bluuebunny/crossref_metadata_2025 huggingface dataset:
Open‐ and closed‐shell states in few‐particle quantum mechanics. II. Classification of atomic states
Authors: Smith Vedene H. , Kutzelnigg Werner
Published: December 2004

The system developed in the first paper of this series for the classification of states as open‐ or closed‐shed type is applied to atomic states. These may be classified in the isoelectronic limit (Z → ∞) from knowledge of the true wave function in this limit. One‐matrix occupation numbers are tabulated for a number of states of the first‐row atoms in the limit Z → ∞ and the states classified.

A classification for finite Z is possible in the framework of the Z‐dependent perturbation theory by use of a thoerem for the stability of a closed‐shed with respect to small perturbations. Such a stability does not hold in general for open‐shel states.
Long‐range interactions between atoms and charges by double‐perturbation treatment
Authors: Landman U.
Published: December 2004

A method of calculating the energy of the long‐range interaction between atoms and charges is presented. Simplification of the solution of the perturbation equations is achieved by a formal use of the “Double‐Perturbation Method”. Numerical results for the energies of the 2pσ state of HeH+2 are obtained.
Remark on lower bounds to eigenvalues
Authors: Weinhold F.
Published: December 2004

It is shown that the familiar Temple, Stevenson‐Crawford, and Weinstein lower bound formulas for eigenvalues are consequences of a much stronger general lower bound formula and the weak “Eckart criterion” for the overlap of the approximate and true wave functions.
Energy levels of paramagnetic ions: Algebra. II
Authors: Kibler Maurice
Published: December 2004

The correspondence rules between the algebra of coupling coefficients of the special unitary group SU(2) and the associated algebra of a subgroup G of SU(2) are presented. The matrix elements of the irreducible representations of G are written in a convenient quantization scheme and different relations between these matrix elements and the Clebsch‐Gordan coefficients of G are derived. Such a formalism is appropriate for numerous spectroscopic problems. As an example, it is applied to crystal field theory and electron paramagnetic resonance. General formulas from which a large number of results are rederived and generalized in a straightforward fashion are given. Numerical values of coupling coefficients for the tetragonal and cubic groups are listed in the Appendix.
Long range intermolecular forces between conjugated systems
Authors: Schweig A.
Published: December 2004

The long range intermolecular forces in terms of the interaction energies between two conjugated molecules are computed and discussed for the cases: (a) a point charge and ethylene, (b) two ethylene molecules, (c) two hexatriene molecules, (d) two benzene molecules, (e) two naphthalene molecules, and (f) two polar merocyanine molecules. The calculations are based on Buckingham's theory of long range intermolecular forces and the author's values for multipole moments and polarizabilities presented previously. The advantage of the treatment is: asymmetric molecules are correctly described and the intermolecular potential is better approximated than by the usual dipole approximation.
A model calculation of protonic mobility in ice
Authors: Kubarev S. I. , Shedrin M. I.
Published: December 2004

The protonic conductivity in ice crystals is considered within the framework of strong coupling developed earlier by the present authors for semiconductors with narrow bands and strong coupling of electrons with phonons. The generalization for a two‐band model is developed. The model used is the one described by Gosar and Pintar, the principal feature of which is the concept of the protonic conduction bands. The analytical expression for the protonic mobility is given. The results of the theory are in qualitative agreement with the experimental data.
The asymptotic Casimir–Polder potential from second‐order perturbation theory and its generalization for anisotropic polarizabilities
Authors: Craig D. P. , Power E. A.
Published: December 2004

It is shown how the leading term for very large R of the Casimir–Polder potential, that is the term varying as R−7, arises in second‐order perturbation theory applied to the interaction Hamiltonian − \documentclass{article}\pagestyle{empty}\begin{document}$ - \sum\limits_\sigma {\frac{1}{2}\alpha (\sigma){\rm E}^{ \bot ^2 } (\sigma)} $\end{document}. The generalization to anisotropic molecules is calculated and the angular dependence of the long range intermolecular potential in this case is given explicitly in terms of the principal polarizabilities and their corresponding directions of the two molecules.
Theory of two shells of atomic electrons using non‐orthogonal radial orbitals
Authors: Jucys A. P. , Bandzaitis A. A. , Grudzinskas J. J.
Published: December 2004

