   
                   
                   
               
               
                   
                 (eV) 
                 E (C2sp 3 ) (eV) 
                 θ′ 
               
               
                 Bond 
                 Final 
                 Final 
                 (°) 
                 θ 1  (°) 
                 θ 2  (°) 
                 d 1  (a 0 ) 
                 d 2  (a 0 ) 
               
               
                   
               
               
                 C—H(CH 3 ) 
                 −14.56512 
                 −14.37426 
                 85.33 
                 94.67 
                 47.00 
                 1.12468 
                 0.07613 
               
               
                 (CH 3 ) 3 Pb—CH 3   
                 −13.78324 
                   
                 147.67 
                 32.33 
                 54.52 
                 1.28781 
                 0.83408 
               
               
                 (CH 3 ) 3 Pb—CH 3   
                 −14.56512 
                 −14.37426 
                 146.47 
                 33.53 
                 52.74 
                 1.34322 
                 0.77867 
               
               
                 C—H(CH 3 ) 
                 −15.75493 
                 −15.56407 
                 77.49 
                 102.51 
                 41.48 
                 1.23564 
                 0.18708 
               
               
                 C—H(CH 2 ) (i) 
                 −16.68412 
                 −16.49325 
                 68.47 
                 111.53 
                 35.84 
                 1.35486 
                 0.29933 
               
               
                 C—H(CH) (i) 
                 −17.61330 
                 −17.42244 
                 61.10 
                 118.90 
                 31.37 
                 1.42988 
                 0.37326 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 −15.75493 
                 −15.56407 
                 63.82 
                 116.18 
                 30.08 
                 1.83879 
                 0.38106 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 −16.68412 
                 −16.49325 
                 56.41 
                 123.59 
                 26.06 
                 1.90890 
                 0.45117 
               
               
                 R—H 2 C a C b (H 2 C c —R′)HCH 2 —(C—C (b)) 
                 −17.61330 
                 −17.42244 
                 48.30 
                 131.70 
                 21.90 
                 1.97162 
                 0.51388 
               
               
                 R—H 2 C a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (c)) 
                 −17.92866 
                 −17.73779 
                 48.21 
                 131.79 
                 21.74 
                 1.95734 
                 0.50570 
               
               
                 isoC a C b (H 2 C c —R′)HCH 2 —(C—C (d)) 
                 −17.61330 
                 −17.42244 
                 48.30 
                 131.70 
                 21.90 
                 1.97162 
                 0.51388 
               
               
                 tertC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (e)) 
                 −17.92866 
                 −17.73779 
                 50.04 
                 129.96 
                 22.66 
                 1.94462 
                 0.49298 
               
               
                 tertC a C b (H 2 C c —R′)HCH 2 —(C—C (f)) 
                 −17.40869 
                 −17.21783 
                 52.78 
                 127.22 
                 24.04 
                 1.92443 
                 0.47279 
               
               
                 isoC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (f)) 
                 −17.92866 
                 −17.73779 
                 50.04 
                 129.96 
                 22.66 
                 1.94462 
                 0.49298 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 157 
               
             
             
               
                   
               
               
                 The energy parameters (eV) of functional groups of lead compounds. 
               
             
          
           
               
                   
                   
                   
                   
                   
                 C—C 
                 C—C 
                 C—C 
                 C—C 
                 C—C 
                 C—C 
               
               
                 Para- 
                 Pb—C 
                 CH 3   
                 CH 2   
                 CH 
                 (a) 
                 (b) 
                 (c) 
                 (d) 
                 (e) 
                 (f) 
               
               
                 meters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
             
          
           
               
                 n 1   
                 1 
                 3 
                 2 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 n 2   
                 0 
                 2 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.375 
                 0.75 
                 0.75 
                 0.75 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
               
               
                 C 2   
                 0.65705 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 2   
                 0.65705 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
               
               
                 c 3   
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
                 1 
                 0 
               
               
                 c 4   
                 2 
                 1 
                 1 
                 1 
                 2 
                 2 
                 2 
                 2 
                 2 
                 2 
               
               
                 c 5   
                 0 
                 3 
                 2 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1o   
                 0.375 
                 0.75 
                 0.75 
                 0.75 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
               
               
                 C 2o   
                 0.65705 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 V e  (eV) 
                 −32.04219 
                 −107.32728 
                 −70.41425 
                 −35.12015 
                 −28.79214 
                 −28.79214 
                 −29.10112 
                 −28.79214 
                 −29.10112 
                 −29.10112 
               
               
                 V p  (eV) 
                 6.41212 
                 38.92728 
                 25.78002 
                 12.87680 
                 9.33352 
                 9.33352 
                 9.37273 
                 9.33352 
                 9.37273 
                 9.37273 
               
               
                 T (eV) 
                 7.22084 
                 32.53914 
                 21.06675 
                 10.48582 
                 6.77464 
                 6.77464 
                 6.90500 
                 6.77464 
                 6.90500 
                 6.90500 
               
               
                 V m  (eV) 
                 −3.61042 
                 −16.26957 
                 −10.53337 
                 −5.24291 
                 −3.38732 
                 −3.38732 
                 −3.45250 
                 −3.38732 
                 −3.45250 
                 −3.45250 
               
               
                 E 
                 −9.61584 
                 −15.56407 
                 −15.56407 
                 −14.63489 
                 −15.56407 
                 −15.56407 
                 −15.35946 
                 −15.56407 
                 −15.35946 
                 −15.35946 
               
               
                 (AO/HO) 
               
               
                 (eV) 
               
               
                 ΔE H     2     MO   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 (AO/HO) 
               
               
                 (eV) 
               
               
                 E T   
                 −9.61584 
                 −15.56407 
                 −15.56407 
                 −14.63489 
                 −15.56407 
                 −15.56407 
                 −15.35946 
                 −15.56407 
                 −15.35946 
                 −15.35946 
               
               
                 (AO/HO) 
               
               
                 (eV) 
               
               
                 E T   
                 −31.63548 
                 −67.69451 
                 −49.66493 
                 −31.63533 
                 −31.63537 
                 −31.63537 
                 −31.63535 
                 −31.63537 
                 −31.63535 
                 −31.63535 
               
               
                 (H 2 MO) 
               
               
                 (eV) 
               
               
                 E T   
                 0.52125 
                 0 
                 0 
                 0 
                 −1.85836 
                 −1.85836 
                 −1.44915 
                 −1.85836 
                 −1.44915 
                 −1.44915 
               
               
                 (atom- 
               
               
                 atom, 
               
               
                 msp 3 .AO) 
               
               
                 (eV) 
               
               
                 E T  (MO) 
                 −31.11411 
                 −67.69450 
                 −49.66493 
                 −31.63537 
                 −33.49373 
                 −33.49373 
                 −33.08452 
                 −33.49373 
                 −33.08452 
                 −33.08452 
               
               
                 (eV) 
               
               
                 ω 
                 6.20930 
                 24.9286 
                 24.2751 
                 24.1759 
                 9.43699 
                 9.43699 
                 15.4846 
                 9.43699 
                 9.55643 
                 9.55643 
               
               
                 (10 15   
               
               
                 rad/s) 
               
               
                 E K  (eV) 
                 4.08707 
                 16.40846 
                 15.97831 
                 15.91299 
                 6.21159 
                 6.21159 
                 10.19220 
                 6.21159 
                 6.29021 
                 6.29021 
               
               
                 Ē D  (eV) 
                 −0.12444 
                 −0.25352 
                 −0.25017 
                 −0.24966 
                 −0.16515 
                 −0.16515 
                 −0.20896 
                 −0.16515 
                 −0.16416 
                 −0.16416 
               
               
                 Ē Kvib   
                 0.14444 [66] 
                 0.35532 
                 0.35532 
                 0.35532 
                 0.12312 [6] 
                 0.17978 [7] 
                 0.09944 [8] 
                 0.12312 [6] 
                 0.12312 [6] 
                 0.12312 [6] 
               
               
                 (eV) 
                   
                 Eq. 
                 Eq. 
                 Eq. 
               
               
                   
                   
                 (13.458) 
                 (13.458) 
                 (13.458) 
               
               
                 Ē osc  (eV) 
                 −0.05222 
                 −0.22757 
                 −0.14502 
                 −0.07200 
                 −0.10359 
                 −0.07526 
                 −0.15924 
                 −0.10359 
                 −0.10260 
                 −0.10260 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                 E T   
                 −31.16633 
                 −67.92207 
                 −49.80996 
                 −31.70737 
                 −33.59732 
                 −33.49373 
                 −33.24376 
                 −33.59732 
                 −33.18712 
                 −33.18712 
               
               
                 (Group) 
               
               
                 (eV) 
               
               
                 E initial   
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
               
               
                 (c 4   
               
               
                 AO/HO) 
               
               
                 (eV) 
               
               
                 E initial   
                 0 
                 −13.59844 
                 −13.59844 
                 −13.59844 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 (c 5   
               
               
                 AO/HO) 
               
               
                 (eV) 
               
               
                 E D   
                 1.89655 
                 12.49186 
                 7.83016 
                 3.32601 
                 4.32754 
                 4.29921 
                 3.97398 
                 4.17951 
                 3.62128 
                 3.91734 
               
               
                 (Group) 
               
               
                 (eV) 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 158 
               
             
             
               
                   
               
               
                 The total bond energies of gaseous-state lead compounds calculated using the functional 
               
               
                 group composition (separate functional groups designated in the first row) and the 
               
               
                 energies of Table 157 compared to the gaseous-state experimental values [86] 
               
               
                 except where indicated. 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                 Calculated 
                   
                   
               
               
                   
                   
                   
                   
                   
                   
                   
                 Total 
               
               
                   
                   
                   
                   
                   
                   
                   
                 Bond 
                 Experimental 
               
               
                   
                   
                   
                   
                   
                   
                   
                 Energy 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Pb—C 
                 CH 3   
                 CH 2   
                 CH 
                 C—C (a) 
                 (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 4 H 12 Pb 
                 Tetramethyl-lead 
                 4 
                 4 
                 0 
                 0 
                 0 
                 57.55366 
                 57.43264 
                 −0.00211 
               
               
                 C 8 H 20 Pb 
                 Tetraethyl-lead 
                 4 
                 4 
                 4 
                 0 
                 4 
                 106.18446 
                 105.49164 
                 −0.00657 
               
               
                   
               
               
                   a Crystal. 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 159 
               
               
                   
               
               
                 The bond angle parameters of lead compounds and experimental values [3]. In the calculation of θ v , the parameters 
               
               
                 from the preceding angle were used. E T  is E T  (atom-atom, msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                 2c′ 
                   
                 Atom 1 
                   
                 Atom 2 
                   
                   
               
               
                   
                 2c′ 
                 2c′ 
                 Terminal 
                   
                 Hybridization 
                   
                 Hybridization 
               
               
                 Atoms of 
                 Bond 1 
                 Bond 2 
                 Atoms 
                 E Coulombic   
                 Designation 
                 E Coulombic   
                 Designation 
                 c 2   
                 c 2   
               
               
                 Angle 
                 (a 0 ) 
                 (a 0 ) 
                 (a 0 ) 
                 Atom 1 
                 (Table 7) 
                 Atom 2 
                 (Table 7) 
                 Atom 1 
                 Atom 2 
               
               
                   
               
               
                 Methyl 
                 2.09711 
                 2.09711 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
                 1 
               
               
                 ∠HC a H 
               
               
                 ∠H a C a Pb 
               
               
                 ∠C a PbC b   
                 4.24378 
                 4.24378 
                 6.9282 
                 −14.82575 
                 1 
                 −14.82575 
                 1 
                 0.91771 
                 0.91771 
               
               
                 Methylene 
                 2.11106 
                 2.11106 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
                 1 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
               
               
                 ∠C a C b H 
               
               
                 Methyl 
                 2.09711 
                 2.09711 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
                 1 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
               
               
                 ∠C a C b H 
               
               
                 ∠C b C a C c   
                 2.91547 
                 2.91547 
                 4.7958 
                 −16.68412 
                 26 
                 −16.68412 
                 26  
                 0.81549 
                 0.81549 
               
               
                 iso C a   
                   
                   
                   
                 C b   
                   
                 C c   
               
               
                 ∠C b C a H 
                 2.91547 
                 2.11323 
                 4.1633 
                 −15.55033 
                 5 
                 −14.82575 
                 1 
                 0.87495 
                 0.91771 
               
               
                 iso C a   
                   
                   
                   
                 C a   
                   
                 C b   
               
               
                 ∠C a C b H 
                 2.91547 
                 2.09711 
                 4.1633 
                 −15.55033 
                 5 
                 −14.82575 
                 1 
                 0.87495 
                 0.91771 
               
               
                 iso C a   
                   
                   
                   
                 C b   
                   
                 C a   
               
               
                 ∠C b C a C b   
                 2.90327 
                 2.90327 
                 4.7958 
                 −16.68412 
                 26 
                 −16.68412 
                 26  
                 0.81549 
                 0.81549 
               
               
                 tert C a   
                   
                   
                   
                 C b   
                   
                 C b   
               
               
                 ∠C b C a C d   
               
               
                   
               
             
          
           
               
                 Atoms of 
                   
                   
                   
                   
                 E T   
                 θ v   
                 θ 1   
                 θ 2   
                 Cal. θ 
                 Exp. θ 
               
               
                 Angle 
                 C 1   
                 C 2   
                 c 1   
                 c 2 ′ 
                 (eV) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
               
               
                   
               
               
                 Methyl 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 109.50 
               
               
                 ∠HC a H 
               
               
                 ∠H a C a Pb 
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                 ∠C a PbC b   
                 1 
                 1 
                 1 
                 0.91771 
                 −1.85836 
                   
                   
                   
                 109.43 
                 109.5 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (tetramethyllead) 
               
               
                 Methylene 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 108.44 
                 107 
               
               
                 ∠HC a H 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (propane) 
               
               
                 ∠C a C b C c   
                   
                   
                   
                   
                   
                 69.51 
                   
                   
                 110.49 
                 112 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (propane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 113.8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (butane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 110.8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C a C b H 
                   
                   
                   
                   
                   
                 69.51 
                   
                   
                 110.49 
                 111.0 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (butane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 111.4 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 Methyl 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 109.50 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                 ∠C a C b H 
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                 ∠C b C a C c   
                 1 
                 1 
                 1 
                 0.81549 
                 −1.85836 
                   
                   
                   
                 110.67 
                 110.8 
               
               
                 iso C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C b C a H 
                 0.75 
                 1 
                 0.75 
                 1.04887 
                 0 
                   
                   
                   
                 110.76 
               
               
                 iso C a   
               
               
                 ∠C a C b H 
                 0.75 
                 1 
                 0.75 
                 1.04887 
                 0 
                   
                   
                   
                 111.27 
                 111.4 
               
               
                 iso C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C b C a C b   
                 1 
                 1 
                 1 
                 0.81549 
                 −1.85836 
                   
                   
                   
                 111.37 
                 110.8 
               
               
                 tert C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C b C a C d   
                   
                   
                   
                   
                   
                 72.50 
                   
                   
                 107.50 
               
               
                   
               
             
          
         
       
     
         [0366]    Alkyl Arsines ((C n H 2n+1 ) 3 As, n=1,2,3,4,5 . . . ∞) 
         [0367]    The alkyl arsines, (C n H 2n+1 ) 3 As, comprise a As—C functional group. The alkyl portion of the alkyl arsine may comprise at least two terminal methyl groups (CH 3 ) at each end of each chain, and may comprise methylene (CH 2 ), and methylyne (CH) functional groups as well as C bound by carbon-carbon single bonds. The methyl and methylene functional groups are equivalent to those of straight-chain alkanes. Six types of C—C bonds can be identified. The n-alkane C—C bond is the same as that of straight-chain alkanes. In addition, the C—C bonds within isopropyl ((CH 3 ) 2 CH) and t-butyl ((CH 3 ) 3 C) groups and the isopropyl to isopropyl, isopropyl to t-butyl, and t-butyl to t-butyl C—C bonds comprise functional groups. The branched-chain-alkane groups in alkyl arsines are equivalent to those in branched-chain alkanes. The As—C group may further join the As4sp 3  HO to an aryl HO. 
         [0368]    As in the case of phosphorous, the bonding in the arsenic atom involves sp 3  hybridized orbitals formed, in this case, from the 4p and 4s electrons of the outer shells. The As—C bond forms between As4sp 3  and C2sp 3  HOs to yield arsines. The semimajor axis a of the As—C functional group is solved using Eq. (15.51). Using the semimajor axis and the relationships between the prolate spheroidal axes, the geometric and energy parameters of the MO are calculated using Eqs. (15.1-15.117) in the same manner as the organic functional groups given in Organic Molecular Functional Groups and Molecules section. 
         [0369]    The energy of arsenic is less than the Coulombic energy between the electron and proton of H given by Eq. (1.231). A minimum energy is achieved while matching the potential, kinetic, and orbital energy relationships given in the Hydroxyl Radical (OH) section with hybridization of the arsenic atom such that in Eqs. (15.51) and (15.61), the sum of the energies of the H 2 -type ellipsoidal MOs is matched to that of the As4sp 3  shell as in the case of the corresponding phosphine molecules. 
         [0370]    The As electron configuration is [Ar]4s 2 3d 10 4p 3  corresponding to the ground state  4 S 3/2 , and the 4sp 3  hybridized orbital arrangement after Eq. (13.422) is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       ↑ 
                       ↓ 
                     
                     
                       0 
                       , 
                       0 
                     
                   
                    
                   
                     
                       
                         ↑ 
                         
                           1 
                           , 
                           
                             - 
                             1 
                           
                         
                       
                        
                       
                         ↑ 
                         
                           1 
                           , 
                           0 
                         
                       
                     
                     
                       4 
                        
                       
                         sp 
                         3 
                       
                        
                       
                           
                       
                        
                       state 
                     
                   
                    
                   
                     ↑ 
                     
                       1 
                       , 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   23.264 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where the quantum numbers (l,m l ) are below each electron. The total energy of the state is given by the sum over the five electrons. The sum E T (As,4sp 3 ) of experimental energies [1] of As, As + , As 2+ , As 3+ , and As 4+  is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             T 
                           
                            
                           
                             ( 
                             
                               As 
                               , 
                               
                                 4 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             62.63 
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             50.13 
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             28.351 
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             18.5892 
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             9.7886 
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           169.48880 
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.265 
                   ) 
                 
               
             
           
         
       
     
         [0000]    By considering that the central field decreases by an integer for each successive electron of the shell, the radius r 4sp     3    of the As4sp 3  shell may be calculated from the Coulombic energy using Eq. (15.13): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           
                             4 
                              
                             
                               sp 
                               3 
                             
                           
                         
                         = 
                           
                          
                         
                           
                             ∑ 
                             
                               n 
                               = 
                               28 
                             
                             32 
                           
                            
                           
                             
                               
                                 ( 
                                 
                                   Z 
                                   - 
                                   n 
                                 
                                 ) 
                               
                                
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               
                                 
                                   πɛ 
                                   0 
                                 
                                  
                                 
                                   ( 
                                   
                                     e 
                                      
                                     
                                         
                                     
                                      
                                     169.48880 
                                      
                                     
                                         
                                     
                                      
                                     eV 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             15 
                              
                             
                                 
                             
                              
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             π 
                              
                             
                                 
                             
                              
                             
                               
                                 ɛ 
                                 0 
                               
                                
                               
                                 ( 
                                 
                                   e 
                                    
                                   
                                       
                                   
                                    
                                   169.48880 
                                    
                                   
                                       
                                   
                                    
                                   eV 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           1.20413 
                            
                           
                               
                           
                            
                           
                             a 
                             0 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.266 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where Z=33 for arsenic. Using Eq. (15.14), the Coulombic energy E Coulomb (As,4sp 3 ) of the outer electron of the As4sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             Coulomb 
                           
                            
                           
                             ( 
                             
                               As 
                               , 
                               
                                 4 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             
                               r 
                               
