bluuebunny/crossref_metadata_2025_split huggingface dataset:
Symmetry analysis of sigmatropic rearrangements
Authors: Sun Chia‐Chung , Sun Wei‐Guo , Zhang Jing‐Chang , Jin Guang‐Zhu 
Published: December 2004

AbstractTwo small groups (E, σν) and (E, C2) are proposed to describe the orbital symmmetry of the whole reaction paths with respect to suprafacial and antarafacial sigmatropic rearrangements. Furthermore, the symmetries of the two small groups are extended to the systems as a many body treatment performed by Matsen.
Interatomic forces and Compton profiles
Authors: Thakkar Ajit J. 
Published: December 2004

AbstractThe virial theorem is used to derive rigorous relationships between the nuclear framework dependence of the impulse approximation Compton profile of a polyatomic molecule and its Born–Oppenheimer potential energy surface along a uniform scaling path. The interatomic energy‐ and force‐related difference Compton profiles for H2 are examined as an illustration.
Effect of modified virtual orbitals on local Coulomb correlation holes in FCN
Authors: Cooper Ian L. , Pounder Christopher N. M. 
Published: December 2004

AbstractLocal Coulomb correlation hole distribution functions may be used to assess the extent to which electron correlation effects are present in large scale SCF + CI wave functions. From a set of modified virtual orbitals, ordered according to their interaction with the SCF configuration, we have constructed a limited SCF + CI wave function with improved convergence characteristics with respect to that formed from the canonical virtual orbital set. These wave functions, of the same size yet with different energies, have been used to examine the range and depth of local Coulomb correlation holes in FCN. In all cases, the depth of the local Coulomb hole is no more than 10% or so of that of the corresponding Fermi hole, and the range Fermi correlation is generally less than that of Fermi correlation. This is particularly marked in the high density regions around the nuclei. The significance of our results is discussed in relation to a recent proposal for the incorporation of Coulomb correlation into the local exchange method.
Effective handling of a large configuration state function expansion for an MCSCF state and improved efficiency for two‐electron integral transformations in MCSCF
Authors: Olsen Jeppe , Yeager Danny L. 
Published: December 2004

AbstractEffective solutions for two difficulties which may be present in MCSCF calculation are discussed: (i) We show how the large configuration state function state expansion case may be handled simply and effectively without the introduction of extraneous projection operators or Lagrange multipliers; (ii) we present a simplified two‐electron integral transformation procedure which significantly reduces the operation count (and hence computational efficiency is increased) for second order and particularly for third order MCSCF procedures. The procedures we introduce use some freedom available in the orthogonal complement Cl space and the virtual orbital space to simplify MCSCF calculations.
Single versus double insertion in a simple intermolecular carbene reaction
Authors: Jug Karl , Mishra P. C. 
Published: December 2004

AbstractThe carbene reaction 1CH2 + C2H6 was studied with the semiempirical method SINDO 1. The pertinent transition states and products were obtained by geometry optimization on a CI surface. We find the insertion reaction forming C3H8 greatly favored compared to the double insertion leading to CH4 + C2H4. The result is qualitatively the same for the reaction of the two possible intermediate radicals CH3 and C2H5. The geometries and energies of all transition states are presented.
Usage de l'Algègbre de Lie su (n) Dans l'Etude des Systèmes Quantiques à n Etats. I. Quelques Conséquences Générales
Authors: Tillieu Jacques , Van Groenedael Augustin 
Published: December 2004

AbstractIn an n level quantum system there is a relation between each density operator and an element of su (n) Lie algebra. This relation is also established between Cartan's subalgebras and the complete sets of compatible observables. A scalar product is then defined in this algebra in order to introduce orthonormal bases and to simplify many calculations about expectation values of observables. Therefore simple general rules were established which show how to determine (completely or partly), from linearly independent observables, the density operator of the system.
On a unified treatment of diffusion and kinetic processes
Authors: Ulmer W. 
Published: December 2004