A theory for handling non‐orthogonal radial orbitals of two shells of atomic electrons based on the mathematical apparatus of irreducible tensor operators is presented. The general expressions for one‐ and two‐electron operator matrix elements are given.
Electronic structure of graphite
Authors: André J.‐M. , Leroy G.
Published: December 2004

Semi‐empirical calculations of the π‐band structure of planar and three‐dimensional graphite are described. Special attention is given to the significance of band parameters. The theoretical results are in good agreement with experiment.
Natural orbital iterations for the ground state of nitric oxide
Authors: Kouba Joseph E. , Öhrn Yngve
Published: December 2004

A method for the use of natural orbital iterations in limited CI calculations is discussed. This method is then applied to the ground X2II state of the nitric oxide molecule at its experimental equilibrium internuclear separation to yield the total energy, dipole moment, spin densities at each nucleus, and approximate natural spin orbitals for this molecule.
All‐electrons band structure of Polyene
Authors: André Jean‐Marie , Leroy Georges
Published: December 2004

In this work, we report an all‐electron SCF–LCGO–CO computation for the ground state wave‐function of an infinite polyenic chain. This work demonstrates that ab initio calculations on the electronic structure of polymers become actually feasible. Our results are compared with previously obtained semi‐empirical ones.
Intermolecular interactions in the region of small overlap
Authors: Basilevsky M. V. , Berenfeld M. M.
Published: December 2004

In order to treat the interaction energy of two molecules a standard Rayleigh‐Schrödinger perturbation theory is developed. The Hartree–Fock functions of the separated molecules are used as one particle basis functions, the initial set of states being truncated and non‐orthogonal. The non‐orthogonality is included into the Hamiltonian by orthogonalization of the basis set. The unperturbed Hamiltonian is chosen so that it possesses the correct symmetry properties with respect to the electron permutations between different molecules. The procedure of this kind automatically results in the appearance of charge transfer states.

A graphical technique is elaborated which is a modified version of the Feynman–Goldstone technique and provides a convenient representation of the interaction energy contributions of any order. As an example the first‐ and the second‐order diagrams are considered.

A correct expression for the dispersion energy is obtained which differs by a factor from that of the theory using a nonsymmetrical zero approximation.
On the theory of electron correlation in atoms and molecules. II. General cluster expansion theory and the general correlated wave functions method
Authors: Roby Keith R.
Published: December 2004

An exact cluster expansion of many electron wave functions is derived, beginning with a finite linear combination of Slater determinants rather than the more usual single determinant. This general cluster expansion is found to apply both in the case where all possible Slater determinants from a finite set of spin orbitals are included in the linear combination, and in the case where the number of determinants is restricted.

The special properties of that finite linear combination of determinants closest to the exact wave function in the least squares sense are studied. These properties lead to the derivation of a general correlated wave functions method, illustrating again the close relationship between methods of this type and cluster expansion theory. Additional approximations, necessary for practical calculations, are set out.
Branch point singularities in the energy of the delta‐function model of one‐electron diatoms
Authors: Certain P. R. , Brown W. Byers
Published: December 2004

Two different perturbation series (the polarization expansion and a united‐atom expansion) of the ground state energy of the delta‐function model for one‐electron diatoms are studied and the radii of convergence are determined. For both expansions the singularity in the energy which limits the radius of convergence is a branch point with exponent one‐half. The physical significance of the branch point is that for particular values of the perturbation parameter, two different energy eigenvalues coalesce. The positions of the branch points are computed as a function of the internuclear separation R. For all values of R, both series converge for all physical values of the perturbation parameters. A lower bound to the radius of convergence of the polarization expansion has been computed previously by Claverie. It is proved in the present paper that the lower bound calculation is in fact an exact determination of the radius of convergence. The results of the model study are applied to real one‐electron diatoms to suggest the possible location of a branch point singularity in the energy of the ground state.
On the determination of radial electron–electron distribution functions
Authors: Benesch Robert
Published: December 2004

The problem of evaluating the radial electron–electron distribution function P0(r12) from the spin‐free 2‐particle density matrix P(2)(r1, r2Ir'1, r'2) is considered in detail. The analysis is first applied to 2‐electron S‐type functions built from l2 configurations. For the special case l = 0, the expression for P0(r12) reduces to the result obtained by Coulson and Neilson.

