bluuebunny/crossref_metadata_2025 huggingface dataset:
Limiting behavior of the ratio of 〈r〉 and 〈r〉 in the helium sequence
Authors: Bhattacharyya Kamal , Bhattacharyya Sankar Prasad
Published: December 2004

The limiting of the 〈r〈/〈r〈 ratio in the He sequence is critically examined at different levels of approximations leading to some interesting results.
Bender–Wu formulas and classical trajectories: Higher dimensions and degeneracies
Authors: Avron J. E.
Published: December 2004

A method for the asymptotics of the perturbation series (Bender‐Wu formulas) which is not restricted to one dimension is outlined. The method has a classical mechanic flavor and involves computing classical trajectories using classical perturbation methods. The method applies also when the unperturbed eigenvalues are degenerate. It is illustrated for the Hydrogen Zeeman Hamiltonian which is not separable and has degeneracies.
Representation theory of so(4,2) for the perturbation treatment of hydrogenic‐type hamiltonians by algebraic methods
Authors: Adams B. G. , Čížek J. , Paldus J.
Published: December 2004

The representations of so(4,2) which are applicable to the perturbation treatment of one‐electron Hamiltonians of the form H = H0 + λV are discussed, where H0 is a hydrogenic Hamiltonian. A unified construction of the representations of so(2,1) and so(3) is outlined and the representations of so(4) [and also so(3,1)] are then obtained using both the vector operator method and angular momentum recoupling techniques. The merging of so(2,1) and so(4) then leads in a natural way to so(4,2). An outline of perturbation theory applications such as the Stark and Zeeman effects is also given.
Double wells
Authors: Damburg R. , Propin R.
Published: December 2004

Asymptotic analysis of the energy levels of double‐well potentials is discussed. Based on a previously developed method, the asymptotic behavior of the perturbation theory coefficients an for the 1/R expansion of the ground state of the hydrogen molecular ion H+2 is presented in analytic form. Nine terms in the expansion of an in powers of 1/n are obtained, and the first four agree with the four obtained by numerical fitting by Čížek et al. The one‐dimensional oscillator double well and more complicated multiple wells are also discussed.
Small‐Angle electron scattering and electron density in carbon dioxide
Authors: Sasaki Yorihiko , Konaka Shigehiro , Iijima Takao , Kimura Masao
Published: December 2004

The total (elastic and inelastic) intensity of electrons scattered by CO2 was measured in the s range of 1 to 12 Å−1 and compared with the theoretical intensity calculated from the Hartree‐Fock molecular wave function and those calculated for the independent‐atom‐model (IAM) molecule. In the range of s ≲ 4 Å−1 the electron correlation effect on the total scattered intensity was found to be represented by that for the IAM molecule.
Symmetry properties of chemical graphs. IV. Rearrangement of tetragonal‐pyramidal complexes
Authors: Randić Milan , Katović Vladimir
Published: December 2004

Using a canonical numbering of vertices for the graph corresponding to a particular rearrangement of tetragonal–pyramidal complexes, all 120 permutations defining the symmetry for the rearrangement are derived. An examination of the permutations points to the symmetric groupS5, which has previously been found for isomerizations of trigonal–bipyramidal complexes and in the rearrangement of homotetrahedryl cations.
Novel graph‐theoretical approach to estimating the relative importance of individual Kekulé valence structures. I. Simple catacondensed systems
Authors: El‐Basil Sherif
Published: December 2004

A novel graph‐theoretical approach for ordering Kekulé valence structures of benzenoid hydrocarbons is presented. The approach involves the transformation of the Kekulé structures into the subspaces of their individual double bonds. The submolecules generated in this way [H. Joela, Theor. Chim. Acta 39, 241 (1975)] are ordered according to suitable connectivity indices. The resulting orders parallel those predicted from the so called Kekulé indices [A. Graocvac, I. Gutman, M. Randić, and N. Trinajstć, J. Am. Chem. Soc. 95, 6267 (1973)]. A relation is thus illustrated between VB and MO theories. The method is new and allows the prediction of the relative stabilities of structures from purely combinatorial vent without resort to computer.
PCILO study of the conformation of 20‐oxopregnane hormones
Authors: Viana Luci Martins , Takahata Yuji
Published: December 2004