AbstractBy the means of gauge invariance of the continuity equation Fick's law of diffusion can be extended to also comprehend the chemical reaction. In the case of first‐order reactions a complete set of eigenfunctions is obtained. These solutions provide a tool for pattern recognition in biochemical and biological problems (e.g., formation of chromosome banding). The transport equation, including reactions of second order, exhibits soliton solutions describing the propagation of a kinetic process in a medium (molecular chain, fluids, etc.). A relationship to the soliton solutions of the nonlinear Schrödinger equation and Korteweg–de Vries equation of hydrodynamics is also indicated. The propagation of a reactive process (transition state) occurs in many problems of molecular biology. The Brownian motion of ions undergoing a reaction of first order in a constant magnetic field is also exactly solved.
Calculation of ns2 configurations for the Helium isoelectronic series without matching
Authors: Segedy John J. , Burke Edward A. 
Published: December 2004

AbstractIn the Hartree–Fock equations for the He isoelectronic series, the two‐point boundary conditions on one of the differential equations is replaced by initial conditions specified at large distances. [The condition Y′(∞) = 0 replaces the condition Y (0) = 0.] This permits eigenvalues of ns2 configurations to be determined as the zeros of a certain function arising from inward integrations, without having to match the solution with a corresponding outward integration. Calculations are performed for n = 1,2,3 for H− through Be2+. Resulting energy values and radial densities are presented. Agreement is found, to the eight significant figures calculated here, with the n = 1 results given by Roothaan and Soukup.
Unitary group approach to the many‐electron problem. I. Matrix element evaluation and shift operators
Authors: Gould M. D. , Chandler G. S. 
Published: December 2004

AbstractThis is the first paper in a series of three directed toward the evaluation of spin‐dependent Hamiltonians directly in the spin‐orbit basis. In this paper we present a new and complete derivation of the matrix elements of the U(n) generators in the electronic Gel'fand basis. The approach employed differs from previous treatments in that the matrix elements of nonelementary generators are obtained directly. A general matrix element formula is derived which explicitly demonstrates the segment level formalism obtained previously by Shavitt using different methods. A simple relationship between the matrix elements of raising and lowering generators is determined which indicates that in CI calculations, only the matrix elements of raising generators need be calculated. Some results on the matrix elements of products of two generators are also presented.
Convergence problems in SCF calculations: Further applications of a new technique based on the use of inverse Fock operator
Authors: Kumar Das Kalyan , Mukherjee Debashis , Bhattacharyya Sankar Prasad , Bhattacharyya Debendra Madhab , Khan Priyotosh 
Published: December 2004

AbstractA recently proposed orbital optimization technique based on the use of the inverse of the level‐shifted Fock operator is successfully applied to a large number of pathologically divergent cases. The possibility of eliminating convergence problems by adopting a similar modification in the operation of the orthogonal gradient method is also successfully tested.
Generalized Hellmann–Feynman and curvature theorems in classical and quantum mechanics
Authors: Silverman Jeremiah N. 
Published: December 2004

AbstractThe generalized Hellmann–Feynman and curvature theorems are derived for the generalized Sturm–Liouville‐type eigenvalue equation which is widely encountered in many branches of physics. In classical mechanics, the Sturm–Liouville eigenvalue equation primarily arises from applying the theory of small oscillations to vibration problems while, in quantum mechanics, the most important example is the time‐independent Schrödinger equation. The generalized theorems, respectively, provide simple useful expressions for the first and second λ derivatives of the eigenvalue where λ is an arbitrary real parameter appearing in the eigenvalue equation. These results, which apply to both classical and quantal systems, include as special cases the well‐known quantum mechanical Hellmann–Feynman and curvature theorems for the time‐independent Schrödinger equation, thus unifying the formalism. This connection between classical and quantum mechanics is of interest per se, and also because classical eigenvalue equations find application in the treatment of some quantum chemical problems. Two derivations of both generalizations are presented, the first proof applying to exact and Rayleigh–Ritz (linear variational) solutions of the eigenvalue problem, and the second, more general one, to arbitrary optimal variational as well as exact solutions. Necessary and sufficient conditions for the validity of the results are discussed. To demonstrate the insight they afford, several applications of the theorems in conjunction with perturbation theory are described.
Symmetry properties of chemical graphs. VI. Isomerizations of octahedral complexes
Authors: Randić Milan , Davis Michael I. 
Published: December 2004