For non‐spherically symmetric states of N‐electron atoms, the angular integrations are handled by a procedure used by Calais and Löwdin in their evaluation of atomic integrals containing functions of r12. Consideration is also given to the evaluation of necessary radial integrals.
Comparison of several expansions in the calculation of static electric dipole π polarizability of conjugated molecules by pertubation theory. The ground and the first excited singlet states
Authors: Matzke P. , Chacon O. , Sanhueza E. , Trsic M.
Published: December 2004

Ground and excited singlet state dipole electric π polarizabilities of a set of conjugated molecules are calculated. Second order perturbation theory is used in the Epstein–Nesbet and Möller–Plesset versions. Hückel and SCF‐LCAO‐MO are used alternatively as a basis. The Möller–Plesset–SCF–LCAO–MO calculation appears well related to experimental values.
The valence electron density distribution of hydrogen bonded systems in the iterative extended Hückel approach. III. The pyrrole–pyridine system
Authors: Almlöf Jan , Mårtensson Olle
Published: December 2004

The valence electron distributions of the hydrogen‐bonded systems C4H4NH … NC5H5 formed from pyrrole and pyridine and C4H4N− … HNC5H+ from pyrrole anion and pyridinium ion have both been investigated using the charge iterative extended Hückel method. The results are presented in the form of contour diagrams showing the charge densities in pertinent sections of the hydrogen‐bonded systems, and also in the corresponding parts of the non‐interacting constituent molecules. The density differences between interacting and non‐interacting systems brought about by hydrogen bonding are also presented. Like earlier investigated hydrogen bond types, an NH … N bond is characterized by an increase of charge density in the covalent NH bond, and a decrease at the acceptor atom. The formation of a rather low maximum in the centre of the H … N bond is also observed. The hydrogen bonding interaction causes a transfer of charge to the donor molecule of the same order of magnitude in both systems considered.
Properties of pyridine and pyrazine from ab initio molecular orbital wave functions
Authors: Ha Tae‐Kyu , O'Konski Chester T.
Published: December 2004

Various molecular properties have been calculated for pyridine and pyrazine from Gaussian lobe ab initio SCF molecular wave functions. Values are compared with available experimental data. In general, agreement is satisfactory with the exception of the rather sensitive asymmetry parameter of the quadrupole coupling tensor. The distributions of total electronic charge, and of selected molecular orbitals have been displayed as plots of the charge density contours in two dimensions.
Modified Gaussian functions and their use in quantum chemistry. I. Integrals
Authors: Gołlebiewski A. , Mrozek J.
Published: December 2004

A modified Gaussian function g(u, v, w, a, R) = const
equation image
s(a, R) is considered where l = u + v + w, s (a, R) is a 1s‐type Gaussian function centered at R, a is the coefficient in the exponent of the 1 s Gaussian function and X, Y, Z are components of R. General formulae are derived for overlap integrals, kinetic energy integrals, nuclear attraction integrals, and electron repulsion integrals, valid for any l. The formulae are much simpler than those derived by Huzinaga for Cartesian Gaussian functions.
Modified Cartesian Gaussian functions and their use in quantum chemistry
Authors: Gołlębiewski A. , Mrozek J.
Published: December 2004

The general formula for the electron‐electron repulsion integral in the modified Cartesian Gaussian basis set derived in Ref. [1] is simplified. A general relation between the standard and modified CG functions is given. A possible use of the modified CG functions to quantum chemical calculations which include the correlation factor rij2 is indicated.
A comparative calculation on excited state energies of some conjugated hydrocarbons
Authors: Mukherjee Debashis
Published: December 2004

The energies of the single‐configuration lowest π – π* singlet and triplet states of some conjugated hydrocarbons have been calculated by the MC‐SCF method using the conjugate‐gradient technique of minimisation. The results are compared with those calculated by other methods currently in use, like (a) single‐configuration calculation with VN−1 potential for virtual orbitals; (b) CI calculation involving singly excited states; and (c) TDHF method. It has been concluded that the results for the MC‐SCF method are very good, considering that only a single open‐shell configuration is involved.
Static and dynamic first‐ and second‐order properties by variational wave functions
Authors: Moccia R.
Published: December 2004