                                 4 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             1.20413 
                              
                             
                                 
                             
                              
                             
                               a 
                               0 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             11.29925 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.267 
                   ) 
                 
               
             
           
         
       
     
         [0000]    During hybridization, the spin-paired 4s electrons are promoted to As4sp 3  shell as paired electrons at the radius r 4sp     3    of the As4sp 3  shell. The energy for the promotion is the difference in the magnetic energy given by Eq. (15.15) at the initial radius of the 4s electrons and the final radius of the As4sp 3  electrons. From Eq. (10.102) with Z=33 and n=30, the radius r 30  of the As4s shell is 
         [0000]      r 30 =1.08564a 0    (23.268) 
         [0000]    Using Eqs. (15.15) and (23.268), the unpairing energy is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           E 
                            
                           
                             ( 
                             magnetic 
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               2 
                                
                               π 
                                
                               
                                   
                               
                                
                               
                                 μ 
                                 0 
                               
                                
                               
                                  
                                 2 
                               
                                
                               
                                 ℏ 
                                 2 
                               
                             
                             
                               m 
                               e 
                               2 
                             
                           
                            
                           
                             ( 
                             
                               
                                 1 
                                 
                                   
                                     ( 
                                     
                                       r 
                                       30 
                                     
                                     ) 
                                   
                                   3 
                                 
                               
                               - 
                               
                                 1 
                                 
                                   
                                     ( 
                                     
                                       r 
                                       
                                         4 
                                          
                                         
                                           sp 
                                           3 
                                         
                                       
                                     
                                     ) 
                                   
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           8 
                            
                           π 
                            
                           
                               
                           
                            
                           
                             μ 
                             o 
                           
                            
                           
                             
                               μ 
                               B 
                               2 
                             
                              
                             
                               ( 
                               
                                 
                                   1 
                                   
                                     
                                       ( 
                                       
                                         1.08564 
                                          
                                         
                                             
                                         
                                          
                                         
                                           a 
                                           0 
                                         
                                       
                                       ) 
                                     
                                     3 
                                   
                                 
                                 - 
                                 
                                   1 
                                   
                                     
                                       ( 
                                       
                                         1.20414 
                                          
                                         
                                           a 
                                           0 
                                         
                                       
                                       ) 
                                     
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           0.02388 
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.269 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Using Eqs. (23.267) and (23.269), the energy E(As,4sp 3 ) of the outer electron of the As4sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           E 
                            
                           
                             ( 
                             
                               As 
                               , 
                               
                                 4 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               - 
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               π 
                                
                               
                                   
                               
                                
                               
                                 ɛ 
                                 0 
                               
                                
                               
                                 r 
                                 
                                   4 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                             
                           
                           + 
                           
                             
                               
                                 2 
                                  
                                 π 
                                  
                                 
                                     
                                 
                                  
                                 
                                   μ 
                                   0 
                                 
                                  
                                 
                                    
                                   2 
                                 
                                  
                                 
                                   ℏ 
                                   2 
                                 
                               
                               
                                 m 
                                 e 
                                 2 
                               
                             
                              
                             
                               ( 
                               
                                 
                                   1 
                                   
                                     
                                       ( 
                                       
                                         r 
                                         30 
                                       
                                       ) 
                                     
                                     3 
                                   
                                 
                                 - 
                                 
                                   1 
                                   
                                     
                                       ( 
                                       
                                         r 
                                         
                                           4 
                                            
                                           
                                             sp 
                                             3 
                                           
                                         
                                       
                                       ) 
                                     
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               11.29925 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             0.02388 
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             11.27537 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.270 
                   ) 
                 
               
             
           
         
       
     
         [0371]    For the As—C functional group, hybridization of the 2s and 2p AOs of each C and the 4s and 4p AOs of each As to form single 2sp 3  and 4sp 3  shells, respectively, forms an energy minimum, and the sharing of electrons between the C2sp 3  and As4sp 3  HOs to form a MO permits each participating orbital to decrease in radius and energy. In branched-chain alkyl arsines, the energy of arsenic is less than the Coulombic energy between the electron and proton of H given by Eq. (1.231). Thus, c 2  in Eq. (15.61) is one, and the energy matching condition is determined by the C 2  parameter. Then, the C2sp 3  HO has an energy of E(C,2sp 3 )=−14.63489 eV (Eq. (15.25)), and the As4sp 3  HO has an energy of E(As,4sp 4 )=−11.27537 eV (Eq. (23.270)). To meet the equipotential condition of the union of the As—C H 2 -type-ellipsoidal-MO with these orbitals, the hybridization factor C 2  of Eq. (15.61) for the As—C-bond MO given by Eqs. (15.77), (15.79), and (13.430) is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             C 
                             2 
                           
                            
                           
                             ( 
                             
                               C 
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                                
                               
                                   
                               
                                
                               to 
                                
                               
                                   
                               
                                
                               As 
                                
                               
                                   
                               
                                
                               4 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               E 
                                
                               
                                 ( 
                                 
                                   As 
                                   , 
                                   
                                     4 
                                      
                                     
                                       sp 
                                       3 
                                     
                                   
                                 
                                 ) 
                               
                             
                             
                               E 
                                
                               
                                 ( 
                                 
                                   C 
                                   , 
                                   
                                     2 
                                      
                                     
                                         
                                     
                                      
                                     
                                       sp 
                                       3 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                            
                           
                             
                               c 
                               2 
                             
                              
                             
                               ( 
                               
                                 C 
                                  
                                 
                                     
                                 
                                  
                                 2 
                                  
                                 
                                   sp 
                                   3 
                                 
                                  
                                 HO 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               
                                 - 
                                 11.27537 
                               
                                
                               
                                   
                               
                                
                               eV 
                             
                             
                               
                                 - 
                                 14.63489 
                               
                                
                               
                                   
                               
                                
                               eV 
                             
                           
                            
                           
                             ( 
                             0.91771 
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         0.70705 
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.271 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The energy of the As—C-bond MO is the sum of the component energies of the H 2 -type ellipsoidal MO given in Eq. (15.51) with E(AO/HO=E(As,4sp 3 ) given by Eq. (23.270), and E T (atom-atom,msp 3 .AO) is zero in order to match the energies of the carbon and arsenic HOs. 
         [0372]    The symbols of the functional groups of branched-chain alkyl arsines are given in Table 160. The geometrical (Eqs. (15.1-15.5) and (15.51)), intercept (Eqs. (15.80-15.87)), and energy (Eqs. (15.6-15.11) and (15.17-15.65)) parameters of alkyl arsines are given in Tables 161, 162, and 163, respectively. The total energy of each alkyl arsine given in Table 164 was calculated as the sum over the integer multiple of each E D (Group) of Table 163 corresponding to functional-group composition of the molecule. The bond angle parameters of alkyl arsines determined using Eqs. (15.88-15.117) are given in Table 165. The color scale, charge-density of exemplary alkyl arsine, triphenylarsine, comprising atoms with the outer shell bridged by one or more H 2 -type ellipsoidal MOs or joined with one or more hydrogen MOs is shown in  FIG. 72 . 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 160 
               
             
             
               
                   
               
               
                 The symbols of functional groups of alkyl arsines. 
               
             
          
           
               
                   
                 Functional Group 
                 Group Symbol 
               
               
                   
                   
               
               
                   
                 As—C 
                 As—C 
               
               
                   
                 CH 3  group 
                 C—H (CH 3 ) 
               
               
                   
                 CH 2  group 
                 C—H (CH 2 ) 
               
               
                   
                 CH 
                 C—H (i) 
               
               
                   
                 CC bond (n-C) 
                 C—C (a) 
               
               
                   
                 CC bond (iso-C) 
                 C—C (b) 
               
               
                   
                 CC bond (tert-C) 
                 C—C (c) 
               
               
                   
                 CC (iso to iso-C) 
                 C—C (d) 
               
               
                   
                 CC (t to t-C) 
                 C—C (e) 
               
               
                   
                 CC (t to iso-C) 
                 C—C (f) 
               
               
                   
                 CC (aromatic bond) 
                 C 3e ═C 
               
               
                   
                 CH (aromatic) 
                 CH (ii) 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 161 
               
               
                   
               
               
                 The geometrical bond parameters of alkyl arsines and experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 As—C 
                 C—H(CH 3 ) 
                 C—H(CH 2 ) 
                 C—H (i) 
                 C—C (a) 
                 C—C (b) 
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 2.33431 
                 1.64920 
                 1.67122 
                 1.67465 
                 2.12499 
                 2.12499 
               
               
                 c′ (a 0 ) 
                 1.81700 
                 1.04856 
                 1.05553 
                 1.05661 
                 1.45744 
                 1.45744 
               
               
                 Bond Length 
                 1.92303 
                 1.10974 
                 1.11713 
                 1.11827 
                 1.54280 
                 1.54280 
               
               
                 2c′ (Å) 
               
               
                 Exp. Bond 
                 1.979 
                 1.107 
                 1.107 
                 1.122 
                 1.532 
                 1.532 
               
               
                 Length 
                 ((CH 3 ) 2 AsCH 3 ) 
                 (C—H propane) 
                 (C—H propane) 
                 (isobutane) 
                 (propane) 
                 (propane) 
               
               
                 (Å) 
                   
                 1.117 
                 1.117 
                   
                 1.531 
                 1.531 
               
               
                   
                   
                 (C—H butane) 
                 (C—H butane) 
                   
                 (butane) 
                 (butane) 
               
               
                 b, c (a 0 ) 
                 1.46544 
                 1.27295 
                 1.29569 
                 1.29924 
                 1.54616 
                 1.54616 
               
               
                 e 
                 0.77839 
                 0.63580 
                 0.63159 
                 0.63095 
                 0.68600 
                 0.68600 
               
               
                   
               
             
          
           
               
                   
                   
                 C—C (c) 
                 C—C (d) 
                 C—C (e) 
                 C—C (f) 
                 C 3e ═C 
                 CH (ii) 
               
               
                   
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
                   
               
               
                   
                 a (a 0 ) 
                 2.10725 
                 2.12499 
                 2.10725 
                 2.10725 
                 1.47348 
                 1.60061 
               
               
                   
                 c′ (a 0 ) 
                 1.45164 
                 1.45744 
                 1.45164 
                 1.45164 
                 1.31468 
                 1.03299 
               
               
                   
                 Bond Length 
                 1.53635 
                 1.54280 
                 1.53635 
                 1.53635 
                 1.39140 
                 1.09327 
               
               
                   
                 2c′ (Å) 
               
               
                   
                 Exp. Bond 
                 1.532 
                 1.532 
                 1.532 
                 1.532 
                 1.399 
                 1.101 
               
               
                   
                 Length 
                 (propane) 
                 (propane) 
                 (propane) 
                 (propane) 
                 (benzene) 
                 (benzene) 
               
               
                   
                 (Å) 
                 1.531 
                 1.531 
                 1.531 
                 1.531 
               
               
                   
                   
                 (butane) 
                 (butane) 
                 (butane) 
                 (butane) 
               
               
                   
                 b, c (a 0 ) 
                 1.52750 
                 1.54616 
                 1.52750 
                 1.52750 
                 0.66540 
                 1.22265 
               
               
                   
                 e 
                 0.68888 
                 0.68600 
                 0.68888 
                 0.68888 
                 0.89223 
                 0.64537 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 162 
               
               
                   
               
               
                 The MO to HO intercept geometrical bond parameters of alkyl arsines. R, R′, R″ are H or alkyl groups. E T  is E T   
               
               
                 (atom-atom, msp 3 .AO. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                 E T   
                 E T   
                 E T   
                 E T   
                 Final Total Energy 
                   
                   
               
               
                   
                   
                 (eV) 
                 (eV) 
                 (eV) 
                 (eV) 
                 C2sp 3   
                 r initial   
                 r final   
               
               
                 Bond 
                 Atom 
                 Bond 1 
                 Bond 2 
                 Bond 3 
                 Bond 4 
                 (eV) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 C—H(CH 3 ) 
                 C 
                 0 
                 0 
                 0 
                 0 
                 −151.61569 
                 0.91771 
                 0.91771 
               
               
                 (CH 3 ) 2 As—CH 3   
                 C 
                 0 
                 0 
                 0 
                 0 
                   
                 0.91771 
                 0.91771 
               
               
                 (CH 3 ) 2 As—CH 3   
                 As 
                 0 
                 0 
                 0 
                 0 
                   
                 0.91771 
                 0.91771 
               
               
                 C—H(CH 3 ) 
                 C 
                 −0.92918 
                 0 
                 0 
                 0 
                 −152.54487 
                 0.91771 
                 0.86359 
               
               
                 C—H(CH 2 ) 
                 C 
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                 −153.47406 
                 0.91771 
                 0.81549 
               
               
                 C—H(CH) 
                 C 
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 C a   
                 −0.92918 
                 0 
                 0 
                 0 
                 −152.54487 
                 0.91771 
                 0.86359 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                 −153.47406 
                 0.91771 
                 0.81549 
               
               
                 R—H 2 C a C b (H 2 C c —R′)HCH 2 —(C—C (b)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 R—H 2 C a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (c)) 
                 C b   
                 −0.92918 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.71860 
                 0.91771 
                 0.75889 
               
               
                 isoC a C b (H 2 C c —R′)HCH 2 —(C—C (d)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 tertC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (e)) 
                 C b   
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.51399 
                 0.91771 
                 0.76765 
               
               
                 tertC a C b (H 2 C c —R′)HCH 2 —(C—C (f)) 
                 C b   
                 −0.72457 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.19863 
                 0.91771 
                 0.78155 
               
               
                 isoC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (f)) 
                 C b   
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.51399 
                 0.91771 
                 0.76765 
               
               
                   
               
             
          
           
               
                   
                 E Coulomb  (eV) 
                 E (C2sp 3 ) (eV) 
                 θ′ 
                 θ 1   
                 θ 2   
                 d 1   
                 d 2   
               
               
                 Bond 
                 Final 
                 Final 
                 (°) 
                 (°) 
                 (°) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 C—H(CH 3 ) 
                 −14.82575 
                 −14.63489 
                 83.62 
                 96.38 
                 45.76 
                 1.15051 
                 0.10195 
               
               
                 (CH 3 ) 2 As—CH 3   
                 −14.82575 
                 −14.63489 
                 89.82 
                 90.18 
                 38.77 
                 1.81991 
                 0.00291 
               
               
                 (CH 3 ) 2 As—CH 3   
                 −14.82575 
                   
                 89.82 
                 90.18 
                 38.77 
                 1.81991 
                 0.00291 
               
               
                 C—H(CH 3 ) 
                 −15.75493 
                 −15.56407 
                 77.49 
                 102.51 
                 41.48 
                 1.23564 
                 0.18708 
               
               
                 C—H(CH 2 ) 
                 −16.68412 
                 −16.49325 
                 68.47 
                 111.53 
                 35.84 
                 1.35486 
                 0.29933 
               
               
                 C—H(CH) 
                 −17.61330 
                 −17.42244 
                 61.10 
                 118.90 
                 31.37 
                 1.42988 
                 0.37326 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 −15.75493 
                 −15.56407 
                 63.82 
                 116.18 
                 30.08 
                 1.83879 
                 0.38106 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 −16.68412 
                 −16.49325 
                 56.41 
                 123.59 
                 26.06 
                 1.90890 
                 0.45117 
               
               
                 R—H 2 C a C b (H 2 C c —R′)HCH 2 —(C—C (b)) 
                 −17.61330 
                 −17.42244 
                 48.30 
                 131.70 
                 21.90 
                 1.97162 
                 0.51388 
               
               
                 R—H 2 C a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (c)) 
                 −17.92866 
                 −17.73779 
                 48.21 
                 131.79 
                 21.74 
                 1.95734 
                 0.50570 
               
               
                 isoC a C b (H 2 C c —R′)HCH 2 —(C—C (d)) 
                 −17.61330 
                 −17.42244 
                 48.30 
                 131.70 
                 21.90 
                 1.97162 
                 0.51388 
               
               
                 tertC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (e)) 
                 −17.92866 
                 −17.73779 
                 50.04 
                 129.96 
                 22.66 
                 1.94462 
                 0.49298 
               
               
                 tertC a C b (H 2 C c —R′)HCH 2 —(C—C (f)) 
                 −17.40869 
                 −17.21783 
                 52.78 
                 127.22 
                 24.04 
                 1.92443 
                 0.47279 
               
               
                 isoC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (f)) 
                 −17.92866 
                 −17.73779 
                 50.04 
                 129.96 
                 22.66 
                 1.94462 
                 0.49298 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 163 
               
               
                   
               
               
                 The energy parameters (eV) of functional groups of alkyl arsines. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 As—C 
                 CH 3   
                 CH 2   
                 CH (i) 
                 C—C (a) 
                 C—C (b) 
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 f 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 n 1   
                 1 
                 3 
                 2 
                 1 
                 1 
                 1 
               
               
                 n 2   
                 0 
                 2 
                 1 
                 0 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.5 
                 0.75 
                 0.75 
                 0.75 
                 0.5 
                 0.5 
               
               
                 C 2   
                 0.70705 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 2   
                 1 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
               
               
                 c 3   
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
               
               
                 c 4   
                 2 
                 1 
                 1 
                 1 
                 2 
                 2 
               
               
                 c 5   
                 0 
                 3 
                 2 
                 1 
                 0 
                 0 
               
               
                 C 1o   
                 0.5 
                 0.75 
                 0.75 
                 0.75 
                 0.5 
                 0.5 
               
               
                 C 2o   
                 0.70705 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 V e  (eV) 
                 −31.18832 
                 −107.32728 
                 −70.41425 
                 −35.12015 
                 −28.79214 
                 −28.79214 
               
               
                 V p  (eV) 
                 7.48806 
                 38.92728 
                 25.78002 
                 12.87680 
                 9.33352 
                 9.33352 
               
               
                 T (eV) 
                 6.68041 
                 32.53914 
                 21.06675 
                 10.48582 
                 6.77464 
                 6.77464 
               
               
                 V m  (eV) 
                 −3.34021 
                 −16.26957 
                 −10.53337 
                 −5.24291 
                 −3.38732 
                 −3.38732 
               
               
                 E (AO/HO) (eV) 
                 −11.27537 
                 −15.56407 
                 −15.56407 
                 −14.63489 
                 −15.56407 
                 −15.56407 
               
               
                 ΔE H     2     MO  (AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 E T  (AO/HO) (eV) 
                 −11.27537 
                 −15.56407 
                 −15.56407 
                 −14.63489 
                 −15.56407 
                 −15.56407 
               
               
                 ET (H 2 MO) (eV) 
                 −31.63542 
                 −67.69451 
                 −49.66493 
                 −31.63533 
                 −31.63537 
                 −31.63537 
               
               
                 E T  (atom-atom, 
                 0 
                 0 
                 0 
                 0 
                 −1.85836 
                 −1.85836 
               
               
                 msp 3 .AO) (eV) 
               
               
                 E T  (MO) (eV) 
                 −31.63537 
                 −67.69450 
                 −49.66493 
                 −31.63537 
                 −33.49373 
                 −33.49373 
               
               
                 ω (10 15  rad/s) 
                 6.89218 
                 24.9286 
                 24.2751 
                 24.1759 
                 9.43699 
                 9.43699 
               
               
                 E K  (eV) 
                 4.53655 
                 16.40846 
                 15.97831 
                 15.91299 
                 6.21159 
                 6.21159 
               
               
                 Ē D  (eV) 
                 −0.13330 
                 −0.25352 
                 −0.25017 
                 −0.24966 
                 −0.16515 
                 −0.16515 
               
               
                 Ē Kvib  (eV) 
                 0.15498 [66] 
                 0.35532 
                 0.35532 
                 0.35532 
                 0.12312 [6] 
                 0.17978 [7] 
               
               
                   
                   
                 (Eq. 
                 (Eq. 
                 (Eq. 
               