AbstractIsomerization of octahedral complexesXY6, by a mechanism known as diagonal twist (in which two ligands incispositions, one to another, exchange sites) is considered. Construction of the corresponding isomerization graph is outlined (reported before by Balaban) and the problem of determining its symmetry is considered. Alternative routes for deducing the order of the automorphism group are described. The group is confirmed to beS6and representative symmetry permutations (one for each of the 11 classes ofS6) are shown. Alternative pictorial representations of the 15‐vertex graph are also shown.
A unitary group formulation of many‐body theory: Diagram systematics and use of the spin shifts
Authors: Mukhopadhyay Atri , Pickup Barry T. 
Published: December 2004

AbstractThis paper shows that the spin‐shift formalism developed in B. T. Pickup and A. Mukhopadhyay [Int. J. Quantum Chem. 26, 101 (1984)] supports a one‐component diagrammatics which has a systematics akin to that in the spin‐orbital many‐body theory. The diagrams are neither Goldstone nor Yutsis type, and characterize the chain U(2R) ⊃ U(R)⊗SU(2) on which the spin‐shift formalism is based. Accordingly, while the lines in such diagrams are labeled by the orbital indices, the diagram structure adequately reflects the irreducible representation of the group U(R). In this sense the paper presents a unitary group approach to the natural generalization of the usual many‐body theory for the spin‐adapted cases. A set of very simple rules is derived; their similarity with the corresponding rules in the ordinary many‐body theory and practical utility are discussed in connection with (a) matrix elements over many‐electron spin states and (b) closed‐ and open‐shell many‐body perturbation theory. A possibility of integral‐driven many‐body perturbation theory for open‐shells is indicated. Connections of this formalism with others are also discussed.
Sur la theorie quantique des equations de hartree–fock dependant du temps. IV. Expression matricielle du tenseur d'hyperpolarisabilité
Authors: Smet F. , Groenendael A. Van 
Published: December 2004

AbstractFollowing a paper drawing up a matrix form of the time‐dependent Hartree–Fock equations which allow the calculation of the nth harmonic generation, we establish the matrix form of the hyperpolarizability tensor. In case of linear polarization, we show that, if the ground‐state orbitals are real, so are the perturbed ones. This involves an easy expression of the hyperpolarizability tensor.
Electron correlation effects in the 4f14 shell
Authors: Jankowski K. , Malinowski P. , Sokołowski A. , Lindgren I. , Mårtensson‐Pendrill A.‐M. 
Published: December 2004

AbstractSecond‐order Rayleigh–Schrödinger Hartree–Fock perturbation theory is applied to evaluate the correlation energy for the 4f14 shell of Yb. The partial‐wave (PW) increments to the pair energies, and the total correlation energy are calculated using first‐order radial pair functions obtained as the solution of two‐dimensional differential equations. These equations are solved using the Chalmers University version of the finite difference method. The total second‐order correlation energy amounts to 0.89573 hartree. The results for the pair energies, which are close to the all‐external pair energies, are compared with related CI values. It turns out that the correlation effects within the 4f shell of rare‐earth systems are dominated by the all‐external effects. The ff and gg PWS are dominant in the description of the correlation effects in the 4f shell and provide 80% of the total correlation energy. Next in importance are the dd, hh, and dg PWS which provide 12% of the total correlation energy.
Ground‐state energies of closed‐shell atoms
Authors: Karwowski J. , Styszyński J. 
Published: December 2004