The problem of the evaluation of first‐ and second‐order energies by the use of arbitrary variational wave functions is examined in detail for time‐independent perturbations as well as for time‐dependent perturbations. By using a compact formalism the general formulae to be used for the case of a fully optimized set of variational parameters are readily obtained and the most prominent features are examined. The generality of the approach is tested by showing how some widely used methods are obtained by using particular types of variational wave functions. The case of incompletely optimized sets of variational parameters is examined examined extensively and several approaches at different levels of approximation are proposed. Emphasis is put upon the importance of considering, in the calculation of higher‐order energies, the variational parameters which may be of negligible importance, and thus often neglected, in the absence of perturbations.
Spin‐projected EHF method. II. The equations for successive optimization of the orbitals in the many‐electron case
Authors: Mayer I. , Kondász J.
Published: December 2004

The extended Hartree–Fock equations of the spin‐projected scheme are derived in a form suitable for the construction of a surely convergent method of solution using successive optimization of the individual orbitals. The derivation is based on a specific form of the generalized Brillouin theorem.
Hartree‐Fock calculation of cohesive energies and equilibrium lattice constants for solid Li and Be
Authors: Stoll H. , Preuss H.
Published: December 2004

A method is described for calculating cohesive energies of solids in the single‐determinant approximation including the full Hartree‐Fock exchange. The method involves (1) the construction of a rapidly convergent series in vectors of the direct and reciprocal lattice for the Fock matrix, (2) a decoupling procedure for the k‐dependence of the Fock matrix, which works even in the case of strong interatomic overlap. An application to Li and Be is given. Agreement with experiment to 10% is achieved for the cohesive energies and to 5% for the equilibrium lattice constants.
Effect of the rotational motion of molecules on their optical and magneto‐optical activity
Authors: Svendsen E. NØRby , Hameka Hendrik F.
Published: December 2004

In the theoretical descriptions of natural and magneto‐optical activity it is customary to average classically over molecular orientations. We develop a theoretical description of the two phenomena that includes the correct quantum mechanical representation of the rotational motion in order to find out whether or not the customary procedure is correct. We find that the inclusion of the quantum mechanical description of the rotational motion leads to the same result in the theory of optical activity and magneto‐optical activity as the naive classical averaging over molecular orientations.
Wechselwirkungen gerichteter ladungsverteilungen. I. Irdo (intermediate retention of differential overlap)‐berechnungen zum einfluß des einsamen elektronenpaars am stickstoff auf die relative acidität des β‐picolins
Authors: Birner P. , Köhler H.‐J. , Weiss C.
Published: December 2004

It is pointed out by using the IRDO treatment of Jesaitis et al. that the failure of the CNDO/2 method in predicting the acidity difference between toluene and β‐picoline has its reason in the incorrect handling of the nitrogen lone pair. To predict correctly the relative acidity of β‐picoline, it is necessary and sufficient to include only those NDDO terms into the IRDO calculation which contain interactions with the nitrogen. The most important interactions are those between the nitrogen and the three centers of the heterocycle which take over a large part of the negative charge in the corresponding β‐delocalized carbanion.
The relationship between the Rayleigh‐Schrödinger and asymptotic perturbation theories of intermolecular forces
Authors: Whitton W. N. , Brown W. Byers
Published: December 2004

The relation of the straightforward Rayleigh‐Schrödinger perturbation theory for the interaction of two atoms to the asymptotic exchange theory is described. The one‐electron case of a hydrogen atom perturbed by a nucleus is examined in detail. It is shown that the asymptotic theory contains an infinite summation of terms in the Rayleigh‐Schrödinger series. The nature of the branching between states and its implications for convergence is elucidated.
Clebsch‐Gordan coefficients for chains of groups of interest in quantum chemistry
Authors: Kibler M. R. , Guichon P. A. M.
Published: December 2004