               
                   
                   
                 (13.458)) 
                 (13.458)) 
                 (13.458)) 
               
               
                 Ē osc  (eV) 
                 −0.05581 
                 −0.22757 
                 −0.14502 
                 −0.07200 
                 −0.10359 
                 −0.07526 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                 E T  (Group) (eV) 
                 −31.69118 
                 −67.92207 
                 −49.80996 
                 −31.70737 
                 −33.59732 
                 −33.49373 
               
               
                 E initial  (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
               
               
                 E initial  (c 5  AO/HO) (eV) 
                 0 
                 −13.59844 
                 −13.59844 
                 −13.59844 
                 0 
                 0 
               
               
                 E D  (Group) (eV) 
                 2.42140 
                 12.49186 
                 7.83016 
                 3.32601 
                 4.32754 
                 4.29921 
               
               
                   
               
               
                   
                 C—C (c) 
                 C—C (d) 
                 C—C (e) 
                 C—C (f) 
                 C 3e ═C 
                 CH (ii) 
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 f 1   
                 1 
                 1 
                 1 
                 1 
                 0.75 
                 1 
               
               
                 n 1   
                 1 
                 1 
                 1 
                 1 
                 2 
                 1 
               
               
                 n 2   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.75 
               
               
                 C 2   
                 1 
                 1 
                 1 
                 1 
                 0.85252 
                 1 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 2   
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.85252 
                 0.91771 
               
               
                 c 3   
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
               
               
                 c 4   
                 2 
                 2 
                 2 
                 2 
                 3 
                 1 
               
               
                 c 5   
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
               
               
                 C 1o   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.75 
               
               
                 C 2o   
                 1 
                 1 
                 1 
                 1 
                 0.85252 
                 1 
               
               
                 V e  (eV) 
                 −29.10112 
                 −28.79214 
                 −29.10112 
                 −29.10112 
                 −101.12679 
                 −37.10024 
               
               
                 V p  (eV) 
                 9.37273 
                 9.33352 
                 9.37273 
                 9.37273 
                 20.69825 
                 13.17125 
               
               
                 T (eV) 
                 6.90500 
                 6.77464 
                 6.90500 
                 6.90500 
                 34.31559 
                 11.58941 
               
               
                 V m  (eV) 
                 −3.45250 
                 −3.38732 
                 −3.45250 
                 −3.45250 
                 −17.15779 
                 −5.79470 
               
               
                 E (AO/HO) (eV) 
                 −15.35946 
                 −15.56407 
                 −15.35946 
                 −15.35946 
                 0 
                 −14.63489 
               
               
                 ΔE H     2     MO  (AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 −1.13379 
               
               
                 E T  (AO/HO) (eV) 
                 −15.35946 
                 −15.56407 
                 −15.35946 
                 −15.35946 
                 0 
                 −13.50110 
               
               
                 E T  (H 2 MO) (eV) 
                 −31.63535 
                 −31.63537 
                 −31.63535 
                 −31.63535 
                 −63.27075 
                 −31.63539 
               
               
                 E T  (atom-atom, 
                 −1.44915 
                 −1.85836 
                 −1.44915 
                 −1.44915 
                 −2.26759 
                 −0.56690 
               
               
                 msp 3 .AO) (eV) 
               
               
                 E T  (MO) (eV) 
                 −33.08452 
                 −33.49373 
                 −33.08452 
                 −33.08452 
                 −65.53833 
                 −32.20226 
               
               
                 ω (10 15  rad/s) 
                 15.4846 
                 9.43699 
                 9.55643 
                 9.55643 
                 49.7272 
                 26.4826 
               
               
                 E K  (eV) 
                 10.19220 
                 6.21159 
                 6.29021 
                 6.29021 
                 32.73133 
                 17.43132 
               
               
                 Ē D  (eV) 
                 −0.20896 
                 −0.16515 
                 −0.16416 
                 −0.16416 
                 −0.35806 
                 −0.26130 
               
               
                 Ē Kvib  (eV) 
                 0.09944 [8] 
                 0.12312 [6] 
                 0.12312 [6] 
                 0.12312 [6] 
                 0.19649 [30] 
                 0.35532 
               
               
                   
                   
                   
                   
                   
                   
                 Eq. (13.458) 
               
               
                 Ē osc  (eV) 
                 −0.15924 
                 −0.10359 
                 −0.10260 
                 −0.10260 
                 −0.25982 
                 −0.08364 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                 E T  (Group) (eV) 
                 −33.24376 
                 −33.59732 
                 −33.18712 
                 −33.18712 
                 −49.54347 
                 −32.28590 
               
               
                 E initial  (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
               
               
                 E initial  (c 5  AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 −13.59844 
               
               
                 E D  (Group) (eV) 
                 3.97398 
                 4.17951 
                 3.62128 
                 3.91734 
                 5.63881 
                 3.90454 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 164 
               
               
                   
               
               
                 The total bond energies of alkyl arsines calculated using the functional group composition and 
               
               
                 the energies of Table 163 compared to the experimental values [87]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 C—C 
                 C—C 
                   
                 C—C 
               
               
                 Formula 
                 Name 
                 As—C 
                 CH 3   
                 CH 2   
                 CH (i) 
                 (a) 
                 (b) 
                 C—C (c) 
                 (d) 
               
               
                   
               
               
                 C 3 H 9 As 
                 Trimethylarsine 
                 3 
                 3 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 6 H 15 As 
                 Triethylarsine 
                 3 
                 3 
                 3 
                 0 
                 3 
                 0 
                 0 
                 0 
               
               
                 C 18 H 15 As 
                 Triphenylarsine 
                 3 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 C—C 
                   
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 (e) 
                 C—C (f) 
                 C 3e ═C 
                 CH (ii) 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 C 3 H 9 As 
                 Trimethylarsine 
                 0 
                 0 
                 0 
                 0 
                 44.73978 
                 45.63114 
                 0.01953 
               
               
                 C 6 H 15 As 
                 Triethylarsine 
                 0 
                 0 
                 0 
                 0 
                 81.21288 
                 81.01084 
                 −0.00249 
               
               
                 C 18 H 15 As 
                 Triphenylarsine 
                 0 
                 0 
                 18 
                 15 
                 167.33081 
                 166.49257 
                 −0.00503 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 165 
               
               
                   
               
               
                 The bond angle parameters of alkyl arsines and experimental values [3]. In the calculation of θ v , the 
               
               
                 parameters from the preceding angle were used. E T  is E T (atom-atom, msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                 2c′ 
                   
                 Atom 1 
                   
                 Atom 2 
                   
                   
               
               
                   
                 2c′ 
                 2c′ 
                 Terminal 
                 E Coulombic   
                 Hybridization 
                   
                 Hybridization 
               
               
                 Atoms of 
                 Bond 1 
                 Bond 2 
                 Atoms 
                 or E 
                 Designation 
                 E Coulombic   
                 Designation 
                 c 2   
                 c 2   
               
               
                 Angle 
                 (a 0 ) 
                 (a 0 ) 
                 (a 0 ) 
                 Atom 1 
                 (Table 7) 
                 Atom 2 
                 (Table 7) 
                 Atom 1 
                 Atom 2 
               
               
                   
               
               
                 Methyl 
                 2.09711 
                 2.09711 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
                 1 
               
               
                 ∠HC a H 
               
               
                 ∠H a C a As 
               
               
                 ∠C a AsC b   
                 3.63400 
                 3.63400 
                 5.5136 
                 −15.75493 
                 7 
                 −15.75493 
                 7 
                 0.86359 
                 0.86359 
               
               
                 Methylene 
                 2.11106 
                 2.11106 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
                 1 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
               
               
                 ∠C a C b H 
               
               
                 Methyl 
                 2.09711 
                 2.09711 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
                 1 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
               
               
                 ∠C a C b H 
               
               
                 ∠C b C a C c   
                 2.91547 
                 2.91547 
                 4.7958 
                 −16.68412 
                 26 
                 −16.68412 
                 26  
                 0.81549 
                 0.81549 
               
               
                 iso C a   
                   
                   
                   
                 C b   
                   
                 C c   
               
               
                 ∠C b C a H 
                 2.91547 
                 2.11323 
                 4.1633 
                 −15.55033 
                 5 
                 −14.82575 
                 1 
                 0.87495 
                 0.91771 
               
               
                 iso C a   
                   
                   
                   
                 C a   
                   
                 C b   
               
               
                 ∠C a C b H 
                 2.91547 
                 2.09711 
                 4.1633 
                 −15.55033 
                 5 
                 −14.82575 
                 1 
                 0.87495 
                 0.91771 
               
               
                 iso C a   
                   
                   
                   
                 C b   
                   
                 C a   
               
               
                 ∠C b C a C b   
                 2.90327 
                 2.90327 
                 4.7958 
                 −16.68412 
                 26 
                 −16.68412 
                 26  
                 0.81549 
                 0.81549 
               
               
                 tert C a   
                   
                   
                   
                 C b   
                   
                 C b   
               
               
                 ∠C b C a C d   
               
               
                   
               
             
          
           
               
                 Atoms of 
                   
                   
                   
                   
                 E T   
                 θ v   
                 θ 1   
                 θ 2   
                 Cal. θ 
                 Exp. θ 
               
               
                 Angle 
                 C 1   
                 C 2   
                 c 1   
                 c 2 ′ 
                 (eV) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
               
               
                   
               
               
                 Methyl 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 109.50 
               
               
                 ∠HC a H 
               
               
                 ∠H a C a As 
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
                 111.4 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (trimethylarsine) 
               
               
                 ∠C a AsC b   
                 1 
                 1 
                 1 
                 0.86359 
                 −1.85836 
                   
                   
                   
                 98.68 
                  98.8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (trimethylarsine) 
               
               
                 Methylene 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 108.44 
                 107   
               
               
                 ∠HC a H 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (propane) 
               
               
                 ∠C a C b C c   
                   
                   
                   
                   
                   
                 69.51 
                   
                   
                 110.49 
                 112   
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (propane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 113.8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (butane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 110.8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C a C b H 
                   
                   
                   
                   
                   
                 69.51 
                   
                   
                 110.49 
                 111.0 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (butane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 111.4 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 Methyl 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 109.50 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                 ∠C a C b H 
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                 ∠C b C a C c   
                 1 
                 1 
                 1 
                 0.81549 
                 −1.85836 
                   
                   
                   
                 110.67 
                 110.8 
               
               
                 iso C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C b C a H 
                 0.75 
                 1 
                 0.75 
                 1.04887 
                 0 
                   
                   
                   
                 110.76 
               
               
                 iso C a   
               
               
                 ∠C a C b H 
                 0.75 
                 1 
                 0.75 
                 1.04887 
                 0 
                   
                   
                   
                 111.27 
                 111.4 
               
               
                 iso C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C b C a C b   
                 1 
                 1 
                 1 
                 0.81549 
                 −1.85836 
                   
                   
                   
                 111.37 
                 110.8 
               
               
                 tert C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C b C a C d   
                   
                   
                   
                   
                   
                 72.50 
                   
                   
                 107.50 
               
               
                   
               
             
          
         
       
     
         [0373]    Alkyl Stibines (C n H 2n+1 ) 3 Sb, n=1,2,3,4,5, . . . ∞) 
         [0374]    The alkyl stibines, (C n H 2n+1 ) 3 Sb, comprise a Sb—C functional group. The alkyl portion of the alkyl stibine may comprise at least two terminal methyl groups (CH 3 ) at each end of each chain, and may comprise methylene (CH 2 ), and methylyne (CH) functional groups as well as C bound by carbon-carbon single bonds. The methyl and methylene functional groups are equivalent to those of straight-chain alkanes. Six types of C—C bonds can be identified. The n-alkane C—C bond is the same as that of straight-chain alkanes. In addition, the C—C bonds within isopropyl ((CH 3 ) 2 CH) and t-butyl ((CH 3 ) 3 C) groups and the isopropyl to isopropyl, isopropyl to t-butyl, and t-butyl to t-butyl C—C bonds comprise functional groups. The branched-chain-alkane groups in alkyl stibines are equivalent to those in branched-chain alkanes. The Sb—C group may further join the Sb5sp 3  HO to an aryl HO. 
         [0375]    As in the case of phosphorous, the bonding in the antimony atom involves sp 3  hybridized orbitals formed, in this case, from the 5p and 5s electrons of the outer shells. The Sb—C bond forms between Sb5sp 3  and C2sp 3  HOs to yield stibines. The semimajor axis a of the Sb—C functional group is solved using Eq. (15.51). Using the semimajor axis and the relationships between the prolate spheroidal axes, the geometric and energy parameters of the MO are calculated using Eqs. (15.1-15.117) in the same manner as the organic functional groups given in Organic Molecular Functional Groups and Molecules section. 
         [0376]    The energy of antimony is less than the Coulombic energy between the electron and proton of H given by Eq. (1.231). A minimum energy is achieved while matching the potential, kinetic, and orbital energy relationships given in the Hydroxyl Radical (OH) section with hybridization of the antimony atom such that in Eqs. (15.51) and (15.61), the sum of the energies of the H 2 -type ellipsoidal MOs is matched to that of the Sb5sp 3  shell as in the case of the corresponding phosphine and arsine molecules. 
         [0377]    The Sb electron configuration is [Kr]5s 2 4d 10 5p 3  corresponding to the ground state  4 S 3/2 , and the 5sp 3  hybridized orbital arrangement after Eq. (13.422) is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       ↑ 
                       ↓ 
                     
                     
                       0 
                       , 
                       0 
                     
                   
                    
                   
                     
                       
                         ↑ 
                         
                           1 
                           , 
                           
                             - 
                             1 
                           
                         
                       
                        
                       
                         ↑ 
                         
                           1 
                           , 
                           0 
                         
                       
                     
                     
                       5 
                        
                       
                         sp 
                         3 
                       
                        
                       
                           
                       
                        
                       state 
                     
                   
                    
                   
                     ↑ 
                     
                       1 
                       , 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   23.272 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where the quantum numbers (l, m l ) are below each electron. The total energy of the state is given by the sum over the five electrons. The sum E T (Sb,5sp 3 ) of experimental energies [1] of Sb, Sb + , Sb 2+ , Sb 3+ , and Sb 4+  is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             T 
                           
                            
                           
                             ( 
                             
                               Sb 
                               , 
                               
                                 5 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             56.0 
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             44.2 
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             25.3 
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             16.63 
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             8.60839 
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           150.73839 
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.273 
                   ) 
                 
               
             
           
         
       
     
         [0000]    By considering that the central field decreases by an integer for each successive electron of the shell, the radius r 5sp     3    of the Sb5sp 3  shell may be calculated from the Coulombic energy using Eq. (15.13): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           
                             5 
                              
                             
                               sp 
                               3 
                             
                           
                         
                         = 
                           
                          
                         
                           
                             ∑ 
                             
                               n 
                               = 
                               46 
                             
                             50 
                           
                            
                           
                             
                               
                                 ( 
                                 
                                   Z 
                                   - 
                                   n 
                                 
                                 ) 
                               
                                
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               
                                 
                                   πɛ 
                                   0 
                                 
                                  
                                 
                                   ( 
                                   
                                     e 
                                      
                                     
                                         
                                     
                                      
                                     150.73839 
                                      
                                     
                                         
                                     
                                      
                                     eV 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             15 
                              
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                                 
                             
                              
                             π 
                              
                             
                                 
                             
                              
                             
                               
                                 ɛ 
                                 0 
                               
                                
                               
                                 ( 
                                 
                                   e 
                                    
                                   
                                       
                                   
                                    
                                   150.73839 
                                    
                                   
                                       
                                   
                                    
                                   eV 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           1.35392 
                            
                           
                             a 
                             0 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.274 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where Z=51 for antimony. Using Eq. (15.14), the Coulombic energy E Coulomb (Sb,5sp 3 ) of the outer electron of the Sb5sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             Coulomb 
                           
                            
                           
                             ( 
                             
                               Sb 
                               , 
                               
                                 5 
                                  
                                 
                                     
                                 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             
                               r 
                               
                                 5 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             1.35392 
                              
                             
                               a 
                               0 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             10.04923 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.275 
                   ) 
                 
               
             
           
         
       
     
         [0000]    During hybridization, the spin-paired 5s electrons are promoted to Sb5sp 3  shell as paired electrons at the radius r 5sp     3    of the Sb5sp 3  shell. The energy for the promotion is the difference in the magnetic energy given by Eq. (15.15) at the initial radius of the 5s electrons and the final radius of the Sb5sp 3  electrons. From Eq. (10.102) with Z=51 and n=48, the radius r 48  of the Sb5s shell is 
         [0000]      r 48 =1.23129a 0    (23.276) 
         [0378]    Using Eqs. (15.15) and (23.276), the unpairing energy is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           E 
                            
                           
                             ( 
                             magnetic 
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               2 
                                
                               π 
                                
                               
                                   
                               
                                
                               
                                 μ 
                                 0 
                               
                                
                               
                                  
                                 2 
                               
                                
                               
                                 ℏ 
                                 2 
                               
                             
                             
                               m 
                               e 
                               2 
                             
                           
                            
                           
                             ( 
                             
                               
                                 1 
                                 
                                   
                                     ( 
                                     
                                       r 
                                       48 
                                     
                                     ) 
                                   
                                   3 
                                 
                               
                               - 
                               
                                 1 
                                 
                                   
                                     ( 
                                     
                                       r 
                                       
                                         5 
                                          
                                         
                                           sp 
                                           3 
                                         
                                       
                                     
                                     ) 
                                   
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           8 
                            
                           π 
                            
                           
                               
                           
                            
                           
                             μ 
                             0 
                           
                            
                           
                             
                               μ 
                               B 
                               2 
                             
                              
                             
                               ( 
                               
                                 
                                   1 
                                   
                                     
                                       ( 
                                       
                                         1.23129 
                                          
                                         
                                           a 
                                           0 
                                         
                                       
                                       ) 
                                     
                                     3 
                                   
                                 
                                 - 
                                 
                                   1 
                                   
                                     
                                       ( 
                                       
                                         1.35392 
                                          
                                         
                                           a 
                                           0 
                                         
                                       
                                       ) 
                                     
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           0.01519 
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.277 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Using Eqs. (23.275) and (23.277), the energy E(Sb,5sp 3 ) of the outer electron of the Sb5sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           E 
                            
                           
                             ( 
                             
                               Sb 
                               , 
                               
                                 5 
                                  
                                 
                                   sp 
                                   
                                     3 
                                      
                                     
                                         
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               - 
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               π 
                                
                               
                                   
                               
                                
                               
                                 ɛ 
                                 0 
                               
                                
                               
                                 r 
                                 
                                   5 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                             
                           
                           + 
                           
                             
                               2 
                                
                               
                                 πμ 
                                 0 
                               
                                
                               
                                  
                                 2 
                               
                                
                               
                                 ℏ 
                                 2 
                               
                             
                             
                               m 
                               e 
                               2 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               10.04923 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             0.01519 
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             10.03404 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.278 
                   ) 
                 
               
             
           
         
       
     
         [0000]    For the Sb—C functional group, hybridization of the 2s and 2p AOs of each C and the 5s and 5p AOs of each Sb to form single 2sp 3  and 5sp 3  shells, respectively, forms an energy minimum, and the sharing of electrons between the C2sp 3  and Sb5sp 3  HOs to form a MO permits each participating orbital to decrease in radius and energy. In branched-chain alkyl stibines, the energy of antimony is less than the Coulombic energy between the electron and proton of H given by Eq. (1.231). Thus, c 2  in Eq. (15.61) is one, and the energy matching condition is determined by the C 2  parameter. Then, the C2sp 3  HO has an energy of E(C,2sp 3 )=−14.63489 eV (Eq. (15.25)), and the Sb5sp 3  HO has an energy of E(Sb,5sp 3 )=−10.03404 eV (Eq. (23.278)). To meet the equipotential condition of the union of the Sb—C H 2 -type-ellipsoidal-MO with these orbitals, the hybridization factor C 2  of Eq. (15.61) for the Sb—C-bond MO given by Eqs. (15.77), (15.79), and (13.430) is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             C 
                             2 
                           
                            
                           
                             ( 
                             
                               C 
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                                
                               
                                   
                               
                                
                               to 
                                
                               
                                   
                               
                                
                               Sb 
                                
                               
                                   
                               
                                
                               5 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               E 
                                
                               
                                 ( 
                                 
                                   Sb 
                                   , 
                                   
                                     5 
                                      
                                     
                                       sp 
                                       3 
                                     
                                   
                                 
                                 ) 
                               
                             
                             
                               E 
                                
                               
                                 ( 
                                 
                                   C 
                                   , 
                                   
                                     2 
                                      
                                     
                                       sp 
                                       3 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                            
                           
                             
                               c 
                               2 
                             
                              
                             
                               ( 
                               
                                 C 
                                  
                                 
                                     
                                 
                                  
                                 2 
                                  
                                 
                                   sp 
                                   3 
                                 
                                  
                                 HO 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               
                                 - 
                                 10.03404 
                               
                                
                               
                                   
                               
                                
                               eV 
                             
                             
                               
                                 - 
                                 14.63489 
                               
                                
                               
                                   
                               
                                
                               eV 
                             
                           
                            
                           
                             ( 
                             0.91771 
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         0.62921 
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.279 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The energy of the Sb—C-bond MO is the sum of the component energies of the H 2 -type ellipsoidal MO given in Eq. (15.51) with E(AO/HO=E(Sb,5sp 3 ) given by Eq. (23.278), and E T (atom-atom, msp 3 .AO) is zero in order to match the energies of the carbon and antimony HOs. 
         [0379]    The symbols of the functional groups of branched-chain alkyl stibines are given in Table 166. The geometrical (Eqs. (15.1-15.5) and (15.51)), intercept (Eqs. (15.80-15.87)), and energy (Eqs. (15.6-15.11) and (15.17-15.65)) parameters of alkyl stibines are given in Tables 167, 168, and 169, respectively. The total energy of each alkyl stibine given in Table 170 was calculated as the sum over the integer multiple of each E D (Group) of Table 169 corresponding to functional-group composition of the molecule. The bond angle parameters of alkyl stibines determined using Eqs. (15.88-15.117) are given in Table 171. The color scale, charge-density of exemplary alkyl stibine, triphenylstibine, comprising atoms with the outer shell bridged by one or more H 2 -type ellipsoidal MOs or joined with one or more hydrogen MOs is shown in  FIG. 73 . 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 166 
               
             
             
               
                   
               
               
                 The symbols of functional groups of alkyl stibines. 
               