AbstractGround‐state energies of He, Be, and Ne isoelectronic series have been calculated. The Dirac–Hartree–Fock energy values have been corrected by adding Breit, vacuum polarization, self‐energy, nuclear mass, and electron correlation corrections. The resulting energies are compared with the experimental values. As a result, an estimate of the correlation‐relativistic cross‐term energy is obtained. The effect, for large‐Z atoms, proves to be quite substantial.
Generalized Dirac identities and explicit relations between the permutational symmetry and the spin operators for systems of identical particles
Authors: Katriel J. , Paldus J. , Pauncz R. 
Published: December 2004

AbstractThe well known one‐to‐one correspondence between the eigenstates of the total spin for a system of spin‐½ particles and irreducible representations of the symmetric group with up to two rows in the Young shape is the basis of interesting formal developments in quantum chemistry and in the theory of magnetism. As an explicit manifestation of this correspondence the class operators of the symmetric group are demonstrated to be expressible in terms of the total spin operator. This correspondence does not hold for higher elementary spins. The extension to arbitrary spin is investigated using Schrödinger's generalization of the Dirac identity, which expresses the transpositions in terms of two‐particle spin operators. It is shown that additional operators, which for σ = ½ reduce to the total spin operator, are needed for a complete classification. Some aspects of the formalism are developed in detail for σ = 1. In this case a classification identical with that provided by the irreducible representations of the symmetric group is obtained in terms of the eigenstates of two commuting operators, one of which is the total spin operator.
Energy levels of paramagnetic ions: Algebra. III. The case of dN ions in cubical symmetry
Authors: Kibler Maurice , Grenet Geneviève 
Published: December 2004

AbstractThe formalism developed in the first two papers of this series is applied to the investigation of a new weak‐field model. This crystal‐field model lies on the use of a symmetry‐adapted weak‐field basis and an effective Hamiltonian involving in a symmetrical way both spin‐ and orbit‐dependent contributions. Some general properties of this Hamiltonian are studied and complete calculation of its matrix elements is conducted in a symmetry‐adapted weak‐field basis in the case of an arbitrary configuration nlN in any symmetry. The case of a configuration ndN in octahedral symmetry is fully explored. In this case, the proposed weak‐field model is restricted to a 12‐parameter model which accounts for isotropic and anisotropic Coulomb interactions, isotropic and anisotropic spin‐orbit interactions, and crystal‐field interactions. A comparison between this 12‐parameter weak‐field model and the 14‐parameter strong‐field model is established. Equivalence between the latter two models requires two constraint relations to be satisfied for some strong‐field parameters. These two relations are examined with various viewpoints.
The relationship between electron densities and the electronic substituent constants for substituted pyridines
Authors: Pilarski Bogusław , Os̀miałowski Krzysztof , Kaliszan Roman 
Published: December 2004

AbstractThe electron density at the pyridine nitrogen atom and the π‐electron density of the pyridine ring were calculated by the CNDO/2‐MO method assuming standard bond lengths and angles. The indices were found to correlate with the pKa values of pyridine derivatives and with the electronic substituent constants of the Hammett type. The correlations were best for four‐substituted pyridines, making the routine CNDO/2‐MO calculations useful for studies of quantitative relations between structure and biological activity of the compounds.
Theoretical studies on the interaction of proteins with base pairs. II. Effect of external H‐bond interactions on the stability of guanine–cytosine and non‐Watson–Crick pairs
Authors: Sarai Akinori , Saito Minoru 
Published: December 2004