PCILO calculations on conformations of the C‐17 side chains of three 20‐oxopregnane hormones, progesterone, corticosterone, and cortisol, reveal that the calculated conformations are generally in close agreement with those observed crystallographically. Average deviation of the calculated rotation angle around the C(17)—C(20) bond from the experiment is 9°. The PCILO calculations also predict the intramolecular hydrogen bond between the 20‐carbonyl group and the 21‐hydroxyl for the three hormones. This is in accordance with experiment. It was concluded that the PCILO method is reliable in predicting conformations of the side chains of hormones whereas the extended Hückel theory (EHT) predicted wrong conformations. Based upon the PCILO calculations, biological activities of the hormones are discussed.
Invariance properties of the multipole expansion
Authors: Piecuch Piotr
Published: December 2004

The calculations of long‐range interaction energy are often based on multipole expansion. The truncated multipole expansion and interaction energy calculated with it are noninvariant with respect to an arbitrary choice of local coordinate systems. In this paper we show that truncated multipole expansion of form Σ CkR−k is “numerically” independent on a choice of local coordinate systems, if convergence conditions are satisfied.
Longuet‐Higgins groups of XeF6
Authors: Brocas J. , Rusu C.
Published: December 2004

A complete permutational analysis of the XeF6 dynamics is presented. The Longuet‐Higgins group for each mode of rearrangement is obtained. On the basis of the splitting scheme of rigid molecule levels and statistical weights and selection rules for the non rigid molecule levels, it appears that transverse digonal twists and turnstile mechanisms have the same spectroscopic effects as the BPR‐6 mechanisms. Hence, the previous interpretation of IR and Raman spectra is consistent with tunneling through transverse digonal twists and turnstile mechanisms as well as through BPR‐6.
Ab initio molecular calculations with pseudopotentials: Higher quality calculations on Li2, LiH, and BeH2
Authors: Gáspár R. , Gáspár R.
Published: December 2004

New psudopotentials of higher quality have been used in ab initio molecular calculations. Simple molecular systems like Li2, LiH, and BeH2 have been investigated with varying basis sets. Energy, geometrical parameters, and dipole moments have been determined. The convergence properties of the various quantities have been investigated. They show characteristic behavior, e.g., stationary value for the energy where such behavior may be expected.
Treatment of hydrogen bonding within CNDO/2 and MINDO/3: CNDO/2H and MINDO/3H
Authors: Mohammad S. Noor , Hopfinger A. J.
Published: December 2004

A formalism has been developed to treat hydrogen‐bonded A—H…︁B systems within the CNDO/2 and the MINDO/3 methodologies. In this formalism the interactions are divided into three distinct classes; those between (a) two hydrogen‐bonded atoms, (b) one hydrogen‐bonded and non‐hydrogen‐bonded atom, and (c) two non‐hydrogen‐bonded atoms. The last class of interactions is treated solely by the existing CNDO/2 or MINDO/3 method. For A –H…︁B systems, the core resonance integrals are individually parametrized depending upon the class of the interaction. Three types of A—H…︁B systems have been thus far parametrized. Nine hydrogen‐bonded dimers have been studied using the new formalism and the current CNDO/2 and the MINDO/3 methods. MINDO/3 predicts very large interatomic (A –B) distances for the equilibrium geometry, and relatively small stabilization values for the hydrogen‐bond energies. CNDO/2 predicts the reverse. The new formalism for both CNDO/2 and MINDO/3 predicts accurate geometries as well as energies for all nine dimers. The new formalisms are called CNDO/2H and MINDO/3H. A general discussion of the nature of hydrogen bonding as exhibited by CNDO/2H and MINDO/3H is presented.
Symmetry analysis of sigmatropic rearrangements
Authors: Sun Chia‐Chung , Sun Wei‐Guo , Zhang Jing‐Chang , Jin Guang‐Zhu
Published: December 2004

Two 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

The 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

Local 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

Effective 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

The 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

In 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.
Chemical graph theory. IV. On the cyclic polynomial
Authors: Seibert J. , Trinajstića N.
Published: December 2004

The definition of the cyclic polynomial of conjugated hydrocarbons is offered. The combinatorial characteristics of this polynomial are investigated. The most important property of the cyclic polynomial is that it can be used for enumeration of conjugated circuits.
On a unified treatment of diffusion and kinetic processes
Authors: Ulmer W.
Published: December 2004

By 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

In 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

This 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

A 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.
Asymptotic analysis of exchange interactions
Authors: Shipsey Edward J.
Published: December 2004