             
          
           
               
                   
                 Functional Group 
                 Group Symbol 
               
               
                   
                   
               
               
                   
                 Sb—C 
                 Sb—C 
               
               
                   
                 CH 3  group 
                 C—H (CH 3 ) 
               
               
                   
                 CH 2  group 
                 C—H (CH 2 ) 
               
               
                   
                 CH 
                 C—H (i) 
               
               
                   
                 CC bond (n-C) 
                 C—C (a) 
               
               
                   
                 CC bond (iso-C) 
                 C—C (b) 
               
               
                   
                 CC bond (tert-C) 
                 C—C (c) 
               
               
                   
                 CC (iso to iso-C) 
                 C—C (d) 
               
               
                   
                 CC (t to t-C) 
                 C—C (e) 
               
               
                   
                 CC (t to iso-C) 
                 C—C (f) 
               
               
                   
                 CC (aromatic bond) 
                 C 3e ═C 
               
               
                   
                 CH (aromatic) 
                 CH (ii) 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 167 
               
               
                   
               
               
                 The geometrical bond parameters of alkyl stibines and experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Sb—C 
                 C—H (CH 3 ) 
                 C—H (CH 2 ) 
                 C—H (i) 
                 C—C (a) 
                 C—C (b) 
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 2.38997 
                 1.64920 
                 1.67122 
                 1.67465 
                 2.12499 
                 2.12499 
               
               
                 c′ (a 0 ) 
                 1.94894 
                 1.04856 
                 1.05553 
                 1.05661 
                 1.45744 
                 1.45744 
               
               
                 Bond Length 
                 2.06267 
                 1.10974 
                 1.11713 
                 1.11827 
                 1.54280 
                 1.54280 
               
               
                 2c′ (Å) 
               
               
                 Exp. Bond 
                   
                 1.107 
                 1.107 
                 1.122 
                 1.532 
                 1.532 
               
               
                 Length 
                   
                 (C—H propane) 
                 (C—H propane) 
                 (isobutane) 
                 (propane) 
                 (propane) 
               
               
                 (Å) 
                   
                 1.117 
                 1.117 
                   
                 1.531 
                 1.531 
               
               
                   
                   
                 (C—H butane) 
                 (C—H butane) 
                   
                 (butane) 
                 (butane) 
               
               
                 b, c (a 0 ) 
                 1.38332 
                 1.27295 
                 1.29569 
                 1.29924 
                 1.54616 
                 1.54616 
               
               
                 e 
                 0.81547 
                 0.63580 
                 0.63159 
                 0.63095 
                 0.68600 
                 0.68600 
               
               
                   
               
             
          
           
               
                   
                 C—C (c) 
                 C—C (d) 
                 C—C (e) 
                 C—C (f) 
                 C 3e ═C 
                 CH (ii) 
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 2.10725 
                 2.12499 
                 2.10725 
                 2.10725 
                 1.47348 
                 1.60061 
               
               
                 c′ (a 0 ) 
                 1.45164 
                 1.45744 
                 1.45164 
                 1.45164 
                 1.31468 
                 1.03299 
               
               
                 Bond Length 
                 1.53635 
                 1.54280 
                 1.53635 
                 1.53635 
                 1.39140 
                 1.09327 
               
               
                 2c′ (Å) 
               
               
                 Exp. Bond 
                 1.532 
                 1.532 
                 1.532 
                 1.532 
                 1.399 
                 1.101 
               
               
                 Length 
                 (propane) 
                 (propane) 
                 (propane) 
                 (propane) 
                 (benzene) 
                 (benzene) 
               
               
                 (Å) 
                 1.531 
                 1.531 
                 1.531 
                 1.531 
               
               
                   
                 (butane) 
                 (butane) 
                 (butane) 
                 (butane) 
               
               
                 b, c (a 0 ) 
                 1.52750 
                 1.54616 
                 1.52750 
                 1.52750 
                 0.66540 
                 1.22265 
               
               
                 e 
                 0.68888 
                 0.68600 
                 0.68888 
                 0.68888 
                 0.89223 
                 0.64537 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 168 
               
               
                   
               
               
                 The MO to HO intercept geometrical bond parameters of alkyl stibines. R, R′, R″ are H or alkyl groups. 
               
               
                 E T  is E T  (atom-atom, msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                 E T   
                 E T   
                 E T   
                 E T   
                 Final Total Energy 
                   
                   
               
               
                   
                   
                 (eV) 
                 (eV) 
                 (eV) 
                 (eV) 
                 C2sp 3   
                 r initial   
                 r final   
               
               
                 Bond 
                 Atom 
                 Bond 1 
                 Bond 2 
                 Bond 3 
                 Bond 4 
                 (eV) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 C—H(CH 3 ) 
                 C 
                 0 
                 0 
                 0 
                 0 
                 −151.61569 
                 0.91771 
                 0.91771 
               
               
                 (CH 3 ) 2 Sb—CH 3   
                 C 
                 0 
                 0 
                 0 
                 0 
                   
                 0.91771 
                 0.91771 
               
               
                 (CH 3 ) 2 Sb—CH 3   
                 Sb 
                 0 
                 0 
                 0 
                 0 
                   
                 1.35392 
                 0.91771 
               
               
                 C—H(CH 3 ) 
                 C 
                 −0.92918 
                 0 
                 0 
                 0 
                 −152.54487 
                 0.91771 
                 0.86359 
               
               
                 C—H(CH 2 ) 
                 C 
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                 −153.47406 
                 0.91771 
                 0.81549 
               
               
                 C—H(CH) 
                 C 
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 C a   
                 −0.92918 
                 0 
                 0 
                 0 
                 −152.54487 
                 0.91771 
                 0.86359 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                 −153.47406 
                 0.91771 
                 0.81549 
               
               
                 R—H 2 C a C b (H 2 C c —R′)HCH 2 —(C—C (b)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 R—H 2 C a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (c)) 
                 C b   
                 −0.92918 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.71860 
                 0.91771 
                 0.75889 
               
               
                 isoC a C b (H 2 C c —R′)HCH 2 —(C—C (d)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 tertC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (e)) 
                 C b   
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.51399 
                 0.91771 
                 0.76765 
               
               
                 tertC a C b (H 2 C c —R′)HCH 2 —(C—C (f)) 
                 C b   
                 −0.72457 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.19863 
                 0.91771 
                 0.78155 
               
               
                 isoC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (f)) 
                 C b   
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.51399 
                 0.91771 
                 0.76765 
               
               
                   
               
             
          
           
               
                   
                 E Coulomb  (eV) 
                 E (C2sp 3 ) (eV) 
                 θ′ 
                 θ 1   
                 θ 2   
                 d 1   
                 d 2   
               
               
                 Bond 
                 Final 
                 Final 
                 (°) 
                 (°) 
                 (°) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 C—H(CH 3 ) 
                 −14.82575 
                 −14.63489 
                 83.62 
                 96.38 
                 45.76 
                 1.15051 
                 0.10195 
               
               
                 (CH 3 ) 2 Sb—CH 3   
                 −14.82575 
                 −14.63489 
                 99.00 
                 81.00 
                 40.94 
                 1.80541 
                 0.14353 
               
               
                 (CH 3 ) 2 Sb—CH 3   
                 −14.82575 
                   
                 99.00 
                 81.00 
                 40.94 
                 1.80541 
                 0.14353 
               
               
                 C—H(CH 3 ) 
                 −15.75493 
                 −15.56407 
                 77.49 
                 102.51 
                 41.48 
                 1.23564 
                 0.18708 
               
               
                 C—H(CH 2 ) 
                 −16.68412 
                 −16.49325 
                 68.47 
                 111.53 
                 35.84 
                 1.35486 
                 0.29933 
               
               
                 C—H(CH) 
                 −17.61330 
                 −17.42244 
                 61.10 
                 118.90 
                 31.37 
                 1.42988 
                 0.37326 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 −15.75493 
                 −15.56407 
                 63.82 
                 116.18 
                 30.08 
                 1.83879 
                 0.38106 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 −16.68412 
                 −16.49325 
                 56.41 
                 123.59 
                 26.06 
                 1.90890 
                 0.45117 
               
               
                 R—H 2 C a C b (H 2 C c —R′)HCH 2 —(C—C (b)) 
                 −17.61330 
                 −17.42244 
                 48.30 
                 131.70 
                 21.90 
                 1.97162 
                 0.51388 
               
               
                 R—H 2 C a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 (C—C (c)) 
                 −17.92866 
                 −17.73779 
                 48.21 
                 131.79 
                 21.74 
                 1.95734 
                 0.50570 
               
               
                 isoC a C b (H 2 C c —R′)HCH 2 —(C—C (d)) 
                 −17.61330 
                 −17.42244 
                 48.30 
                 131.70 
                 21.90 
                 1.97162 
                 0.51388 
               
               
                 tertC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (e)) 
                 −17.92866 
                 −17.73779 
                 50.04 
                 129.96 
                 22.66 
                 1.94462 
                 0.49298 
               
               
                 tertC a C b (H 2 C c —R′)HCH 2 —(C—C (f)) 
                 −17.40869 
                 −17.21783 
                 52.78 
                 127.22 
                 24.04 
                 1.92443 
                 0.47279 
               
               
                 isoC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (f)) 
                 −17.92866 
                 −17.73779 
                 50.04 
                 129.96 
                 22.66 
                 1.94462 
                 0.49298 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 169 
               
               
                   
               
               
                 The energy parameters (eV) of functional groups of alkyl stibines. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Sb—C 
                 CH 3   
                 CH 2   
                 CH (i) 
                 C—C (a) 
                 C—C (b) 
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 f 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 n 1   
                 1 
                 3 
                 2 
                 1 
                 1 
                 1 
               
               
                 n 2   
                 0 
                 2 
                 1 
                 0 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.5 
                 0.75 
                 0.75 
                 0.75 
                 0.5 
                 0.5 
               
               
                 C 2   
                 0.62921 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 2   
                 1 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
               
               
                 c 3   
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
               
               
                 c 4   
                 2 
                 1 
                 1 
                 1 
                 2 
                 2 
               
               
                 c 5   
                 0 
                 3 
                 2 
                 1 
                 0 
                 0 
               
               
                 C 1o   
                 0.5 
                 0.75 
                 0.75 
                 0.75 
                 0.5 
                 0.5 
               
               
                 C 2o   
                 0.62921 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 V e  (eV) 
                 −31.92151 
                 −107.32728 
                 −70.41425 
                 −35.12015 
                 −28.79214 
                 −28.79214 
               
               
                 V p  (eV) 
                 6.98112 
                 38.92728 
                 25.78002 
                 12.87680 
                 9.33352 
                 9.33352 
               
               
                 T (eV) 
                 6.67822 
                 32.53914 
                 21.06675 
                 10.48582 
                 6.77464 
                 6.77464 
               
               
                 V m  (eV) 
                 −3.33911 
                 −16.26957 
                 −10.53337 
                 −5.24291 
                 −3.38732 
                 −3.38732 
               
               
                 E (AO/HO) (eV) 
                 −10.03404 
                 −15.56407 
                 −15.56407 
                 −14.63489 
                 −15.56407 
                 −15.56407 
               
               
                 ΔE H     2     MO  (AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 E T  (AO/HO) (eV) 
                 −10.03404 
                 −15.56407 
                 −15.56407 
                 −14.63489 
                 −15.56407 
                 −15.56407 
               
               
                 E T  (H 2 MO) (eV) 
                 −31.63532 
                 −67.69451 
                 −49.66493 
                 −31.63533 
                 −31.63537 
                 −31.63537 
               
               
                 E T  (atom-atom, msp 3 .AO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 −1.85836 
                 −1.85836 
               
               
                 E T  (MO) (eV) 
                 −31.63537 
                 −67.69450 
                 −49.66493 
                 −31.63537 
                 −33.49373 
                 −33.49373 
               
               
                 ω (10 15  rad/s) 
                 6.27593 
                 24.9286 
                 24.2751 
                 24.1759 
                 9.43699 
                 9.43699 
               
               
                 E K  (eV) 
                 4.13093 
                 16.40846 
                 15.97831 
                 15.91299 
                 6.21159 
                 6.21159 
               
               
                 Ē D  (eV) 
                 −0.12720 
                 −0.25352 
                 −0.25017 
                 −0.24966 
                 −0.16515 
                 −0.16515 
               
               
                 Ē Kvib  (eV) 
                 0.14878 [66] 
                 0.35532 
                 0.35532 
                 0.35532 
                 0.12312 [6] 
                 0.17978 [7] 
               
               
                   
                   
                 (Eq. (13.458)) 
                 (Eq. (13.458)) 
                 (Eq. (13.458)) 
               
               
                 Ē osc  (eV) 
                 −0.05281 
                 −0.22757 
                 −0.14502 
                 −0.07200 
                 −0.10359 
                 −0.07526 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                 E T  (Group) (eV) 
                 −31.68818 
                 −67.92207 
                 −49.80996 
                 −31.70737 
                 −33.59732 
                 −33.49373 
               
               
                 E initial  (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
               
               
                 E initial  (c 5  AO/HO) (eV) 
                 0 
                 −13.59844 
                 −13.59844 
                 −13.59844 
                 0 
                 0 
               
               
                 E D  (Group) (eV) 
                 2.41840 
                 12.49186 
                 7.83016 
                 3.32601 
                 4.32754 
                 4.29921 
               
               
                   
               
               
                   
                 C—C (c) 
                 C—C (d) 
                 C—C (e) 
                 C—C (f) 
                 C 3e ═C 
                 CH (ii) 
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 f 1   
                 1 
                 1 
                 1 
                 1 
                 0.75 
                 1 
               
               
                 n 1   
                 1 
                 1 
                 1 
                 1 
                 2 
                 1 
               
               
                 n 2   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.75 
               
               
                 C 2   
                 1 
                 1 
                 1 
                 1 
                 0.85252 
                 1 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 2   
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.85252 
                 0.91771 
               
               
                 c 3   
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
               
               
                 c 4   
                 2 
                 2 
                 2 
                 2 
                 3 
                 1 
               
               
                 c 5   
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
               
               
                 C 10   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.75 
               
               
                 C 20   
                 1 
                 1 
                 1 
                 1 
                 0.85252 
                 1 
               
               
                 V e  (eV) 
                 −29.10112 
                 −28.79214 
                 −29.10112 
                 −29.10112 
                 −101.12679 
                 −37.10024 
               
               
                 V p  (eV) 
                 9.37273 
                 9.33352 
                 9.37273 
                 9.37273 
                 20.69825 
                 13.17125 
               
               
                 T (eV) 
                 6.90500 
                 6.77464 
                 6.90500 
                 6.90500 
                 34.31559 
                 11.58941 
               
               
                 V m  (eV) 
                 −3.45250 
                 −3.38732 
                 −3.45250 
                 −3.45250 
                 −17.15779 
                 −5.79470 
               
               
                 E (AO/HO) (eV) 
                 −15.35946 
                 −15.56407 
                 −15.35946 
                 −15.35946 
                 0 
                 −14.63489 
               
               
                 ΔE H     2     MO  (AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 −1.13379 
               
               
                 E T  (AO/HO) (eV) 
                 −15.35946 
                 −15.56407 
                 −15.35946 
                 −15.35946 
                 0 
                 −13.50110 
               
               
                 E T  (H 2 MO) (eV) 
                 −31.63535 
                 −31.63537 
                 −31.63535 
                 −31.63535 
                 −63.27075 
                 −31.63539 
               
               
                 E T  (atom-atom, msp 3 .AO) (eV) 
                 −1.44915 
                 −1.85836 
                 −1.44915 
                 −1.44915 
                 −2.26759 
                 −0.56690 
               
               
                 E T  (MO) (eV) 
                 −33.08452 
                 −33.49373 
                 −33.08452 
                 −33.08452 
                 −65.53833 
                 −32.20226 
               
               
                 ω (10 15  rad/s) 
                 15.4846 
                 9.43699 
                 9.55643 
                 9.55643 
                 49.7272 
                 26.4826 
               
               
                 E K  (eV) 
                 10.19220 
                 6.21159 
                 6.29021 
                 6.29021 
                 32.73133 
                 17.43132 
               
               
                 Ē D  (eV) 
                 −0.20896 
                 −0.16515 
                 −0.16416 
                 −0.16416 
                 −0.35806 
                 −0.26130 
               
               
                 Ē Kvib  (eV) 
                 0.09944 [8] 
                 0.12312 [6] 
                 0.12312 [6] 
                 0.12312 [6] 
                 0.19649 [30] 
                 0.35532 
               
               
                   
                   
                   
                   
                   
                   
                 Eq. (13.458) 
               
               
                 Ē osc  (eV) 
                 −0.15924 
                 −0.10359 
                 −0.10260 
                 −0.10260 
                 −0.25982 
                 −0.08364 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                 E T  (Group) (eV) 
                 −33.24376 
                 −33.59732 
                 −33.18712 
                 −33.18712 
                 −49.54347 
                 −32.28590 
               
               
                 E initial  (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
               
               
                 E initial  (c 5  AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 −13.59844 
               
               
                 E D  (Group) (eV) 
                 3.97398 
                 4.17951 
                 3.62128 
                 3.91734 
                 5.63881 
                 3.90454 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 170 
               
               
                   
               
               
                 The total bond energies of alkyl stibines calculated using the functional group composition 
               
               
                 and the energies of Table 169 compared to the experimental values [88]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 C—C 
                 C—C 
                 C—C 
                   