AbstractWe studied the stability of guanine–cytosine and non‐Watson–Crick pairs in the presence of H‐bond interactions with various amino acid side chains, by using ab initio MO method. The external H‐bond interactions stabilize or destabilize the base pairs, depending on the type of interacting residues and the site of the interaction. The pattern of the H‐bond effect on the base‐pair stability is quite different than in the case of adenine–uracil pair previously reported. From the present results, together with the previous results on adenine–uracil pair, we obtain a general rule for the effect of external H‐bond interactions on the stability of base pairs. The site‐specific effect of the H‐bond interactions can be consistently explained by the cooperative interaction between external and base‐pair H bonds. We discuss the application of the present results in the following biological processes: One is the protein‐induced specific melting of double‐stranded DNA, which is involved in transcription process. The present results suggest that H‐bond interactions of protein residues at specific site of base pairs can weaken base‐pair H bonding, which would assist the opening of double‐stranded DNA. The other is the control of mutation in replication process. We suggest that proteins can discriminate non‐Watson–Crick pairs against Watson–Crick pairs by H‐bond interactions and can either induce or suppress mutation during DNA replication.
Overlap integrals for atom–metal surface interactions
Authors: Murphy William C. , George Thomas F. 
Published: December 2004

AbstractAtom–metal surface overlap integrals are of utmost importance in surface energy calculations. Direct numerical evaluation of these triple integrals can be very time‐consuming. However, we have developed an exact algebraic expression, where formulas for the coefficients are given for both the general case and the special case where the parallel wave vector is zero. Some numerical examples of the overlap for H on Al are given.
The role of d orbitals in tetrahedral hybrid orbitals of oxy‐ions
Authors: Yang Cao 
Published: December 2004

AbstractThe hybrid orbitals of tetrahedral oxy‐ions containing some d character have been calculated by maximum overlap method. The d characters of hybrid orbitals increase in the order of SiO, PO, SO, ClO, and decrease in order of GeO, AsO, SeO, BrO. The bond strengths are also obtained for these ions. The hybrid Orbital of VO, CrO, and MnO are of the type d3s as the result of calculation.
Energy levels of paramagnetic ions: Algebra. IV. The case of fN ions in cubical symmetry
Authors: Kibler Maurice , Grenet Geneviève 
Published: December 2004

AbstractThe symmetry‐adapted formalism and the weak‐field model described in the first three papers of this series are applied to the case of a configuration nfN in octahedral symmetry. In this case, the latter weakfield model is restricted to a 30‐parameter model which accounts for isotropic and anisotropic Coulomb (repulsion) interactions, isotropic and anisotropic spin‐orbit interactions, and crystal‐field interactions. A comparison between this 30‐parameter weak‐field model and a 33‐parameter strong‐field model is established. Equivalence between these two models requires three constraint relations to be satisfied for some strong‐field parameters. The three relations are examined on various viewpoints.
A new algebraic approach to the eigenvalue problems of linear differential operators without integrations
Authors: Demiralp Metin 
Published: December 2004

AbstractIn this work, a new approximation scheme based on the evaluation of the pointwise expectation of the Hamiltonian (H) via a conveniently chosen basis set is proposed. This scheme does not necessitate integration; however, physical and mathematical considerations in choosing the basis set are considerably important when very precise and rapidly convergent results are desired.In this method, the best linear combination of “well‐selected” basis functions are sought in a way such that H ψ / ψ is flat in the neighborhood of a conveniently chosen point in the domain of H. This yields an algebraic eigenvalue problem. Some concrete applications that have already been realized confirm the efficiency of this approach.
Nuclear charges and molecular total energies: A rule on nested reaction globes
Authors: Mezey Paul G. 
Published: December 2004

AbstractA simple convexity relation for the nuclear charges of isoelectronic molecules implies some energy relations and topological constraints on their respective reaction globes. These energy relations take the form of a “rule on nested reaction globes.” These reaction globes and their special cases of conformational globes describe the interrelations within families of chemical reactions and conformational changes, respectively. The nuclear charge relations lead to constraints on the relative positioning of reaction globes. These relative positions provide a concise description of energy relations for families of reactions. Conditions are given for a special case, when one reaction globe is completely enclosed by another. The general conclusions are illustrated by results of ab initio potential surface calculations on the conformational problem of 1,4‐disubstituted 2‐butenes.