The algebra of the representation of the special unitary group SU(2), the universal covering of the proper rotation group SO(3), is studied in a nonstandard basis. We are using a basis adapted to a chain of type SU(2) ⊃ …︁ ⊃ G″ ⊃ G′ ⊃ G. The introduction of such a chain enables us to label, at least partially, the elements of the irreducible tensorial sets under SU(2) with irreducible representations of G, G″ G″, …. We are thus led to introduce the restriction SU(2) → …︁ → G″ → G′ → G in the Wigner‐Racah algebra of the group SU(2). The physical interest of this machinery lies in the fact that the double group of any point symmetry group belongs, up to an isomorphism, to the considered chain. The formalism described in this paper thus appears to be useful in molecular and solid‐state calculations. It is particularly efficient in the fields of vibrational‐rotational and electronic spectroscopy of molecules. In Appendix A the master formulae, principally the Wigner‐Eckart‐Racah theorem, for the Wigner‐Racah algebra of a chain of compact topological groups (discrete or continuous) are briefly discussed. Lastly, a programme for computing Clebsch‐Gordan coefficients for a chain SU(2) ⊃ …︁ ⊃ G″ ⊃ G′ ⊃ G and numerical results for chains isomorphic to SU(2) ⊃ O′ ⊃ D′4 ⊃ D′2 are described in Appendix B.
Influence de la Structure de Diverses Fonctions sur l'Evaluation de l'Energie de Correlation
Authors: Et André Julg Alain Pellegatti
Published: December 2004

The influence of various correlation functions, multiplying the monoelectronic space function, is studied and applied to the Helium atom and its isoelectronic series. We used Slater‐type basis orbitals and the ground and first excited states have been studied, taking into account the virial and cusp conditions. In the ground state, a very good value for the correlation energy is obtained, using a function of the type

For the excited states, this type of function overestimates the assumed value of the correlation energy.
A finite‐difference approach to the electron correlation problem
Authors: Fimple W. R. , Unwin M. J.
Published: December 2004

A variant of the transcorrelated method of Boys and Handy employing finite differences is presented. It is based upon the following two properties of the transcorrelated Hamiltonian operator C−1HC: (1) C−1HC possesses an energy eigenvalue spectrum which is identical to that associated with H itself; and (2) if \documentclass{article}\pagestyle{empty}\begin{document}$$ C \equiv \begin{array}{*{20}c} \pi & {e^{r_{ij} /2} } \\ {i > j} & {} \\ \end{array} $$\end{document} then C−1HC is free of the singularities of H at the points where the interelectron separation rij is zero. A bivariational principle for approximating the eigenvalues and the left and right eigenfunctions of C−1HC is introduced and the resulting set of coupled integro‐differential equations are solved in finite‐difference form by means of a coupled self‐consistent field, Newton Raphson algorithm. As a preliminary test of the method, a calculation of the ground‐state energy of the helium atom is presented.
A characterization of pairs of subspaces for quantum chemical applications of the Galerkin–Petrov method
Authors: Jankowski K.
Published: December 2004

A method is proposed for characterizing pairs of finite dimensional subspaces of the Hilbert space. The method might be helpful for the proper selection of coordinate and projective spaces leading to reliable realizations of the Galerkin–Petrov method for use in quantum chemistry. In order to illustrate the method some numerical results are presented.
Modified one‐electron hamiltonian method in the MC SCF theory
Authors: Kuprievich V. A. , Klymenko V. E.
Published: December 2004

For orbital optimization within the MC SCF theory a modification of the OEH method is proposed with the direction of descent determined according to the Fletcher–Reeves gradient method. The combined method developed on this basis ensures the convergence of the iterative process when the Hessian singularities occur. The convergence properties of the method proposed are studied by performing the ab initio water molecule calculations using two types of multiconfigurational wave functions.
Charge distribution analysis in terms of Berlin's binding and antibinding regions for Li2 and F2
Authors: Zuvia Marilena , Ludeña Eduardo V.
Published: December 2004

The MCSCF wave functions of Das for Li2, and Das and Wahl for F2, have been analyzed in terms of Berlin's binding and antibinding regions. The effect of electronic correlation on the charge distributions in these regions is studied. The process of bond formation in going from separated atoms to the correlated molecule is also discussed with reference to Berlin's regions.
Spin‐projected EHF method. IV. Comparison of potential curves given by different one‐electron methods
Authors: Mayer I.
Published: December 2004

Some aspects of the computer realization of the spin‐projected extended Hartree–Fock (EHF) method at the ab initio level are briefly discussed for the algorithm of solution developed in the previous papers of this series. Calculations have been performed for the BH molecule by using a small basis of contracted Gaussian lobes with the purpose of comparing the potential curves given by the different one‐electron methods RHF, UHF, UHF with subsequent spin projection, and EHF. It is concluded that the UHF and, in particular, the EHF methods give a qualitatively correct shape of the potential curve; the RHF method shows the known incorrect dissociation behavior while the potential curve obtained by subsequent spin projection of the UHF wave function exhibits spurious extrema at intermediate internuclear separations.
Approximate fourth‐order perturbation theory of the electron correlation energy
Authors: Krishnan R. , Pople J. A.
Published: December 2004