               
               
                 Formula 
                 Name 
                 Sb—C 
                 CH 3   
                 CH 2   
                 CH (i) 
                 (a) 
                 (b) 
                 (c) 
                 C—C (d) 
               
               
                   
               
               
                 C 3 H 9 Sb 
                 Trimethylstibine 
                 3 
                 3 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 6 H 15 Sb 
                 Triethylstibine 
                 3 
                 3 
                 3 
                 0 
                 3 
                 0 
                 0 
                 0 
               
               
                 C 18 H 15 Sb 
                 Triphenylstibine 
                 3 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 C—C 
                 C—C 
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 (e) 
                 (f) 
                 C 3e ═C 
                 CH (ii) 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 C 3 H 9 Sb 
                 Trimethylstibine 
                 0 
                 0 
                 0 
                 0 
                 44.73078 
                 45.02378 
                 0.00651 
               
               
                 C 6 H 15 Sb 
                 Triethylstibine 
                 0 
                 0 
                 0 
                 0 
                 81.20388 
                 80.69402 
                 −0.00632 
               
               
                 C 18 H 15 Sb 
                 Triphenylstibine 
                 0 
                 0 
                 18 
                 15 
                 167.32181 
                 165.81583 
                 −0.00908 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 171 
               
               
                   
               
               
                 The bond angle parameters of alkyl stibines and experimental values [3]. In the calculation of θ v , the parameters from 
               
               
                 the preceding angle were used. E T  is E T  (atom-atom, msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                 2c′ 
                   
                 Atom 1 
                   
                 Atom 2 
                   
                   
                   
               
               
                   
                 2c′ 
                 2c′ 
                 Terminal 
                 E Coulombic   
                 Hybridization 
                   
                 Hybridization 
               
               
                 Atoms 
                 Bond 1 
                 Bond 2 
                 Atoms 
                 or E 
                 Designation 
                 E Coulombic   
                 Designation 
                 c 2   
                 c 2   
               
               
                 of Angle 
                 (a 0 ) 
                 (a 0 ) 
                 (a 0 ) 
                 Atom 1 
                 (Table 7) 
                 Atom 2 
                 (Table 7) 
                 Atom 1 
                 Atom 2 
               
               
                   
               
               
                 Methyl 
                 2.09711 
                 2.09711 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
                 1 
               
               
                 ∠HC a H 
               
               
                 ∠H a C a Sb 
               
               
                 ∠C a SbC b   
                 3.89789 
                 3.89789 
                 5.7446 
                 −15.55033 
                 5 
                 −15.55033 
                 5 
                 0.87495 
                 0.87495 
               
               
                 Methylene 
                 2.11106 
                 2.11106 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
                 1 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
               
               
                 ∠C a C b H 
               
               
                 Methyl 
                 2.09711 
                 2.09711 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
                 1 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
               
               
                 ∠C a C b H 
               
               
                 ∠C b C a C c   
                 2.91547 
                 2.91547 
                 4.7958 
                 −16.68412 
                 26 
                 −16.68412 
                 26 
                 0.81549 
                 0.81549 
               
               
                 iso C a   
                   
                   
                   
                 C b   
                   
                 C c   
               
               
                 ∠C b C a H 
                 2.91547 
                 2.11323 
                 4.1633 
                 −15.55033 
                 5 
                 −14.82575 
                 1 
                 0.87495 
                 0.91771 
               
               
                 iso C a   
                   
                   
                   
                 C a   
                   
                 C b   
               
               
                 ∠C a C b H 
                 2.91547 
                 2.09711 
                 4.1633 
                 −15.55033 
                 5 
                 −14.82575 
                 1 
                 0.87495 
                 0.91771 
               
               
                 iso C a   
                   
                   
                   
                 C b   
                   
                 C a   
               
               
                 ∠C b C a C b   
                 2.90327 
                 2.90327 
                 4.7958 
                 −16.68412 
                 26 
                 −16.68412 
                 26 
                 0.81549 
                 0.81549 
               
               
                 tert C a   
                   
                   
                   
                 C b   
                   
                 C b   
               
               
                 ∠C b C a C d   
               
               
                   
               
             
          
           
               
                 Atoms of 
                   
                   
                   
                   
                 E T   
                 θ v   
                 θ 1   
                 θ 2   
                 Cal. θ 
                 Exp. θ 
               
               
                 Angle 
                 C 1   
                 C 2   
                 c 1   
                 c 2 ′ 
                 (eV) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
               
               
                   
               
               
                 Methyl 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 109.50 
               
               
                 ∠HC a H 
               
               
                 ∠H a C a Sb 
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                 ∠C a SbC b   
                 1 
                 1 
                 1 
                 0.87495 
                 −1.85836 
                   
                   
                   
                 94.93 
                  94.2 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (trimethylstibine) 
               
               
                 Methylene 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 108.44 
                 107 
               
               
                 ∠HC a H 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (propane) 
               
               
                 ∠C a C b C c   
                   
                   
                   
                   
                   
                 69.51 
                   
                   
                 110.49 
                 112 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (propane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 113.8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (butane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 110.8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C a C b H 
                   
                   
                   
                   
                   
                 69.51 
                   
                   
                 110.49 
                 111.0 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (butane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 111.4 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 Methyl 
                 1 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 109.50 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                 ∠C a C b H 
                   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                 ∠C b C a C c   
                 1 
                 1 
                 1 
                 0.81549 
                 −1.85836 
                   
                   
                   
                 110.67 
                 110.8 
               
               
                 iso C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C b C a H 
                 0.75 
                 1 
                 0.75 
                 1.04887 
                 0 
                   
                   
                   
                 110.76 
               
               
                 iso C a   
               
               
                 ∠C a C b H 
                 0.75 
                 1 
                 0.75 
                 1.04887 
                 0 
                   
                   
                   
                 111.27 
                 111.4 
               
               
                 iso C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C b C a C b   
                 1 
                 1 
                 1 
                 0.81549 
                 −1.85836 
                   
                   
                   
                 111.37 
                 110.8 
               
               
                 tert C a   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                 ∠C b C a C d   
                   
                   
                   
                   
                   
                 72.50 
                   
                   
                 107.50 
               
               
                   
               
             
          
         
       
     
         [0380]    Alkyl Bismuths ((C n H 2n+1 ) 3 Bi, n=1,2,3,4,5 . . . ∞) 
         [0381]    The alkyl bismuths, (C n H 2n+1 ) 3 Bi, comprise a Bi—C functional group. The alkyl portion of the alkyl bismuth may comprise at least two terminal methyl groups (CH 3 ) at each end of each chain, and may comprise methylene (CH 2 ), and methylyne (CH) functional groups as well as C bound by carbon-carbon single bonds. The methyl and methylene functional groups are equivalent to those of straight-chain alkanes. Six types of C—C bonds can be identified. The n-alkane C—C bond is the same as that of straight-chain alkanes. In addition, the C—C bonds within isopropyl ((CH 3 ) 2 CH) and t-butyl ((CH 3 ) 3 C) groups and the isopropyl to isopropyl, isopropyl to t-butyl, and t-butyl to t-butyl C—C bonds comprise functional groups. The branched-chain-alkane groups in alkyl bismuths are equivalent to those in branched-chain alkanes. The Bi—C group may further join the Bi6sp 3  HO to an aryl HO. 
         [0382]    As in the case of phosphorous, arsenic, and antimony, the bonding in the bismuth atom involves sp 3  hybridized orbitals formed, in this case, from the 6p and 6s electrons of the outer shells. The Bi—C bond forms between Bi6sp 3  and C2sp 3  HOs to yield bismuths. The semimajor axis a of the Bi—C functional group is solved using Eq. (15.51). Using the semimajor axis and the relationships between the prolate spheroidal axes, the geometric and energy parameters of the MO are calculated using Eqs. (15.1-15.117) in the same manner as the organic functional groups given in Organic Molecular Functional Groups and Molecules section. 
         [0383]    The energy of bismuth is less than the Coulombic energy between the electron and proton of H given by Eq. (1.231). A minimum energy is achieved while matching the potential, kinetic, and orbital energy relationships given in the Hydroxyl Radical (OH) section with hybridization of the bismuth atom such that in Eqs. (15.51) and (15.61), the sum of the energies of the H 2 -type ellipsoidal MOs is matched to that of the Bi6sp 3  shell as in the case of the corresponding phosphines, arsines, and stibines. 
         [0384]    The Bi electron configuration is [Xe]6s 2 4f 14 5d 10 6p 3  corresponding to the ground state  4 S 3/2 , and the 6sp 3  hybridized orbital arrangement after Eq. (13.422) is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       ↑ 
                       ↓ 
                     
                     
                       0 
                       , 
                       0 
                     
                   
                    
                   
                     
                       
                         ↑ 
                         
                           1 
                           , 
                           
                             - 
                             1 
                           
                         
                       
                        
                       
                         ↑ 
                         
                           1 
                           , 
                           0 
                         
                       
                     
                     
                       6 
                        
                       
                         sp 
                         3 
                       
                        
                       
                           
                       
                        
                       state 
                     
                   
                    
                   
                     ↑ 
                     
                       1 
                       , 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   23.280 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where the quantum numbers (l, m l ) are below each electron. The total energy of the state is given by the sum over the five electrons. The sum E T (Bi,6sp 3 ) of experimental energies [1] of Bi, Bi + , Bi 2+ , Bi 3+ , and Bi 4+  is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             T 
                           
                            
                           
                             ( 
                             
                               Bi 
                               , 
                               
                                 6 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             56.0 
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             45.3 
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             25.56 
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             16.703 
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             7.2855 
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           150.84850 
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.281 
                   ) 
                 
               
             
           
         
       
     
         [0000]    By considering that the central field decreases by an integer for each successive electron of the shell, the radius r 6sp     3    of the Bi6sp 3  shell may be calculated from the Coulombic energy using Eq. (15.13): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           
                             6 
                              
                             
                               sp 
                               3 
                             
                           
                         
                         = 
                           
                          
                         
                           
                             ∑ 
                             
                               n 
                               = 
                               78 
                             
                             82 
                           
                            
                           
                             
                               
                                 ( 
                                 
                                   Z 
                                   - 
                                   n 
                                 
                                 ) 
                               
                                
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               
                                 
                                   πɛ 
                                   0 
                                 
                                  
                                 
                                   ( 
                                   
                                     e 
                                      
                                     
                                         
                                     
                                      
                                     150.84850 
                                      
                                     
                                         
                                     
                                      
                                     eV 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             15 
                              
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 ( 
                                 
                                   e 
                                    
                                   
                                       
                                   
                                    
                                   150.84850 
                                    
                                   
                                       
                                   
                                    
                                   eV 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           1.35293 
                            
                           
                             a 
                             0 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.282 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where Z=83 for bismuth. Using Eq. (15.14), the Coulombic energy E Coulomb (Bi,6sp 3 ) of the outer electron of the Bi6sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             Coulomb 
                           
                            
                           
                             ( 
                             
                               Bi 
                               , 
                               
                                 6 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             
                               r 
                               
                                 6 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             1.35293 
                              
                             
                               a 
                               0 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             10.05657 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.283 
                   ) 
                 
               
             
           
         
       
     
         [0000]    During hybridization, the spin-paired 6s electrons are promoted to Bi6sp 3  shell as paired electrons at the radius r 6sp     3    of the Bi6sp 3  shell. The energy for the promotion is the difference in the magnetic energy given by Eq. (15.15) at the initial radius of the 6s electrons and the final radius of the Bi6sp 3  electrons. From Eq. (10.102) with Z=83 and n=80, the radius r 80  of the Bi6s shell is 
         [0000]      r 80 =1.20140a 0    (23.284) 
         [0000]    Using Eqs. (15.15) and (23.284), the unpairing energy is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           E 
                            
                           
                             ( 
                             magnetic 
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               2 
                                
                               
                                 πμ 
                                 0 
                               
                                
                               
                                  
                                 2 
                               
                                
                               
                                 ℏ 
                                 2 
                               
                             
                             
                               m 
                               e 
                               2 
                             
                           
                            
                           
                             ( 
                             
                               
                                 1 
                                 
                                   
                                     ( 
                                     
                                       r 
                                       80 
                                     
                                     ) 
                                   
                                   3 
                                 
                               
                               - 
                               
                                 1 
                                 
                                   
                                     ( 
                                     
                                       r 
                                       
                                         6 
                                          
                                         
                                           sp 
                                           3 
                                         
                                       
                                     
                                     ) 
                                   
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           8 
                            
                           
                             πμ 
                             o 
                           
                            
                           
                             
                               μ 
                               B 
                               2 
                             
                              
                             
                               ( 
                               
                                 
                                   1 
                                   
                                     
                                       ( 
                                       
                                         1.20140 
                                          
                                         
                                           a 
                                           0 
                                         
                                       
                                       ) 
                                     
                                     3 
                                   
                                 
                                 - 
                                 
                                   1 
                                   
                                     
                                       ( 
                                       
                                         1.35293 
                                          
                                         
                                           a 
                                           0 
                                         
                                       
                                       ) 
                                     
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           0.01978 
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.285 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Using Eqs. (23.283) and (23.285), the energy E(Bi,6sp 3 ) of the outer electron of the Bi6sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           E 
                            
                           
                             ( 
                             
                               Bi 
                               , 
                               
                                 6 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               - 
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 r 
                                 
                                   6 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                             
                           
                           + 
                           
                             
                               
                                 2 
                                  
                                 
                                   πμ 
                                   0 
                                 
                                  
                                 
                                    
                                   2 
                                 
                                  
                                 
                                   ℏ 
                                   2 
                                 
                               
                               
                                 m 
                                 e 
                                 2 
                               
                             
                              
                             
                               ( 
                               
                                 
                                   1 
                                   
                                     
                                       ( 
                                       
                                         r 
                                         80 
                                       
                                       ) 
                                     
                                     3 
                                   
                                 
                                 - 
                                 
                                   1 
                                   
                                     
                                       ( 
                                       
                                         r 
                                         
                                           6 
                                            
                                           
                                             sp 
                                             3 
                                           
                                         
                                       
                                       ) 
                                     
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               10.05657 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             0.01978 
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             10.03679 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.286 
                   ) 
                 
               
             
           
         
       
     
         [0385]    Next, consider the formation of the Bi-L-bond MO of bismuth compounds wherein L is a very stable ligand and each bismuth atom has a Bi6sp 3  electron with an energy given by Eq. (23.286). The total energy of the state of each bismuth atom is given by the sum over the five electrons. The sum E T (Pb Pb-L ,6sp 3 ) of energies of Bi6sp 3  (Eq. (23.286)), Bi + , Bi 2+ , Bi 3+ , and Bi 4+  is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             T 
                           
                            
                           
                             ( 
                             
                               
                                 Bi 
                                 
                                   Bi 
                                   - 
                                   L 
                                 
                               
                               , 
                               
                                 6 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           - 
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       56.0 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       45.3 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       25.56 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       16.703 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       E 
                                        
                                       
                                         ( 
                                         
                                           Bi 
                                           , 
                                           
                                             6 
                                              
                                             
                                               sp 
                                               3 
                                             
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           - 
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       56.0 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       45.3 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       25.56 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       16.703 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       10.03679 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             153.59979 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.287 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where E (Bi,6sp 3 ) is the sum of the energy of Bi, −7.2855 eV, and the hybridization energy. 
         [0386]    A minimum energy is achieved while matching the potential, kinetic, and orbital energy relationships given in the Hydroxyl Radical (OH) section with the donation of electron density from the participating Bi6sp 3  HO to each Bi-L-bond MO. Consider the case wherein each Bi6sp 3  HO donates an excess of 25% of its electron density to the Pb-L-bond MO to form an energy minimum. By considering this electron redistribution in the bismuth molecule as well as the fact that the central field decreases by an integer for each successive electron of the shell, in general terms, the radius r Bi-Lsp     3    of the Bi6sp 3  shell may be calculated from the Coulombic energy using Eq. (15.18): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           
                             Bi 
                             - 
                             
                               L 
                                
                               
                                   
                               
                                
                               6 
                                
                               
                                 sp 
                                 3 
                               
                             
                           
                         
                         = 
                           
                          
                         
                           
                             ( 
                             
                               
                                 
                                   ∑ 
                                   
                                     n 
                                     = 
                                     78 
                                   
                                   82 
                                 
                                  
                                 
                                   ( 
                                   
                                     Z 
                                     - 
                                     n 
                                   
                                   ) 
                                 
                               
                               - 
                               0.25 
                             
                             ) 
                           
                            
                           
                             
                                
                               2 
                             
                             
                               8 
                                
                               
                                 
                                   πɛ 
                                   0 
                                 
                                  
                                 
                                   ( 
                                   
                                     e 
                                      
                                     
                                         
                                     
                                      
                                     153.59979 
                                      
                                     
                                         
                                     
                                      
                                     eV 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             14.75 
                              
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 ( 
                                 
                                   e 
                                    
                                   
                                       
                                   
                                    
                                   153.59979 
                                    
                                   
                                       
                                   
                                    
                                   eV 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           1.30655 
                            
                           
                             a 
                             0 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.288 
                   ) 
                 
               
             
           
         
       
     
         [0387]    Using Eqs. (15.19) and (23.288), the Coulombic energy E Coulomb (Bi Bi-L ,6sp 3 ) of the outer electron of the Bi6sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             Coulomb 
                           
                            
                           
                             ( 
                             
                               
                                 Bi 
                                 
                                   Bi 
                                   - 
                                   L 
                                 
                               
                               , 
                               
                                 6 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             
                               r 
                               
                                 Bi 
                                 - 
                                 
                                   L 
                                    
                                   
                                       
                                   
                                    
                                   6 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             1.30655 
                              
                             
                               a 
                               0 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             10.41354 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.289 
                   ) 
                 
               
             
           
         
       
     
         [0000]    During hybridization, the spin-paired 6s electrons are promoted to Bi6sp 3  shell as paired electrons at the radius r 6sp     3    of the Bi6sp 3  shell. The energy for the promotion is the difference in the magnetic energy given by Eq. (15.15) at the initial radius of the 6s electrons and the final radius of the Bi6sp 3  electrons. Using Eqs. (23.285) and (23.289), the energy E(Bi Bi-L ,6sp 3 ) of the outer electron of the Bi6sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           E 
                            
                           
                             ( 
                             
                               
                                 Bi 
                                 
                                   Bi 
                                   - 
                                   L 
                                 
                               
                               , 
                               
                                 6 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               - 
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 r 
                                 
                                   Bi 
                                   - 
                                   
                                     L 
                                      
                                     
                                         
                                     
                                      
                                     6 
                                      
                                     
                                       sp 
                                       3 
                                     
                                   
                                 
                               
                             
                           
                           + 
                           
                             
                               2 
                                
                               
                                 πμ 
                                 0 
                               
                                
                               
                                  
                                 2 
                               
                                
                               
                                 ℏ 
                                 2 
                               
                             
                             
                               
                                 
                                   m 
                                   e 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     r 
                                     80 
                                   
                                   ) 
                                 
                               
                               3 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               10.41354 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             0.01978 
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             10.39377 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.290 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Thus, E T (Bi-L,6sp 3 ), the energy change of each Bi6sp 3  shell with the formation of the Bi-L-bond MO is given by the difference between Eq. (23.290) and Eq. (23.286): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             T 
                           
                            
                           
                             ( 
                             
                               
                                 Bi 
                                 - 
                                 L 
                               
                               , 
                               
                                 6 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             E 
                              
                             
                               ( 
                               
                                 
                                   Bi 
                                   
                                     Bi 
                                     - 
                                     L 
                                   
                                 
                                 , 
                                 
                                   6 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                           - 
                           
                             E 
                              
                             
                               ( 
                               
                                 Bi 
                                 , 
                                 
                                   6 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               10.39377 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           - 
                           
                             ( 
                             
                               
                                 - 
                                 10.03679 
                               
                                
                               
                                   
                               