The leading term in the asymptotic expansions of the three‐center contributions to the exchange matrix elements for a system of three hydrogen atoms is derived. The approximations are used to estimate the importance of three center interactions in “spin‐aligned hydrogen”.
Generalized Hellmann–Feynman and curvature theorems in classical and quantum mechanics
Authors: Silverman Jeremiah N.
Published: December 2004

The 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

Isomerization 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

This 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

Following 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

Second‐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

Ground‐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

The 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

The 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

The 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

We 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

Atom–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

The 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

The 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

In 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

A 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.
Factors influencing proton positions in biomolecules
Authors: Scheiner Steve , Redfern Paul , Hillenbrand Eric A.
Published: December 2004

Results of quantum mechanical calculations are presented that suggest a number of mechanisms whereby protons may be shifted from one group to another along an H bond. The first factor to be considered is a stretching of the bond that drastically raises the energy barrier to transfer. It is possible to predict barriers for an arbitrary system based only on results for a simple system and knowledge of the relevant bond length in the isolated subsystems. Factors that increase the intrinsic basicity of the B group in A‐H‐B lead not only to a lowering of the energy of the A‐HB state relative to AH‐B but also to a reduction in the barrier to transfer of the proton from A to B. Ions in the vicinity of the H bond exert a powerful influence and can shift the proton to the less basic group across a gradient of several pK units. Rather than shielding the proton from the external ion, the H bond acts instead to amplify the effects of the electric field. Reorientation of the A and B groups relative to one another, i.e., bends of the H bond, also produce surprisingly large changes in the relative energies of the AH‐B and A‐HB states. Such bends are capable of pushing the proton across to the normally less basic group, providing a mechanism of coupling conformational changes to proton ‘pumping’ activity. It is found that the high and low pH states of a given H bond can have dramatically differnt relative populations of the AH‐B and A‐HB configurations. These observations are explained in terms of fundamental concepts involving electrostatic interaction energies.
Double symmetrization and the linearly independent spin eigenfunctions
Authors: Lim T. K.
Published: December 2004

It is shown that the exclusion principle merely requires the electrons to be divided into two distinct groups, then, according to our assumption of the distinguishability of electrons, its mathematical representation can be the spatial double antisymmetrization or the spatial‐spin antisymmetrization; in the latter case an auxiliary spin double symmetrization is also required in order to distinguish the two types of electrons. The second requirement is used to recognize the fact that, although all electrons can be assumed to be indistinguishable under certain condition, their natural characteristic of two distinct groups must still be preserved.It is further shown that the double antisymmetrization (or double symmetrization) determines the spin quantum number M, whereas the Löwdin spin projector for nonorthogonal eigenfunctions and the Wigner matric basis for orthogonal eigenfunctions will decide the spin quantum number S, Both the spatial double antisymmetrizer and the spin double symmetrizer will reject all the unnecessary eigenfunctions and project out only one unique set of linearly independent eigenfunctions.
Critical phenomena in isoelectronic diatomic sequences—the 14‐electron sequence
Authors: Laurenzi Bernard J. , Mall Madeline F.
Published: December 2004

A theory of isoelectronic molecules which describes stable and metastable members of a sequence has been developed. To achieve this synthesis, it has been necessary to require that the total electronic energy surface E(R,Z,Z') for the sequence contain critical points—that is, values of the nuclear charges Z and Z' at which energy minimum, maximum [at Re(min) and Re(max)], and horizontal inflection points occur. For ground state sequences a primary physical source of these extreme points is the screened, coulombic repulsion of like‐charged atomic centers in the diatomics. With this realization, we can write analytical forms that have the correct scaling behavior and which properly model the screened, coulombic repulsion for E along certain straight‐line trajectories in the (Z,Z') plane. This leads to the observation that Re(max) values diverge logarithmically in λ‐like transitions wherever the screened coulombic repulsion becomes small as the nuclear charges vary along those trajectories.