An approximate fourth‐order expression for the electron correlation energy in the Møller–Plesset perturbation scheme is proposed. It takes into account all the contributions to the fourthorder energy neglecting only those of the triple‐substituted determinants. It is size consistent and correct to fourth order for an assembly of isolated two‐electron systems. Illustrative calculations are reported for a series of small molecules.
Iterative hypervirial‐scaling method for obtaining wave functions and eigenvalues
Authors: Castro Eduardo A.
Published: December 2004

A procedure to improve trial wave functions is given in terms of the off‐diagonal hypervirial theorem. This procedure is closely related to the optimum scaling method which is valid for the diagonal hypervirial theorem. The second excited state of the one‐dimensional oscillator model is employed as an example, and improved wave functions and expectation values are calculated. The results are compared with previous values based on the diagonal hypervirial theorem.
Energy band structure of (SN)x chain: Unrestricted Hartree–Fock and charge density wave solutions
Authors: Kertesz M. , Koller J. , Ažman A.
Published: December 2004

The ab initio Hartree–Fock crystal orbital method is used for the calculation of the energy band structure of a one‐dimensional model of (SN)x. Two energy band structures are described corresponding to the self‐consistent spin density wave (SDW) and the self‐consistent charge density wave (CDW) solution, respectively.
Some aspects of the model potential method
Authors: Höujer Germund , Chung Johnson
Published: December 2004

The theoretical justification of the model potential method is studied in some detail. The correct equations within the framework of Roothaan's open‐shell scheme are derived and the approximations necessary to get a workable method are discussed. Analysis of the local part of the model potential suggests a new analytical form for it. The new expression is theoretically more consistent than the original one, and it can be determined in a more straightforward way. A basis set approximation, which is particularly suitable for approximate evaluation of two‐electron integrals when only valence orbitals are involved, is discussed and tested with encouraging results. The ideas are tested on the Fe and I atoms.
Polarization model representation of hydrogen fluoride for use in gas‐ and condensed‐phase studies
Authors: Stillinger Frank H.
Published: December 2004

The polarization model, originally developed to describe deformable and ionizable water molecules, has been extended to hydrogen fluoride. Since electronic polarization is explicitly included, the interaction energy in aggregates of molecules (with or without ions) is nonadditive. The model properly describes the structure of (HF)2, including off‐axis bending of the proton acceptor molecule. Calculations are presented to illustrate elementary gas‐phase reactions involving proton transfer between HF and F−, and H2F+ and F−.
Some symmetry aspects of the local‐mode description of vibrational structure
Authors: Gelbart William M. , Stannard Paul R. , Elert Mark L.
Published: December 2004

In the local‐mode description of vibrational structure, the nuclear coordinates—unlike the usual normal coordinates—do not reflect the molecular symmetry. Accordingly, the local‐mode product wave functions must be symmetry adapted. We discuss this simple procedure in light of its implications for the localization of vibrational energy and the dissociation limits of molecular excited states. These properties are in turn related to the separability of the total nuclear Hamiltonian and to the different ways in which the vibrational anharmonicity is “absorbed” by the local and normal coordinates.
Binding of an electron to a molecular dipole: BeF
Authors: Seiders Barbara A. B. , Luken William L. , Jordan Kenneth D.
Published: December 2004

Results of extended‐basis SCF calculations indicate that BeF may exist as a metastable species. Comparison of results obtained from SCF calculations on neutral BeF2 with those of BeF shows that the orbital occupied by the electron of BeF is well approximated by the lowest unoccupied molecular orbital of neutral BeF2.
Theoretical study of [F−; e+] and [CN−; e+]
Authors: Kurtz H. A. , Jordan K. D.
Published: December 2004

Ab initio calculations are presented for the [F−; e+] and [CN−; e+] complexes. Positron affinities of 4.99 and 3.79 eV are obtained for F− and CN−, respectively. The excitation energies to the low‐lying excited states of the positron complexes are also calculated.
Interrelations among x‐ray scattering, electron densities, and ionization potentials
Authors: Hyman Arthur S. , Yaniger Stuart I. , Liebman Joel F.
Published: December 2004