                                
                               eV 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             0.35698 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.291 
                   ) 
                 
               
             
           
         
       
     
         [0388]    Next, consider the formation of the Bi—C-bond MO by bonding with a carbon having a C2sp 3  electron with an energy given by Eq. (14.146). The total energy of the state is given by the sum over the five electrons. The sum E T (C ethane ,2sp 3 ) of calculated energies of C2sp 3 , C + , C 2+ , and C 3+  from Eqs. (10.123), (10.113-10.114), (10.68), and (10.48), respectively, is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             T 
                           
                            
                           
                             ( 
                             
                               
                                 C 
                                 ethane 
                               
                               , 
                               
                                 2 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           - 
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       64.3921 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       48.3125 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       24.2762 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       E 
                                        
                                       
                                         ( 
                                         
                                           C 
                                           , 
                                           
                                             2 
                                              
                                             
                                               sp 
                                               3 
                                             
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           - 
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       64.3921 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       48.3125 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       24.2762 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                     + 
                                     
                                       14.63489 
                                        
                                       
                                           
                                       
                                        
                                       eV 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             151.61569 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.292 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where E(C,2sp 3 ) is the sum of the energy of C, −11.27671 eV, and the hybridization energy. 
         [0389]    The sharing of electrons between the Bi6sp 3  Ho and C2sp 3  HOs to form a Bi—C-bond MO permits each participating hybridized orbital to decrease in radius and energy. A minimum energy is achieved while satisfying the potential, kinetic, and orbital energy relationships, when the Bi6sp 3  HO donates, and the C2sp 3  HO receives, excess electron density equivalent to an electron within the Bi—C-bond MO. By considering this electron redistribution in the alkyl bismuth molecule as well as the fact that the central field decreases by an integer for each successive electron of the shell, the radius r Bi-C2sp     3    of the C2sp 3  shell of the Bi—C-bond MO may be calculated from the Coulombic energy using Eqs. (15.18) and (23.292): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           r 
                           
                             Pb 
                             - 
                             
                               C 
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                 sp 
                                 3 
                               
                             
                           
                         
                         = 
                           
                          
                         
                           
                             ( 
                             
                               
                                 
                                   ∑ 
                                   
                                     n 
                                     = 
                                     2 
                                   
                                   5 
                                 
                                  
                                 
                                   ( 
                                   
                                     Z 
                                     - 
                                     n 
                                   
                                   ) 
                                 
                               
                               + 
                               1 
                             
                             ) 
                           
                            
                           
                             
                                
                               2 
                             
                             
                               8 
                                
                               
                                 
                                   πɛ 
                                   0 
                                 
                                  
                                 
                                   ( 
                                   
                                     e 
                                      
                                     
                                         
                                     
                                      
                                     151.61569 
                                      
                                     
                                         
                                     
                                      
                                     eV 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             11 
                              
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 ( 
                                 
                                   e 
                                    
                                   
                                       
                                   
                                    
                                   151.61569 
                                    
                                   
                                       
                                   
                                    
                                   eV 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           0.98713 
                            
                           
                             a 
                             0 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.293 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Using Eqs. (15.19) and (23.293), the Coulombic energy E Coulomb (C Bi-C 2, sp 3 ) of the outer electron of the C2sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             Coulomb 
                           
                            
                           
                             ( 
                             
                               
                                 C 
                                 
                                   Bi 
                                   - 
                                   C 
                                 
                               
                               , 
                               
                                 2 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             
                               r 
                               
                                 Bi 
                                 - 
                                 
                                   C 
                                    
                                   
                                       
                                   
                                    
                                   2 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             
                                
                               2 
                             
                           
                           
                             8 
                              
                             
                               πɛ 
                               0 
                             
                              
                             0.98713 
                              
                             
                               a 
                               0 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             13.78324 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.294 
                   ) 
                 
               
             
           
         
       
     
         [0000]    During hybridization, the spin-paired 2s electrons are promoted to C2sp 3  shell as unpaired electrons. The energy for the promotion is the magnetic energy given by Eq. (14.145). Using Eqs. (14.145) and (23.294), the energy E(C Bi—C ,2sp 3 ) of the outer electron of the C2sp 3  shell is 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           E 
                            
                           
                             ( 
                             
                               
                                 C 
                                 
                                   Bi 
                                   - 
                                   C 
                                 
                               
                               , 
                               
                                 2 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               - 
                               
                                  
                                 2 
                               
                             
                             
                               8 
                                
                               
                                 πɛ 
                                 0 
                               
                                
                               
                                 r 
                                 
                                   Bi 
                                   - 
                                   
                                     C 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                      
                                     
                                         
                                     
                                      
                                     
                                       sp 
                                       3 
                                     
                                   
                                 
                               
                             
                           
                           + 
                           
                             
                               2 
                                
                               
                                 πμ 
                                 0 
                               
                                
                               
                                  
                                 2 
                               
                                
                               
                                 ℏ 
                                 2 
                               
                             
                             
                               
                                 
                                   m 
                                   e 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     r 
                                     3 
                                   
                                   ) 
                                 
                               
                               3 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               13.78324 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           + 
                           
                             0.19086 
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             13.59238 
                           
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.295 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Thus, E T (Bi—C,2sp 3 ), the energy change of each C2sp 3  shell with the formation of the Bi—C-bond MO is given by the difference between Eq. (23.295) and Eq. (14.146): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             T 
                           
                            
                           
                             ( 
                             
                               
                                 Bi 
                                 - 
                                 C 
                               
                               , 
                               
                                 2 
                                  
                                 
                                   sp 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             E 
                              
                             
                               ( 
                               
                                 
                                   C 
                                   
                                     Bi 
                                     - 
                                     C 
                                   
                                 
                                 , 
                                 
                                   2 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                           - 
                           
                             E 
                              
                             
                               ( 
                               
                                 C 
                                 , 
                                 
                                   2 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               13.59238 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           - 
                           
                             ( 
                             
                               
                                 - 
                                 14.63489 
                               
                                
                               
                                   
                               
                                
                               eV 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           1.04251 
                            
                           
                               
                           
                            
                           eV 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.296 
                   ) 
                 
               
             
           
         
       
     
         [0390]    Now, consider the formation of the Bi-L-bond MO of bismuth compounds wherein L is a ligand including carbon. For the Bi—C functional group, hybridization of the 2s and 2p AOs of each C and the 6s and 6p AOs of each Bi to form single 2sp 3  and 6sp 3  shells, respectively, forms an energy minimum, and the sharing of electrons between the C2sp 3  and Bi6sp 3  HOs to form a MO permits each participating orbital to decrease in radius and energy. In branched-chain alkyl bismuths, the energy of bismuth is less than the Coulombic energy between the electron and proton of H given by Eq. (1.231). Thus, the energy matching condition is determined by the c 2  and C 2  parameters in Eq. (15.61). Then, the C2sp 3  HO has an energy of E(C,2sp 3 )=−14.63489 eV (Eq. (15.25)), and the Bi6sp 3  HO has an energy of E(Bi,6sp 3 )=−10.03679 eV (Eq. (23.286)). To meet the equipotential condition of the union of the Bi—C H 2 -type-ellipsoidal-MO with these orbitals, the hybridization factors c 2  and C 2  of Eq. (15.61) for the Bi—C-bond MO given by Eqs. (15.77) are 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             c 
                             2 
                           
                            
                           
                             ( 
                             
                               C 
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                                
                               
                                   
                               
                                
                               to 
                                
                               
                                   
                               
                                
                               Bi 
                                
                               
                                   
                               
                                
                               6 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             C 
                             2 
                           
                            
                           
                             ( 
                             
                               C 
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                                
                               
                                   
                               
                                
                               to 
                                
                               
                                   
                               
                                
                               Bi 
                                
                               
                                   
                               
                                
                               6 
                                
                               
                                   
                               
                                
                               
                                 sp 
                                 3 
                               
                                
                               HO 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             E 
                              
                             
                               ( 
                               
                                 Bi 
                                 , 
                                 
                                   6 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                           
                             E 
                              
                             
                               ( 
                               
                                 C 
                                 , 
                                 
                                   2 
                                    
                                   
                                     sp 
                                     3 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               10.03679 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                           
                             
                               - 
                               14.63489 
                             
                              
                             
                                 
                             
                              
                             eV 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         0.68581 
                       
                     
                   
                 
               
               
                 
                   ( 
                   23.297 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The energy of the Bi—C-bond MO is the sum of the component energies of the H 2 -type ellipsoidal MO given in Eq. (15.51) with E(AO/HO)=E(Bi,6sp 3 ) given by Eq. (23.286), and E T (atom-atom,msp 3 .AO) is E T (Bi—C,2sp 3 ) (Eq. (23.296)) in order to match the energies of the carbon and bismuth HOs. 
         [0391]    The symbols of the functional groups of branched-chain alkyl bismuths are given in Table 172. The geometrical (Eqs. (15.1-15.5) and (15.51)), intercept (Eqs. (15.80-15.87)), and energy (Eqs. (15.6-15.11) and (15.17-15.65)) parameters of alkyl bismuths are given in Tables 173, 174, and 175, respectively. The total energy of each alkyl bismuth given in Table 176 was calculated as the sum over the integer multiple of each E D (Group) of Table 175 corresponding to functional-group composition of the molecule. The bond angle parameters of alkyl bismuths determined using Eqs. (15.88-15.117) are given in Table 177. The color scale, charge-density of exemplary alkyl bismuth, triphenylbismuth, comprising atoms with the outer shell bridged by one or more H 2 -type ellipsoidal MOs or joined with one or more hydrogen MOs is shown in  FIG. 74 . 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 172 
               
             
             
               
                   
               
               
                 The symbols of functional groups of alkyl bismuths. 
               
             
          
           
               
                   
                 Functional Group 
                 Group Symbol 
               
               
                   
                   
               
               
                   
                 Bi—C 
                 Bi—C 
               
               
                   
                 CH 3  group 
                 C—H (CH 3 ) 
               
               
                   
                 CH 2  group 
                 C—H (CH 2 ) 
               
               
                   
                 CH 
                 C—H (i) 
               
               
                   
                 CC bond (n-C) 
                 C—C (a) 
               
               
                   
                 CC bond (iso-C) 
                 C—C (b) 
               
               
                   
                 CC bond (tert-C) 
                 C—C (c) 
               
               
                   
                 CC (iso to iso-C) 
                 C—C (d) 
               
               
                   
                 CC (t to t-C) 
                 C—C (e) 
               
               
                   
                 CC (t to iso-C) 
                 C—C (f) 
               
               
                   
                 CC (aromatic bond) 
                 C 3e ═C 
               
               
                   
                 CH (aromatic) 
                 CH (ii) 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 173 
               
               
                   
               
               
                 The geometrical bond parameters of alkyl bismuths and experimental values [3]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Bi—C 
                 C—H(CH 3 ) 
                 C—H(CH 2 ) 
                 C—H (i) 
                 C—C (a) 
                 C—C (b) 
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 2.18901 
                 1.64920 
                 1.67122 
                 1.67465 
                 2.12499 
                 2.12499 
               
               
                 c′ (a 0 ) 
                 2.06296 
                 1.04856 
                 1.05553 
                 1.05661 
                 1.45744 
                 1.45744 
               
               
                 Bond Length 2c′ (Å) 
                 2.18334 
                 1.10974 
                 1.11713 
                 1.11827 
                 1.54280 
                 1.54280 
               
               
                 Exp. Bond Length 
                 2.263 
                 1.107 
                 1.107 
                 1.122 
                 1.532 
                 1.532 
               
               
                 (Å) 
                 (Bi(CH 3 ) 3 ) 
                 (C—H 
                 (C—H 
                 (isobutane) 
                 (propane) 
                 (propane) 
               
               
                   
                   
                 propane) 
                 propane) 
                   
                 1.531 
                 1.531 
               
               
                   
                   
                 1.117 
                 1.117 
                   
                 (butane) 
                 (butane) 
               
               
                   
                   
                 (C—H 
                 (C—H 
               
               
                   
                   
                 butane) 
                 butane) 
               
               
                 b, c (a 0 ) 
                 0.73210 
                 1.27295 
                 1.29569 
                 1.29924 
                 1.54616 
                 1.54616 
               
               
                 e 
                 0.94242 
                 0.63580 
                 0.63159 
                 0.63095 
                 0.68600 
                 0.68600 
               
               
                   
               
             
          
           
               
                   
                 C—C (c) 
                 C—C (d) 
                 C—C (e) 
                 C—C (f) 
                 C 3e ═C 
                 CH (ii) 
               
               
                 Parameter 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 a (a 0 ) 
                 2.10725 
                 2.12499 
                 2.10725 
                 2.10725 
                 1.47348 
                 1.60061 
               
               
                 c′ (a 0 ) 
                 1.45164 
                 1.45744 
                 1.45164 
                 1.45164 
                 1.31468 
                 1.03299 
               
               
                 Bond Length 2c′ (Å) 
                 1.53635 
                 1.54280 
                 1.53635 
                 1.53635 
                 1.39140 
                 1.09327 
               
               
                 Exp. Bond Length 
                 1.532 
                 1.532 
                 1.532 
                 1.532 
                 1.399 
                 1.101 
               
               
                 (Å) 
                 (propane) 
                 (propane) 
                 (propane) 
                 (propane) 
                 (benzene) 
                 (benzene) 
               
               
                   
                 1.531 
                 1.531 
                 1.531 
                 1.531 
               
               
                   
                 (butane) 
                 (butane) 
                 (butane) 
                 (butane) 
               
               
                 b, c (a 0 ) 
                 1.52750 
                 1.54616 
                 1.52750 
                 1.52750 
                 0.66540 
                 1.22265 
               
               
                 e 
                 0.68888 
                 0.68600 
                 0.68888 
                 0.68888 
                 0.89223 
                 0.64537 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 174 
               
               
                   
               
               
                 The MO to HO intercept geometrical bond parameters of alkyl bismuths. R, R′, R″ are H or alkyl groups. E T  is E T   
               
               
                 (atom-atom, msp 3 .AO. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 Final 
                   
                   
               
               
                   
                   
                   
                   
                   
                   
                 Total 
               
               
                   
                   
                 E T   
                 E T   
                 E T   
                 E T   
                 Energy 
               
               
                   
                   
                 (eV) 
                 (eV) 
                 (eV) 
                 (eV) 
                 C2sp 3   
                 r initial   
                 r final   
               
               
                 Bond 
                 Atom 
                 Bond 1 
                 Bond 2 
                 Bond 3 
                 Bond 4 
                 (eV) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
               
               
                 C—H(CH 3 ) 
                 C 
                 0.52125 
                 0 
                 0 
                 0 
                 −151.09444 
                 0.91771 
                 0.95116 
               
               
                 (CH 3 ) 2 Bi—CH 3   
                 C 
                 0.52125 
                 0 
                 0 
                 0 
                   
                 0.91771 
                 0.95116 
               
               
                 (CH 3 ) 2 Bi—CH 3   
                 Bi 
                 0.52125 
                 0.52125 
                 0.52125 
                 0 
                   
                 1.35293 
                 1.02592 
               
               
                 C—H(CH 3 ) 
                 C 
                 −0.92918 
                 0 
                 0 
                 0 
                 −152.54487 
                 0.91771 
                 0.86359 
               
               
                 C—H(CH 2 ) 
                 C 
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                 −153.47406 
                 0.91771 
                 0.81549 
               
               
                 C—H(CH) 
                 C 
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 C a   
                 −0.92918 
                 0 
                 0 
                 0 
                 −152.54487 
                 0.91771 
                 0.86359 
               
               
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 0 
                 0 
                 −153.47406 
                 0.91771 
                 0.81549 
               
               
                 R—H 2 C a C b (H 2 C c —R′)HCH 2 —(C—C (b)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 R—H 2 C a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (c)) 
                 C b   
                 −0.92918 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.71860 
                 0.91771 
                 0.75889 
               
               
                 isoC a C b (H 2 C c —R′)HCH 2 —(C—C (d)) 
                 C b   
                 −0.92918 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.40324 
                 0.91771 
                 0.77247 
               
               
                 tertC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (e)) 
                 C b   
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.51399 
                 0.91771 
                 0.76765 
               
               
                 tertC a C b (H 2 C c —R′)HCH 2 —(C—C (f)) 
                 C b   
                 −0.72457 
                 −0.92918 
                 −0.92918 
                 0 
                 −154.19863 
                 0.91771 
                 0.78155 
               
               
                 isoC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (f)) 
                 C b   
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −0.72457 
                 −154.51399 
                 0.91771 
                 0.76765 
               
               
                   
               
             
          
           
               
                   
                   
                 E Coulomb   
                 E (C2sp 3 ) 
                   
                   
                   
                   
                   
               
               
                   
                   
                 (eV) 
                 (eV) 
                 θ′ 
                 θ 1   
                 θ 2   
                 d 1   
                 d 2   
               
               
                   
                 Bond 
                 Final 
                 Final 
                 (°) 
                 (°) 
                 (°) 
                 (a 0 ) 
                 (a 0 ) 
               
               
                   
                   
               
               
                   
                 C—H(CH 3 ) 
                 −14.30450 
                 −14.11363 
                 87.03 
                 92.97 
                 48.26 
                 1.09791 
                 0.04936 
               
               
                   
                 (CH 3 ) 2 Bi—CH 3   
                 −14.30450 
                 −14.11363 
                 141.99 
                 38.01 
                 53.13 
                 1.31349 
                 0.74947 
               
               
                   
                 (CH 3 ) 2 Bi—CH 3   
                 −13.26199 
                   
                 143.89 
                 36.11 
                 55.68 
                 1.23415 
                 0.82881 
               
               
                   
                 C—H(CH 3 ) 
                 −15.75493 
                 −15.56407 
                 77.49 
                 102.51 
                 41.48 
                 1.23564 
                 0.18708 
               
               
                   
                 C—H(CH 2 ) 
                 −16.68412 
                 −16.49325 
                 68.47 
                 111.53 
                 35.84 
                 1.35486 
                 0.29933 
               
               
                   
                 C—H(CH) 
                 −17.61330 
                 −17.42244 
                 61.10 
                 118.90 
                 31.37 
                 1.42988 
                 0.37326 
               
               
                   
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 −15.75493 
                 −15.56407 
                 63.82 
                 116.18 
                 30.08 
                 1.83879 
                 0.38106 
               
               
                   
                 H 3 C a C b H 2 CH 2 —(C—C (a)) 
                 −16.68412 
                 −16.49325 
                 56.41 
                 123.59 
                 26.06 
                 1.90890 
                 0.45117 
               
               
                   
                 R—H 2 C a C b (H 2 C c —R′)HCH 2 —(C—C (b)) 
                 −17.61330 
                 −17.42244 
                 48.30 
                 131.70 
                 21.90 
                 1.97162 
                 0.51388 
               
               
                   
                 R—H 2 C a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (c)) 
                 −17.92866 
                 −17.73779 
                 48.21 
                 131.79 
                 21.74 
                 1.95734 
                 0.50570 
               
               
                   
                 isoC a C b (H 2 C c —R′)HCH 2 —(C—C (d)) 
                 −17.61330 
                 −17.42244 
                 48.30 
                 131.70 
                 21.90 
                 1.97162 
                 0.51388 
               
               
                   
                 tertC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (e)) 
                 −17.92866 
                 −17.73779 
                 50.04 
                 129.96 
                 22.66 
                 1.94462 
                 0.49298 
               
               
                   
                 tertC a C b (H 2 C c —R′)HCH 2 —(C—C (f)) 
                 −17.40869 
                 −17.21783 
                 52.78 
                 127.22 
                 24.04 
                 1.92443 
                 0.47279 
               
               
                   
                 isoC a (R′—H 2 C d )C b (R″—H 2 C c )CH 2 —(C—C (f)) 
                 −17.92866 
                 −17.73779 
                 50.04 
                 129.96 
                 22.66 
                 1.94462 
                 0.49298 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 175 
               
               
                   
               
               