At the horizontal inflection points the E surface contains A2 folds, as required by Thom's theorem for analytical surfaces containing one control parameter. Within the isoelectronic sequence molecular subgroups have been noted and explained in terms of the underlying atomic shell structures of the molecules' constituent atoms. Using input data for seven stable molecules together with the analytical surface selected for study, we have estimated the equilibrium bond distances Re(min), dissociation energies De(min), and harmonic force constants E(2)(min) for 18 other neutral and charged species.
Usage de l'algebre de lie su(n) dans l'etude des systems à n etats. VI. Equations linéaires d'evolution positive
Authors: Van Groenendael A.
Published: December 2004

The n‐level quantum system density‐operators evolution is not usually given by the Liouville equation, but by a more general one. This equation must keep density‐operators trace, hermiticity, and positiveness. These three conditions restrict the available kinds of evolution equations. In this paper we investigate linear equations for systems without memory effects. By using the first two conditions and the formalism we introduced in earlier papers, the evolution equation takes the form of a first order differential equation concerning the n2 – 1 dimension “coherence‐vector.” The third one is the essential object of this paper. Moreover, we obtain a cononical splitting of this equation into four parts that may be separately studied.
The spin‐projected Hartree‐Fock method: Direct optimization schemes and stability conditions
Authors: Karadakov Peter
Published: December 2004

The necessary theory to construct different direct orbital optimization schemes in the framework of the spin‐projected Hartree‐Fock (spin‐PHF) method for systems with an even number of electrons and for the proper characterization of the pertinent spin‐PHF solutions is developed using the formalism of second quantization. The treatment is based on a unitary transformation of a reference DODS (different orbitals for different spins) Slater determinant. The energy expectation value corresponding to the transformed DODS Slater determinant is expanded in a Taylor series about the reference DODS Slater determinant, including second‐order terms. On the basis of this expansion we propose several direct iterative approaches to optimize the spin‐PHF energy expectation value: for example, implementations of steepest descent and conjugated gradient techniques, and Newton–Raphson, Fletcher, and limited configuration interaction approaches. The analysis of the second‐order term in the Taylor series expansion of the spin‐PHF energy expectation value about a spin‐PHF solution is used to define stability conditions for spin‐PHF solutions. Explicit expressions are reported for all matrix elements between different spin‐projected DODS Slater determinants appearing in the treatment.
Theoretical calculation of electrode potentials: Electron‐withdrawing compounds
Authors: Lister Simon G. , Reynolds Christopher A. , Richards W. Graham
Published: December 2004

The electrode potential of 2,3‐dicyanobenzoquinone in aqueous solution has been calculated relative to parabenzoquinone using a thermodynamic cycle approach that includes accurate gasphase ab initio calculations and calculation of differences in free energies of hydration using the free‐energy perturbation method. The discrepancy between the calculated and experimental electrode potential is disappointingly large (99 mV) compared to previous studies using this approach. This, along with the experimental evidence, suggests that the experimental value itself is too large and that theoretical approaches may indeed be as reliable as experimental ones for determining redox properties of molecules such as 2,3‐dicyanobenzoquinone. In the light of this discrepancy we have examined the variation of the results with the basis set, inclusion of electron correlation and changes in the parameters used in the molecular dynamics free‐energy simulations. The results are shown to be dependent upon the torsional parameters and especially dependent upon the basis set or semiempirical method used to obtain the electrostatic potential‐derived charges. The best charge set was determined using the ab initio criteria of completeness—as far as it can be applied to large molecules—and also by studying the effect of hydration on these charges. This was done by allowing the solvent to perturb the wave function prior to the electrostatic potential determination. Thus, 3‐21G and 6‐31G* basis sets were found to give satisfactory results. Similar results were obtained using semiempirical and ab initio geometries.
Vector coupling coefficients for calculations of transition‐metal atoms and ions by the SCF coupling operator method
Authors: Plakhutin B. N. , Zhidomirov G. M. , Arbuznikov A. V.
Published: December 2004

We derived the necessary conditions to which the vector coupling coefficients (VCC) a and b describing atomic L,S‐multiplets of the configurations dN (1 ≤ N ≤ 9), should satisfy. Special attention is paid to the states of non‐Roothaan type for which VCC depend on the choice of degenerate d‐orbitals basis set determined within the accuracy up to an orthogonal transformation u. It is shown that for such states the direct sum of matrices ‖a‖ and ‖b‖ must be the non‐symmetric matrix. Obtained VCC were used for the ab initio calculations (basis set (14s9p5d)/[8s4p2d] from [15]) on first‐row transition atoms (from Sc to Cu) to compare to similar calculations [16], in which the Peterson's VCC have been used, and with calculations [15] carried out by the atomic SCF program [4] as well.
Molecular dynamics simulation for liquid water using a polarizable and flexible potential
Authors: Corongiu Giorgina
Published: December 2004