From the general formalism of elastic x‐ray scattering and a few meaningful assumptions we have shown that for an atom, ∫ρ2dτ is an experimentally measurable quantity related to the intensity scattered by an element. We have labeled this quantity (p), the “average electron density.” If ψ obeys the virial theorem, within the Thomas–Fermi approximation we show (within a multiplicative constant) that 〈ρ〉 is a lower bound to (∑ ionization potentials )3/2. Thus, the scattered intensity of x rays is related quantitatively to the energy of the scattering atoms. Inequalities have been developed to express these relationships and have been confirmed for the more exact Hartree–Fock wave functions.
Monte carlo simulation of water solvent with biomolecules. Glycine and the corresponding zwitterion
Authors: Romano Silvano , Clementi Enrico
Published: December 2004

Monte Carlo calculations for clusters consisting of 200 water molecules surrounding glycine in the neutral and zwitterionic forms were carried out at 300 K; all the relevant interaction potentials have been obtained by means of quantum–mechanical calculations. Water–water and amino acid–water energies were calculated, and the zwitterion was found to be strongly favored with respect to the neutral molecule, as expected. A detailed analysis of the energetic results yielded some information on the special extension of the solute‐induced perturbation. The structural results were found to be in reasonable agreement with predictions that can be obtained by analyzing isoenergy contour maps, calculated for the two‐body amino acid–water potential.
Electronic factors affecting receptor binding of dibenzo‐p‐dioxins and dibenzofurans
Authors: Cheney B. Vernon , Tolly Timothy
Published: December 2004

The electronic structure of a series of 25 chlorinated dibenzo‐p‐dioxins and dibenzofurans has been characterized by means of the ab initio molecular fragment technique. This information has been employed to investigate some of the factors affecting the affinity of the molecules for the hepatic cytosol binding species described by Poland, Glover, and Kende. A quantitative structure–activity relationship involving electronic and steric parameters could be established from the data. It appears that the toxins act as electron acceptors in a charge‐transfer complex with the receptor.
Circular dichroism of large molecules
Authors: Tinoco Ignacio
Published: December 2004

The circular dichroism of molecules, which are large compared to the wavelength of light, is considered. Explicit expressions are obtained for the circular dichroism and absorption of an exciton dimer and of a free particle on a helix. The dimensions are described for which the dipole approximation for the optical properties fails.
Some aspects of the DNA hypochromic effect theory
Authors: Volkov S. N.
Published: December 2004

The expressions for the polymer absorption band hypochromism and oscillator strength are studied in frames of the first‐order perturbation theory. The physically justified approximations for a polymer hypochromism calculation are indicated. The uniform interpretation of the effect origin is given independently on the approximation used. In frames of the perturbation theory the DNA hypochromism formula is obtained, from which the known experimental dependences of hypochromism on chain length and polymer helicity degree follows directly. The analytic expression of the DNA hypochromism dependence on AT pairs content is obtained. It is established that in most cases for natural DNA the nucleotide sequence does not influence in practice the value of the hypochromic effect.
Theory of chemical reactions in condensed media and its applications to biological processes
Authors: Christov S. G.
Published: December 2004

The general aspects of a theory of dense‐phase reactions, based on an accurate quantum‐mechanical formulation of the rate equation, are considered. Using an adiabatic one‐frequency oscillator model, the theory is applied to several important biological processes at low temperatures: the photinduced oxidation of cytochrome C by bacteriochlorophyll, the electron transfer from primary to secondary acceptors in bacterial photosynthesis, and the ligand rebinding of carbon oxide and β‐chain of hemoglobin. A very good agreement between theory and experiment is found making use of no more than one or two (or even without any) adjustable parameters.
Molecular structure–biological activity relationships on the basis of quantum‐chemical calculations
Authors: Sklenar Heinz , Jäger Joachim
Published: December 2004

Detailed quantum‐chemical calculations by means of semiempirical all‐valence electrons methods and a generalized (multivariable) rank correlation analysis are the fundamentals of a novel strategy of search for QSAR within homologous series of compounds. The set of molecular parameters (describing the electronic and conformational properties as well as potential interactions of the drugs) is calculated theoretically. Owing to the rank correlation method, no linear model (like LFER) for the dependence of the biological activity upon the molecular parameters is presumed. The computed correlation coefficients are valued by carefully determined levels of statistical significance. Significant correlations are used to predict unknown activities in terms of ranks relative to the basic sample.
Dispersion interaction between helium pair from hydrodynamic analogy to quantum mechanics
Authors: Shukla G. C. , Easa S. I.
Published: December 2004