                 The energy parameters (eV) of functional groups of alkyl bismuths. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Bi—C 
                 CH 3   
                 CH 2   
                 CH (i) 
                 C—C (a) 
                 C—C (b) 
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 f 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 n 1   
                 1 
                 3 
                 2 
                 1 
                 1 
                 1 
               
               
                 n 2   
                 0 
                 2 
                 1 
                 0 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.375 
                 0.75 
                 0.75 
                 0.75 
                 0.5 
                 0.5 
               
               
                 C 2   
                 0.68581 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 2   
                 0.68581 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
               
               
                 c 3   
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
               
               
                 c 4   
                 2 
                 1 
                 1 
                 1 
                 2 
                 2 
               
               
                 c 5   
                 0 
                 3 
                 2 
                 1 
                 0 
                 0 
               
               
                 C 1o   
                 0.375 
                 0.75 
                 0.75 
                 0.75 
                 0.5 
                 0.5 
               
               
                 C 2o   
                 0.68581 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 V e  (eV) 
                 −31.82881 
                 −107.32728 
                 −70.41425 
                 −35.12015 
                 −28.79214 
                 −28.79214 
               
               
                 V p  (eV) 
                 6.59529 
                 38.92728 
                 25.78002 
                 12.87680 
                 9.33352 
                 9.33352 
               
               
                 T (eV) 
                 7.27014 
                 32.53914 
                 21.06675 
                 10.48582 
                 6.77464 
                 6.77464 
               
               
                 V m  (eV) 
                 −3.63507 
                 −16.26957 
                 −10.53337 
                 −5.24291 
                 −3.38732 
                 −3.38732 
               
               
                 E (AO/HO) (eV) 
                 −10.03679 
                 −15.56407 
                 −15.56407 
                 −14.63489 
                 −15.56407 
                 −15.56407 
               
               
                 ΔE H     2     MO  (AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 E T  (AO/HO) (eV) 
                 −10.03679 
                 −15.56407 
                 −15.56407 
                 −14.63489 
                 −15.56407 
                 −15.56407 
               
               
                 E T  (H 2 MO) (eV) 
                 −31.63524 
                 −67.69451 
                 −49.66493 
                 −31.63533 
                 −31.63537 
                 −31.63537 
               
               
                 E T  (atom-atom, 
                 1.04251 
                 0 
                 0 
                 0 
                 −1.85836 
                 −1.85836 
               
               
                 msp 3 .AO) (eV) 
               
               
                 E T  (MO) (eV) 
                 −30.59286 
                 −67.69450 
                 −49.66493 
                 −31.63537 
                 −33.49373 
                 −33.49373 
               
               
                 ω (10 15  rad/s) 
                 33.4696 
                 24.9286 
                 24.2751 
                 24.1759 
                 9.43699 
                 9.43699 
               
               
                 E K  (eV) 
                 22.03030 
                 16.40846 
                 15.97831 
                 15.91299 
                 6.21159 
                 6.21159 
               
               
                 Ē D  (eV) 
                 −0.28408 
                 −0.25352 
                 −0.25017 
                 −0.24966 
                 −0.16515 
                 −0.16515 
               
               
                 Ē Kvib  (eV) 
                 0.14878 [66] 
                 0.35532 
                 0.35532 
                 0.35532 
                 0.12312 [6] 
                 0.17978 [7] 
               
               
                   
                   
                 (Eq. 
                 (Eq. 
                 (Eq. 
               
               
                   
                   
                 (13.458)) 
                 (13.458)) 
                 (13.458)) 
               
               
                 Ē osc  (eV) 
                 −0.20968 
                 −0.22757 
                 −0.14502 
                 −0.07200 
                 −0.10359 
                 −0.07526 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                 E T  (Group) (eV) 
                 −30.80254 
                 −67.92207 
                 −49.80996 
                 −31.70737 
                 −33.59732 
                 −33.49373 
               
               
                 E initial  (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
               
               
                 E initial  (c 5  AO/HO) (eV) 
                 0 
                 −13.59844 
                 −13.59844 
                 −13.59844 
                 0 
                 0 
               
               
                 E D  (Group) (eV) 
                 1.53276 
                 12.49186 
                 7.83016 
                 3.32601 
                 4.32754 
                 4.29921 
               
               
                   
               
               
                   
                 C—C (c) 
                 C—C (d) 
                 C—C (e) 
                 C—C (f) 
                 C 3e ═C 
                 CH (ii) 
               
               
                 Parameters 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
                 Group 
               
               
                   
               
               
                 f 1   
                 1 
                 1 
                 1 
                 1 
                 0.75 
                 1 
               
               
                 n 1   
                 1 
                 1 
                 1 
                 1 
                 2 
                 1 
               
               
                 n 2   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 n 3   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 1   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.75 
               
               
                 C 2   
                 1 
                 1 
                 1 
                 1 
                 0.85252 
                 1 
               
               
                 c 1   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 c 2   
                 0.91771 
                 0.91771 
                 0.91771 
                 0.91771 
                 0.85252 
                 0.91771 
               
               
                 c 3   
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
               
               
                 c 4   
                 2 
                 2 
                 2 
                 2 
                 3 
                 1 
               
               
                 c 5   
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
               
               
                 C 1o   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.75 
               
               
                 C 2o   
                 1 
                 1 
                 1 
                 1 
                 0.85252 
                 1 
               
               
                 V e  (eV) 
                 −29.10112 
                 −28.79214 
                 −29.10112 
                 −29.10112 
                 −101.12679 
                 −37.10024 
               
               
                 V p  (eV) 
                 9.37273 
                 9.33352 
                 9.37273 
                 9.37273 
                 20.69825 
                 13.17125 
               
               
                 T (eV) 
                 6.90500 
                 6.77464 
                 6.90500 
                 6.90500 
                 34.31559 
                 11.58941 
               
               
                 V m  (eV) 
                 −3.45250 
                 −3.38732 
                 −3.45250 
                 −3.45250 
                 −17.15779 
                 −5.79470 
               
               
                 E (AO/HO) (eV) 
                 −15.35946 
                 −15.56407 
                 −15.35946 
                 −15.35946 
                 0 
                 −14.63489 
               
               
                 ΔE H     2     MO  (AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 −1.13379 
               
               
                 E T  (AO/HO) (eV) 
                 −15.35946 
                 −15.56407 
                 −15.35946 
                 −15.35946 
                 0 
                 13.50110 
               
               
                 E T  (H 2 MO) (eV) 
                 −31.63535 
                 −31.63537 
                 −31.63535 
                 −31.63535 
                 −63.27075 
                 −31.63539 
               
               
                 E T  (atom-atom, 
                 −1.44915 
                 −1.85836 
                 −1.44915 
                 −1.44915 
                 −2.26759 
                 −0.56690 
               
               
                 msp 3 .AO) (eV) 
               
               
                 E T  (MO) (eV) 
                 −33.08452 
                 −33.49373 
                 −33.08452 
                 −33.08452 
                 −65.53833 
                 −32.20226 
               
               
                 ω (10 15  rad/s) 
                 15.4846 
                 9.43699 
                 9.55643 
                 9.55643 
                 49.7272 
                 26.4826 
               
               
                 E K  (eV) 
                 10.19220 
                 6.21159 
                 6.29021 
                 6.29021 
                 32.73133 
                 17.43132 
               
               
                 Ē D  (eV) 
                 −0.20896 
                 −0.16515 
                 −0.16416 
                 −0.16416 
                 −0.35806 
                 −0.26130 
               
               
                 Ē Kvib  (eV) 
                 0.09944 [8] 
                 0.12312 [6] 
                 0.12312 [6] 
                 0.12312 [6] 
                 0.19649 [30] 
                 0.35532 
               
               
                   
                   
                   
                   
                   
                   
                 Eq. (13.458) 
               
               
                 Ē osc  (eV) 
                 −0.15924 
                 −0.10359 
                 −0.10260 
                 −0.10260 
                 −0.25982 
                 −0.08364 
               
               
                 E mag  (eV) 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
                 0.14803 
               
               
                 E T  (Group) (eV) 
                 −33.24376 
                 −33.59732 
                 −33.18712 
                 −33.18712 
                 −49.54347 
                 −32.28590 
               
               
                 E initial  (c 4  AO/HO) (eV) 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
                 −14.63489 
               
               
                 E initial  (c 5  AO/HO) (eV) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 −13.59844 
               
               
                 E D  (Group) (eV) 
                 3.97398 
                 4.17951 
                 3.62128 
                 3.91734 
                 5.63881 
                 3.90454 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 176 
               
               
                   
               
               
                 The total bond energies of alkyl bismuths calculated using the functional group composition and 
               
               
                 the energies of Table 175 compared to the experimental values [88]. 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Formula 
                 Name 
                 Bi—C 
                 CH 3   
                 CH 2   
                 CH (i) 
                 C—C (a) 
                 C—C (b) 
                 C—C (c) 
                 C—C (d) 
               
               
                   
               
               
                 C 3 H 9 Bi 
                 Trimethylbismuth 
                 3 
                 3 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C 6 H 15 Bi 
                 Triethylbismuth 
                 3 
                 3 
                 3 
                 0 
                 3 
                 0 
                 0 
                 0 
               
               
                 C 18 H 15 Bi 
                 Triphenylbismuth 
                 3 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                   
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                   
                   
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 C—C (e) 
                 C—C (f) 
                 C 3e ═C 
                 CH (ii) 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 C 3 H 9 Bi 
                 Trimethylbismuth 
                 0 
                 0 
                 0 
                 0 
                 42.07387 
                 42.79068 
                 0.01675 
               
               
                 C 6 H 15 Bi 
                 Triethylbismuth 
                 0 
                 0 
                 0 
                 0 
                 78.54697 
                 78.39153 
                 −0.00198 
               
               
                 C 18 H 15 Bi 
                 Triphenylbismuth 
                 0 
                 0 
                 18 
                 15 
                 164.66490 
                 163.75184 
                 −0.00558 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 177 
               
               
                   
               
               
                 The bond angle parameters of alkyl bismuths and experimental values [3]. In the calculation of θ v , the parameters from 
               
               
                 the preceding angle were used. E T  is E T  (atom-atom,msp 3 .AO). 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                 2c′ 
                   
                 Atom 1 
                   
                 Atom 2 
                   
                   
                   
               
               
                   
                 2c′ 
                 2c′ 
                 Terminal 
                 E Coulombic   
                 Hybridization 
                   
                 Hybridization 
               
               
                 Atoms of 
                 Bond 1 
                 Bond 2 
                 Atoms 
                 or E 
                 Designation 
                 E Coulombic   
                 Designation 
                 c 2   
                 c 2   
               
               
                 Angle 
                 (a 0 ) 
                 (a 0 ) 
                 (a 0 ) 
                 Atom 1 
                 (Table 7) 
                 Atom 2 
                 (Table 7) 
                 Atom 1 
                 Atom 2 
                 C 1   
               
               
                   
               
               
                 Methyl 
                 2.09711 
                 2.09711 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
                 1 
                 1 
               
               
                 ∠HC a H 
               
               
                 ∠H a C a Bi 
               
               
                 ∠C a BiC b   
                 4.12592 
                 4.12592 
                 6.1806 
                 −15.18804 
                 2 
                 −15.18804 
                 2 
                 0.89582 
                 0.89582 
                 1 
               
               
                 Methylene 
                 2.11106 
                 2.11106 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
                 1 
                 1 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
               
               
                 ∠C a C b H 
               
               
                 Methyl 
                 2.09711 
                 2.09711 
                 3.4252 
                 −15.75493 
                 7 
                 H 
                 H 
                 0.86359 
                 1 
                 1 
               
               
                 ∠HC a H 
               
               
                 ∠C a C b C c   
               
               
                 ∠C a C b H 
               
               
                 ∠C b C a C c   
                 2.91547 
                 2.91547 
                 4.7958 
                 −16.68412 
                 26 
                 −16.68412 
                 26  
                 0.81549 
                 0.81549 
                 1 
               
               
                 iso C a   
                   
                   
                   
                 C b   
                   
                 C c   
               
               
                 ∠C b C a H 
                 2.91547 
                 2.11323 
                 4.1633 
                 −15.55033 
                 5 
                 −14.82575 
                 1 
                 0.87495 
                 0.91771 
                 0.75 
               
               
                 iso C a   
                   
                   
                   
                 C a   
                   
                 C b   
               
               
                 ∠C a C b H 
                 2.91547 
                 2.09711 
                 4.1633 
                 −15.55033 
                 5 
                 −14.82575 
                 1 
                 0.87495 
                 0.91771 
                 0.75 
               
               
                 iso C a   
                   
                   
                   
                 C b   
                   
                 C a   
               
               
                 ∠C b C a C b   
                 2.90327 
                 2.90327 
                 4.7958 
                 −16.68412 
                 26 
                 −16.68412 
                 26  
                 0.81549 
                 0.81549 
                 1 
               
               
                 tert C a   
                   
                   
                   
                 C b   
                   
                 C b   
               
               
                 ∠C b C a C d   
               
               
                   
               
             
          
           
               
                   
                 Atoms of 
                   
                   
                   
                 E T   
                 θ v   
                 θ 1   
                 θ 2   
                 Cal. θ 
                 Exp. θ 
               
               
                   
                 Angle 
                 C 2   
                 c 1   
                 c 2 ′ 
                 (eV) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
                 (°) 
               
               
                   
                   
               
               
                   
                 Methyl 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 109.50 
               
               
                   
                 ∠HC a H 
               
               
                   
                 ∠H a C a Bi 
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                   
                 ∠C a BiC b   
                 1 
                 1 
                 0.89582 
                 −1.85836 
                   
                   
                   
                 97.01 
                  97.1 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (trimethylbismuth) 
               
               
                   
                 Methylene 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 108.44 
                 107   
               
               
                   
                 ∠HC a H 
                   
                   
                   
                   
                   
                   
                   
                   
                 (propane) 
               
               
                   
                 ∠C a C b C c   
                   
                   
                   
                   
                 69.51 
                   
                   
                 110.49 
                 112   
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (propane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 113.8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (butane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 110.8 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                   
                 ∠C a C b H 
                   
                   
                   
                   
                 69.51 
                   
                   
                 110.49 
                 111.0 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (butane) 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 111.4 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                   
                 Methyl 
                 1 
                 0.75 
                 1.15796 
                 0 
                   
                   
                   
                 109.50 
               
               
                   
                 ∠HC a H 
               
               
                   
                 ∠C a C b C c   
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                   
                 ∠C a C b H 
                   
                   
                   
                   
                 70.56 
                   
                   
                 109.44 
               
               
                   
                 ∠C b C a C c   
                 1 
                 1 
                 0.81549 
                 −1.85836 
                   
                   
                   
                 110.67 
                 110.8 
               
               
                   
                 iso C a   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                   
                 ∠C b C a H 
                 1 
                 0.75 
                 1.04887 
                 0 
                   
                   
                   
                 110.76 
               
               
                   
                 iso C a   
               
               
                   
                 ∠C a C b H 
                 1 
                 0.75 
                 1.04887 
                 0 
                   
                   
                   
                 111.27 
                 111.4 
               
               
                   
                 iso C a   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                   
                 ∠C b C a C b   
                 1 
                 1 
                 0.81549 
                 −1.85836 
                   
                   
                   
                 111.37 
                 110.8 
               
               
                   
                 tert C a   
                   
                   
                   
                   
                   
                   
                   
                   
                 (isobutane) 
               
               
                   
                 ∠C b C a C d   
                   
                   
                   
                   
                 72.50 
                   
                   
                 107.50 
               
               
                   
                   
               
             
          
         
       
     
         [0392]    Summary Tables of Organometallic and Coordinate Molecules 
         [0393]    The bond energies, calculated using closed-form equations having integers and fundamental constants only for classes of molecules whose designation is based on the main functional group, are given in the following tables with the experimental values. 
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 178 
               
             
             
               
                   
               
               
                 Summary results of organoaluminum compounds. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 2 H 7 Al 
                 dimethylaluminum hydride 
                 34.31171 
                 34.37797 a   
                 0.00193 
               
               
                   
                   
                   
                 [11] 
               
               
                 C 3 H 9 Al 
                 trimethyl aluminum 
                 47.10960 
                 46.95319 
                 −0.00333 
               
               
                 C 4 H 11 Al 
                 diethylaluminum hydride 
                 58.62711 
                 60.10948 b   
                 0.02466 
               
               
                 C 6 H 15 Al 
                 triethylaluminum hydride 
                 83.58270 
                 83.58176 
                 −0.00001 
               
               
                 C 6 H 15 Al 
                 di-n-propylaluminum hydride 
                 82.94251 
                 84.40566 b   
                 0.01733 
               
               
                 C 9 H 21 Al 
                 tri-n-propyl aluminum 
                 120.05580 
                 121.06458 b   
                 0.00833 
               
               
                 C 8 H 19 Al 
                 di-n-butylaluminum hydride 
                 107.25791 
                 108.71051 b   
                 0.01336 
               
               
                 C 8 H 19 Al 
                 di-isobutylaluminum hydride 
                 107.40303 
                 108.77556 b   
                 0.01262 
               
               
                 C 12 H 27 Al 
                 tri-n-butyl aluminum 
                 156.52890 
                 157.42429 b   
                 0.00569 
               
               
                 C 12 H 27 Al 
                 tri-isobutyl aluminum 
                 156.74658 
                 157.58908 b   
                 0.00535 
               
               
                   
               
               
                   a Estimated. 
               