A molecular dynamics simulation for liquid water at room temperature is reported. A sample of 1000 water molecules has been analyzed with the Nieser–Corongiu–Clementi polarizable potential, to which is added vibrational flexibility. The sample was contained in a cubic box subject to periodic boundary conditions, a cutoff radius of 15.54 Å was used in evaluating energies and forces, the long‐range interactions were taken into account with the reaction field method, and the integration of the equation of motion has been performed using a sixth‐order Gear predictor–corrector algorithm. The simulation, after 35 ps of equilibration time, has been carried out for 10.4 ps with a time step of 1.25 × 10−16 s. The trajectories and velocities, collected in the production phase of the simulation, have been used to compute the geometry of the water molecule within the liquid, thermodynamical quantities, the pair correlation functions, the Dore neutron pair correlation function, X‐ray and neutron scattering structure functions, translational, rotational, orientational autocorrelation functions and their Fourier transforms, mean square displacements, diffusion coefficients, and NMR relaxation times. A detailed study on the spectral density is presented, and good agreement is found with the most recent infrared, Raman, and neutron scattering laboratory data. All the simulated properties so far analyzed are in good agreement with experimental data, and, with confidence, we can assess that our ab initio polarizable potential with inclusion of vibrations is the most reliable water potential in today's literature for the description of water.
Toward designing molecular‐electronics devices: A potential significance of highly mobile equilibrium interconversions
Authors: Slanina Zdeněk
Published: December 2004

Possible applications of computational molecular‐engineering approaches to the design of bistable conformational systems, to be potentially employed in molecular electronics, have been analyzed in isomeric–thermodynamic terms. Constructing such systems led to (conflicting) requirements, viz. an easy interconversion of the two structures (the isomerization equilibrium constant close to unity). At the same time there is a need for both isomers to be sufficiently stable and mutually different (enthalpy–entropy compensation can still ensure the equilibrium‐constant requirement). Moreover, the equilibrium criteria have to be necessarily combined with considerations of kinetics. The design problems are illustrated on two model systems: Si6H6 isomeric species and deuterium‐ and hydrogen‐bonded water dimers, HOD · OHD and DOH · OHD, respectively.
Effect of hydrogen bonding and cooperativity on stretching force constants of formamide
Authors: Shivaglal M. C. , Singh Surjit
Published: December 2004

Stretching force constants for formamide and its seven associated species involving two to four molecules hydrogen‐bonded through linear and cyclic configurations and 10 structures containing formamide hydrogen‐bonded with one to five water molecules are reported. Since ab initio calculations are rather inconvenient to perform on such big clusters and are time‐consuming, CNINDO MO calculations were carried out using the gradient method. The results demonstrate, on the one hand, the feasibility of semiempirical calculations for the evaluation of trends in force constants for big clusters where generally ab initio calculations become much involved and, on the other hand, explain the effect of hydrogen bonding and cooperativity on force constants and vibrational spectra of biologically important systems composed of formamide in the condensed phase and its aqueous solutions. The CO and NH stretching force constants are found to reduce significantly on hydrogen bonding. The reduction in force constant is further enhanced when two cyclic dimers become associated through a linear hydrogen bond. The results indicate justification for the stabilization of the formamide structure with two cyclic dimers hydrogen‐bonded together. The reduction in the force constants on hydrogen bonding also reflect the cooperativity contribution. The CO and CN stretching force constants for the structures corresponding to formamide in liquid and aqueous solution phases are in agreement with the experimental vibrational frequencies reported.
AM1 calculation of hydration to aldehyde group in nitro‐substituted benzaldehydes
Authors: Shinoda Hiroyuki , Sayama Michio , Mori Masa‐Aki , Kozuka Hiroshi
Published: December 2004

Hydration to the aldehyde group in nitro‐substituted benzaldehydes was studied theoretically by using an AM1 method. The calculated values of activation energy and heat of reaction showed good correlations with the experimental values of rate constants and equilibrium constants, respectively. To examine the hydration mechanism, localized molecular orbitals were calculated. Furthermore, expression of the molecular orbitals of supermolecular complexes in terms of occupied and vacant orbitals of the component molecules elucidated that the interaction between the lonepair orbital of water and the antibonding CO π‐orbital of aldehyde was important. 2,6‐DNBAl was concluded to be less reactive toward water than was 2.4‐DNBAl. This is consistent with the experimental result that the mutagenic activity of 2,4‐DNBAl depends not only on the reduction of the nitro group by a bacterial enzyme but also on the acetyl conjugation, but that in the case of 2,6‐DNBAl the mutagenic activity is manifested through the reduction by a bacterial enzyme. © 1993 John Wiley & Sons, Inc.