               
                   b Crystal 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 179 
               
             
             
               
                   
               
               
                 Summary results of scandium coordinate compounds. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 ScF 
                 scandium fluoride 
                 6.34474 
                 6.16925 
                 −0.02845 
               
               
                 ScF 2   
                 scandium difluoride 
                 12.11937 
                 12.19556 
                 0.00625 
               
               
                 ScF 3   
                 scandium trifluoride 
                 19.28412 
                 19.27994 
                 −0.00022 
               
               
                 ScCl 
                 scandium chloride 
                 4.05515 
                 4.00192 
                 −0.01330 
               
               
                 ScO 
                 scandium oxide 
                 7.03426 
                 7.08349 
                 0.00695 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 180 
               
             
             
               
                   
               
               
                 Summary results of titanium coordinate compounds. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 TiF 
                 titanium fluoride 
                 6.44997 
                 6.41871 
                 [21] 
                 −0.00487 
               
               
                 TiF 2   
                 titanium difluoride 
                 13.77532 
                 13.66390 
                 [21] 
                 −0.00815 
               
               
                 TiF 3   
                 titanium trifluoride 
                 19.63961 
                 19.64671 
                 [21] 
                 0.00036 
               
               
                 TiF 4   
                 titanium tetrafluoride 
                 24.66085 
                 24.23470 
                 [21] 
                 −0.01758 
               
               
                 TiCl 
                 titanium chloride 
                 4.56209 
                 4.56198 
                 [22] 
                 −0.00003 
               
               
                 TiCl 2   
                 titanium dichoride 
                 10.02025 
                 9.87408 
                 [22] 
                 −0.01517 
               
               
                 TiCl 3   
                 titanium trichloride 
                 14.28674 
                 14.22984 
                 [22] 
                 −0.00400 
               
               
                 TiCl 4   
                 titanium tetrachloride 
                 17.94949 
                 17.82402 
                 [22] 
                 −0.00704 
               
               
                 TiBr 
                 titanium bromide 
                 3.77936 
                 3.78466 
                 [19] 
                 0.00140 
               
               
                 TiBr 2   
                 titanium dibromide 
                 8.91650 
                 8.93012 
                 [19] 
                 0.00153 
               
               
                 TiBr 3   
                 titanium tribromide 
                 12.07765 
                 12.02246 
                 [19] 
                 −0.00459 
               
               
                 TiBr 4   
                 titanium tetrabromide 
                 14.90122 
                 14.93239 
                 [19] 
                 0.00209 
               
               
                 TiI 
                 titanium iodide 
                 3.16446 
                 3.15504 
                 [20] 
                 −0.00299 
               
               
                 TiI 2   
                 titanium diiodide 
                 7.35550 
                 7.29291 
                 [20] 
                 −0.00858 
               
               
                 TiI 3   
                 titanium triiodide 
                 9.74119 
                 9.71935 
                 [20] 
                 −0.00225 
               
               
                 TiI 4   
                 titanium tetraiodide 
                 12.10014 
                 12.14569 
                 [20] 
                 0.00375 
               
               
                 TiO 
                 titanium oxide 
                 7.02729 
                 7.00341 
                 [23] 
                 −0.00341 
               
               
                 TiO 2   
                 titanium dioxide 
                 13.23528 
                 13.21050 
                 [23] 
                 −0.00188 
               
               
                 TiOF 
                 titanium fluoride oxide 
                 12.78285 
                 12.77353 
                 [23] 
                 −0.00073 
               
               
                 TiOF 2   
                 titanium difluoride oxide 
                 18.94807 
                 18.66983 
                 [23] 
                 −0.01490 
               
               
                 TiOCl 
                 titanium chloride oxide 
                 11.10501 
                 11.25669 
                 [23] 
                 0.01347 
               
               
                 TiOCl 2   
                 titanium dichloride oxide 
                 15.59238 
                 15.54295 
                 [23] 
                 −0.00318 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 181 
               
             
             
               
                   
               
               
                 Summary results of vanadium coordinate compounds. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 VF 5   
                 vanadium pentafluoride 
                 24.06031 
                 24.24139 
                 [15] 
                 0.00747 
               
               
                 VCl 4   
                 vanadium tetrachloride 
                 15.84635 
                 15.80570 
                 [15] 
                 −0.00257 
               
               
                 VN 
                 vanadium nitride 
                 4.85655 
                 4.81931 
                 [24] 
                 −0.00775 
               
               
                 VO 
                 vanadium oxide 
                 6.37803 
                 6.60264 
                 [15] 
                 0.03402 
               
               
                 VO 2   
                 vanadium dioxide 
                 12.75606 
                 12.89729 
                 [34] 
                 0.01095 
               
               
                 VOCl 3   
                 vanadium trichloride oxide 
                 18.26279 
                 18.87469 
                 [15] 
                 0.03242 
               
               
                 V(CO) 6   
                 vanadium hexacarbonyl 
                 75.26791 
                 75.63369 
                 [32] 
                 0.00484 
               
               
                 V(C 6 H 6 )) 2   
                 dibenzene vanadium 
                 119.80633 
                 121.20193 a   
                 [33] 
                 0.01151 
               
               
                   
               
               
                   a Liquid. 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 182 
               
             
             
               
                   
               
               
                 Summary results of chromium coordinate compounds. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 CrF 2   
                 chromium difluoride 
                 10.91988 
                 10.92685 
                 [15] 
                 0.00064 
               
               
                 CrCl 2   
                 chromium dichloride 
                 7.98449 
                 7.96513 
                 [15] 
                 −0.00243 
               
               
                 CrO 
                 chromium oxide 
                 4.73854 
                 4.75515 
                 [37] 
                 0.00349 
               
               
                 CrO 2   
                 chromium dioxide 
                 10.02583 
                 10.04924 
                 [37] 
                 0.00233 
               
               
                 CrO 3   
                 chromium trioxide 
                 14.83000 
                 14.85404 
                 [37] 
                 0.00162 
               
               
                 CrO 2 Cl 2   
                 chromium dichloride dioxide 
                 17.46158 
                 17.30608 
                 [15] 
                 −0.00899 
               
               
                 Cr(CO) 6   
                 chromium hexacarbonyl 
                 74.22588 
                 74.61872 
                 [44] 
                 0.00526 
               
               
                 Cr(C 6 H 6 ) 2   
                 dibenzene chromium 
                 117.93345 
                 117.97971 
                 [44] 
                 0.00039 
               
               
                 Cr((CH 3 ) 3 C 6 H 3 ) 2   
                 di-(1,2,4-trimethylbenzene) 
                 191.27849 
                 192.42933 a   
                 [44] 
                 0.00598 
               
               
                   
                 chromium 
               
               
                   
               
               
                   a Liquid. 
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 183 
               
             
             
               
                   
               
               
                 Summary results of manganese coordinate compounds. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 MnF 
                 manganese 
                 4.03858 
                 3.97567 [15] 
                 −0.01582 
               
               
                   
                 fluoride 
               
               
                 MnCl 
                 manganese 
                 3.74528 
                 3.73801 [15] 
                 −0.00194 
               
               
                   
                 chloride 
               
               
                 Mn 2 (CO) 10   
                 dimanganese 
                 123.78299 
                 122.70895 [49]  
                 −0.00875 
               
               
                   
                 decacarbonyl 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 184 
               
             
             
               
                   
               
               
                 Summary results of iron coordinate compounds. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 FeF 
                 iron fluoride 
                 4.65726 
                 4.63464 
                 [15] 
                 −0.00488 
               
               
                 FeF 2   
                 iron difluoride 
                 10.03188 
                 9.98015 
                 [15] 
                 −0.00518 
               
               
                 FeF 3   
                 iron trifluoride 
                 15.31508 
                 15.25194 
                 [15] 
                 −0.00414 
               
               
                 FeCl 
                 iron chloride 
                 2.96772 
                 2.97466 
                 [15] 
                 0.00233 
               
               
                 FeCl 2   
                 iron dichoride 
                 8.07880 
                 8.28632 
                 [15] 
                 0.02504 
               
               
                 FeCl 3   
                 iron trichloride 
                 10.82348 
                 10.70065 
                 [50] 
                 −0.01148 
               
               
                 FeO 
                 iron oxide 
                 4.09983 
                 4.20895 
                 [15] 
                 0.02593 
               
               
                 Fe(CO) 5   
                 iron penta- 
                 61.75623 
                 61.91846 
                 [29] 
                 0.00262 
               
               
                   
                 carbonyl 
               
               
                 Fe(C 5 H 5 ) 2   
                 bis-cylopenta- 
                 98.90760 
                 98.95272 
                 [53] 
                 0.00046 
               
               
                   
                 dienyl iron 
               
               
                   
                 (ferrocene) 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 185 
               
             
             
               
                   
               
               
                 Summary results of cobalt coordinate compounds. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 CoF 2   
                 cobalt difluoride 
                 9.45115 
                 9.75552 [54] 
                 0.03120 
               
               
                 CoCl 
                 cobalt chloride 
                 3.66504 
                 3.68049 [15] 
                 0.00420 
               
               
                 Col 2   
                 cobalt dichloride 
                 7.98467 
                 7.92106 [15] 
                 −0.00803 
               
               
                 CoCl 3   
                 cobalt trichloride 
                 9.83521 
                 9.87205 [15] 
                 0.00373 
               
               
                 CoH(CO) 4   
                 cobalt tetra- 
                 50.33217 
                 50.36087 [53]  
                 0.00057 
               
               
                   
                 carbonyl hydride 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 186 
               
             
             
               
                   
               
               
                 Summary results of nickel coordinate compounds. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 NiCl 
                 nickel chloride 
                 3.84184 
                 3.82934 [59] 
                 −0.00327 
               
               
                 NiCl 2   
                 nickel dichloride 
                 7.76628 
                 7.74066 [59] 
                 −0.00331 
               
               
                 Ni(CO) 4   
                 nickel tetra- 
                 50.79297 
                 50.77632 [55]  
                 −0.00033 
               
               
                   
                 carbonyl 
               
               
                 Ni(C 5 H 5 ) 2   
                 bis-cylopenta- 
                 97.73062 
                 97.84649 [53]  
                 0.00118 
               
               
                   
                 dienyl nickel 
               
               
                   
                 (nickelocene) 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 187 
               
             
             
               
                   
               
               
                 Summary results of copper coordinate compounds. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 CuF 
                 copper fluoride 
                 4.39399 
                 4.44620 [63] 
                 0.01174 
               
               
                 CuF 2   
                 copper difluoride 
                 7.91246 
                 7.89040 [63] 
                 −0.00280 
               
               
                 CuCl 
                 copper chloride 
                 3.91240 
                 3.80870 [15] 
                 −0.02723 
               
               
                 CuO 
                 copper oxide 
                 2.93219 
                 2.90931 [63] 
                 −0.00787 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 188 
               
             
             
               
                   
               
               
                 Summary results of zinc coordinate compounds. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 ZnCl 
                 zinc chloride 
                 2.56175 
                 2.56529 
                 [15] 
                 0.00138 
               
               
                 ZnCl 2   
                 zinc dichloride 
                 6.68749 
                 6.63675 
                 [15] 
                 −0.00764 
               
               
                 Zn(CH 3 ) 2   
                 dimethylzinc 
                 29.35815 
                 29.21367 
                 [15] 
                 −0.00495 
               
               
                 (CH 3 CH 2 ) 2 Zn 
                 diethylzinc 
                 53.67355 
                 53.00987 
                 [65] 
                 −0.01252 
               
               
                 (CH 3 CH 2 CH 2 ) 2 Zn 
                 di-n-propylzinc 
                 77.98895 
                 77.67464 
                 [65] 
                 −0.00405 
               
               
                 (CH 3 CH 2 CH 2 CH 2 ) 2 Zn 
                 di-n-butylzinc 
                 102.30435 
                 101.95782 
                 [65] 
                 −0.00340 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE 189 
               
             
             
               
                   
               
               
                 Summary results of germanium compounds. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
               
                 C 8 H 20 Ge 
                 tetraethylgermanium 
                 109.99686 
                 110.18166 
                 0.00168 
               
               
                 C 12 H 28 Ge 
                 tetra-n-propyl- 
                 158.62766 
                 158.63092 
                 0.00002 
               
               
                   
                 germanium 
               
               
                 C 12 H 30 Ge 2   
                 hexaethyldi- 
                 167.88982 
                 167.89836 
                 0.00005 
               
               
                   
                 germanium 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 190 
               
             
             
               
                   
               
               
                 Summary results of tin compounds. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 SnCl 4   
                 tin tetrachloride 
                 12.95756 
                 13.03704 
                 [82] 
                 0.00610 
               
               
                 CH 3 Cl 3 Sn 
                 methyltin trichloride 
                 24.69530 
                 25.69118 a   
                 [83] 
                 0.03876 
               
               
                 C 2 H 6 Cl 2 Sn 
                 dimethyltin dichloride 
                 36.43304 
                 37.12369 
                 [84] 
                 0.01860 
               
               
                 C 3 H 9 ClSn 
                 trimethylin chloride 
                 48.17077 
                 49.00689 
                 [84] 
                 0.01706 
               
               
                 SnBr 4   
                 tin tetrabromide 
                 10.98655 
                 11.01994 
                 [82] 
                 0.00303 
               
               
                 C 3 H 9 BrSn 
                 trimethyltin bromide 
                 47.67802 
                 48.35363 
                 [84] 
                 0.01397 
               
               
                 C 12 H 10 Br 2 Sn 
                 diphenyltin dibromide 
                 117.17489 
                 117.36647 a   
                 [83] 
                 0.00163 
               
               
                 C 12 H 27 BrSn 
                 tri-n-butyltin bromide 
                 157.09732 
                 157.26555 a   
                 [83] 
                 0.00107 
               
               
                 C 18 H 15 BrSn 
                 triphenyltin bromide 
                 170.26905 
                 169.91511 a   
                 [83] 
                 −0.00208 
               
               
                 SnI 4   
                 tin tetraiodide 
                 9.71697 
                 9.73306 
                 [85] 
                 0.00165 
               
               
                 C 3 H 9 ISn 
                 trimethyltin iodide 
                 47.36062 
                 47.69852 
                 [84] 
                 0.00708 
               
               
                 C 18 H 15 SnI 
                 triphenyltin iodide 
                 169.95165 
                 167.87948 a   
                 [84] 
                 −0.01234 
               
               
                 SnO 
                 tin oxide 
                 5.61858 
                 5.54770 
                 [82] 
                 −0.01278 
               
               
                 SnH 4   
                 stannane 
                 10.54137 
                 10.47181 
                 [82] 
                 −0.00664 
               
               
                 C 2 H 8 Sn 
                 dimethylstannane 
                 35.22494 
                 35.14201 
                 [84] 
                 −0.00236 
               
               
                 C 3 H 10 Sn 
                 trimethylstannane 
                 47.56673 
                 47.77353 
                 [84] 
                 0.00433 
               
               
                 C 4 H 12 Sn 
                 diethylstannane 
                 59.54034 
                 59.50337 
                 [84] 
                 −0.00062 
               
               
                 C 4 H 12 Sn 
                 tetramethyltin 
                 59.90851 
                 60.13973 
                 [82] 
                 0.00384 
               
               
                 C 5 H 12 Sn 
                 trimethylvinyltin 
                 66.08296 
                 66.43260 
                 [84] 
                 0.00526 
               
               
                 C 5 H 14 Sn 
                 trimethylethyltin 
                 72.06621 
                 72.19922 
                 [83] 
                 0.00184 
               
               
                 C 6 H 16 Sn 
                 trimethylisopropyltin 
                 84.32480 
                 84.32346 
                 [83] 
                 −0.00002 
               
               
                 C 8 H 12 Sn 
                 tetravinyltin 
                 84.64438 
                 86.53803 a   
                 [83] 
                 0.02188 
               
               
                 C 6 H 18 Sn 2   
                 hexamethyldistannane 
                 91.96311 
                 91.75569 
                 [83] 
                 −0.00226 
               
               
                 C 7 H 18 Sn 
                 trimethyl-t-butyltin 
                 96.81417 
                 96.47805 
                 [82] 
                 −0.00348 
               
               
                 C 9 H 14 Sn 
                 trimethylphenyltin 
                 100.77219 
                 100.42716 
                 [83] 
                 −0.00344 
               
               
                 C 8 H 18 Sn 
                 triethylvinyltin 
                 102.56558 
                 102.83906 a   
                 [83] 
                 −0.00266 
               
               
                 C 8 H 20 Sn 
                 tetraethyltin 
                 108.53931 
                 108.43751 
                 [83] 
                 −0.00094 
               
               
                 C 10 H 16 Sn 
                 trimethylbenzyltin 
                 112.23920 
                 112.61211 
                 [83] 
                 0.00331 
               
               
                 C 10 H 14 O 2 Sn 
                 trimethyltin benzoate 
                 117.28149 
                 119.31199 a   
                 [83] 
                 0.01702 
               
               
                 C 10 H 20 Sn 
                 tetra-allyltin 
                 133.53558 
                 139.20655 a   
                 [83] 
                 0.04074 
               
               
                 C 12 H 28 Sn 
                 tetra-n-propyltin 
                 157.17011 
                 157.01253 
                 [83] 
                 −0.00100 
               
               
                 C 12 H 28 Sn 
                 tetraisopropyltin 
                 157.57367 
                 156.9952 
                 [83] 
                 −0.00366 
               
               
                 C 12 H 30 Sn 2   
                 hexaethyldistannane 
                 164.90931 
                 164.76131 a   
                 [83] 
                 −0.00090 
               
               
                 C 19 H 18 Sn 
                 triphenylmethyltin 
                 182.49954 
                 180.97881 a   
                 [84] 
                 −0.00840 
               
               
                 C 20 H 20 Sn 
                 triphenylethyltin 
                 194.65724 
                 192.92526 a   
                 [84] 
                 −0.00898 
               
               
                 C 16 H 36 Sn 
                 tetra-n-butyltin 
                 205.80091 
                 205.60055 
                 [83] 
                 −0.00097 
               
               
                 C 16 H 36 Sn 
                 tetraisobutyltin 
                 206.09115 
                 206.73234 
                 [83] 
                 0.00310 
               
               
                 C 21 H 24 Sn 2   
                 triphenyl-trimethyldistannane 
                 214.55414 
                 212.72973 a   
                 [84] 
                 −0.00858 
               
               
                 C 24 H 20 Sn 
                 tetraphenyltin 
                 223.36322 
                 221.61425 
                 [83] 
                 −0.00789 
               
               
                 C 24 H 44 Sn 
                 tetracyclohexyltin 
                 283.70927 
                 284.57603 
                 [83] 
                 0.00305 
               
               
                 C 36 H 30 Sn 2   
                 hexaphenyldistannane 
                 337.14517 
                 333.27041 
                 [83] 
                 −0.01163 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 191 
               
             
             
               
                   
               
               
                 Summary results of lead compounds. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 4 H 12 Pb 
                 tetramethyl-lead 
                 57.55366 
                 57.43264 
                 −0.00211 
               
               
                 C 8 H 20 Pb 
                 tetraethyl-lead 
                 106.18446 
                 105.49164 
                 −0.00657 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 192 
               
             
             
               
                   
               
               
                 Summary results of alkyl arsines. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 3 H 9 As 
                 trimethylarsine 
                 44.73978 
                 45.63114 
                 0.01953 
               
               
                 C 6 H 15 As 
                 triethylarsine 
                 81.21288 
                 81.01084 
                 −0.00249 
               
               
                 C 18 H 15 As 
                 triphenylarsine 
                 167.33081 
                 166.49257 
                 −0.00503 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 193 
               
             
             
               
                   
               
               
                 Summary results of alkyl stibines. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 3 H 9 Sb 
                 trimethylstibine 
                 44.73078 
                 45.02378 
                 0.00651 
               
               
                 C 6 H 15 Sb 
                 triethylstibine 
                 81.20388 
                 80.69402 
                 −0.00632 
               
               
                 C 18 H 15 Sb 
                 triphenylstibine 
                 167.32181 
                 165.81583 
                 −0.00908 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 194 
               
             
             
               
                   
               
               
                 Summary results of alkyl bismuths. 
               
             
          
           
               
                   
                   
                 Calculated 
                 Experimental 
                   
               
               
                   
                   
                 Total Bond 
                 Total Bond 
                 Relative 
               
               
                 Formula 
                 Name 
                 Energy (eV) 
                 Energy (eV) 
                 Error 
               
               
                   
               
             
          
           
               
                 C 3 H 9 Bi 
                 trimethylbismuth 
                 42.07387 
                 42.79068 
                 0.01675 
               
               
                 C 6 H 15 Bi 
                 triethylbismuth 
                 78.54697 
                 78.39153 
                 −0.00198 
               
               
                 C 18 H 15 Bi 
                 triphenylbismuth 
                 164.66490 
                 163.75184 
                 −0.00558 
               
               
                   
               
             
          
         
       
     
       REFERENCES 
       [0000]    
       
         1. D. R. Lide,  CRC Handbook of Chemistry and Physics,  86th Edition, CRC Press, Taylor &amp; Francis, Boca Raton, (2005-6), pp. 10-202 to 10-204. 
         2. B. G. Willis, K. F. Jensen, “An evaluation of density functional theory and ab initio predictions for bridge-bonded aluminum compounds,” J. Phys. Chem. A, Vol. 102, (1998), pp. 2613-2623. 
         3. D. R. Lide,  CRC Handbook of Chemistry and Physics,  86th Edition, CRC Press, Taylor &amp; Francis, Boca Raton, (2005-6), pp. 9-19 to 9-45. 
         4. T. Shinzawa, F. Uesugi, I. Nishiyama, K. Sugai, S. Kishida, H. Okabayashi, “New molecular compound precursor for aluminum chemical vapor deposition,” Applied Organometallic Chem., Vol. 14, (2000), pp. 14-24. 
         5. D. R. Lide,  CRC Handbook of Chemistry and Physics,  86th Edition, CRC Press, Taylor &amp; Francis, Boca Raton, (2005-6), p. 9-82. 
         6. G. Herzberg,  Molecular Spectra and Molecular Structure II. Infrared and Raman Spectra of Polyatomic Molecules,  Van Nostrand Reinhold Company, New York, N.Y., (1945), p. 344. 
         7. R. J. Fessenden, J. S. Fessenden,  Organic Chemistry,  Willard Grant Press. Boston, Mass., (1979), p. 320. 
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