Frequency‐dependent multipole polarizabilities of the He sequence have been calculated from a hydrodynamic model of quantum mechanics and using an independent‐particle model Hamiltonian. Our present scheme is parallel to the uncoupled Hartree–Fock approximation so our values of polarizabilities, multipole transition energies and dispersion force coefficients between the HeHe pair are comparable with earlier works using the uncoupled Hartree–Fock approximation.
Configuration interaction matrix elements. I. Algebraic approach to the relationship between unitary group generators and permutations
Authors: Wormer P. E. S. , Paldus J.
Published: December 2004

Matrix elements of unitary group generators between spin‐adapted antisymmetric states are shown to be proportional to spin matrix elements of so‐called “line‐up” permutations. The proportionality factor is given explicitly as a simple function of the orbital occupation numbers. If one bases the theory on ordered orbital products, the line‐up permutations are given a priori. The final formulas have a very simple structure; this is a direct consequence of the fact that the spin functions have been taken to be geminally antisymmetric.
Calculation of molecular electric polarizabilities and dipole moments. III. BH molecule
Authors: Waltz Carl E. , Kim Hae‐Won , Hameka Hendrik F.
Published: December 2004

We use a previously proposed variation‐perturbation method to calculate the electric polarizabilities and the electric dipole moment at equilibrium nuclear distance of the BH molecule. We obtain 3.56 × 10−24 cm3 for the perpendicular polarizability αxx and 3.22 × 10−24 cm3 for the parallel polarizability αzz. Our result for the electric dipole moment μ0 is 1.734 debye units; there is no reliable experimental result to compare it with.
Incomplete basis set problem. IV. Perturbative corrections to pair energies
Authors: McDowell Keith
Published: December 2004

A partitioning of the molecular Hamiltonian into the occupied and virtual orbital spaces and their orthogonal complement is introduced and used to develop a perturbation expansion of the exact ground‐state energy relative to the Hartree–Fock energy computed using an incomplete basis set. The leading perturbation corrections to pair energies due to using the incomplete basis set are considered in detail. Summations of certain classes of pair contributions are discussed and a resummed correction is obtained.
Global analysis of composite particles
Authors: Story Troy L.
Published: December 2004

The theory of vibrations of a composite particle when vibrational amplitudes are not constrained to be small according to the Eckart conditions is developed using the methods of differential topology. A global classical Hamiltonian appropriate for this system is given, and for the case of the molecular vibration–rotation problem, it is transformed into a global quantum Hamiltonian operator. It is shown that the zeroth‐order term in the global Hamiltonian operator is identical to the Wilson–Howard Hamiltonian; higher‐order terms are shown to give successively better approximations to the large amplitude problem. Generalized Eckart conditions are derived for the global classical Hamiltonian; the quantum equivalent of these conditions along with the quantum equivalent of the Eckart conditions are given. The spectrum of the global Hamiltonian operator is discussed and it is shown that the calculation of the vibration–rotation energy states of the system reduces to the same straight‐forward procedure, the solution of a secular determinant, as was carried out for the Wilson–Howard Hamiltonian at a later time by Nielsen.
Ab initio Hartree–Fock–Slater calculations of polysulfanes H2Sn (n = 1–4) and the ions HS and S
Authors: Trsic M. , Laidlaw W. G.
Published: December 2004

An ab initio Hartree–Fock–Slater procedure was applied to the calculation of the electronic structure of polysulfanes, H2Sn (n = 1–4) and the ions HS and S. Charge densities, overlap populations, and deprotonation energies are calculated; the latter appear well correlated with the first and second acidity constants.
Nonadditivity of the SCF interaction energy in the (LiH)3 complex
Authors: Szczȩśniak Małgorzata M. , Ratajczak Henryk
Published: December 2004

The role of nonadditivity of the interaction energy between three LiH molecules was investigated within the SCF ab initio framework. The nonadditive part of the interaction energy is more important in the case of a cyclic structure than in a linear trimer, and is stabilizing in both cases. The value of the ratio of three‐body and two‐body terms for different points on the energy hypersurface is discussed.
Nonrigidity effects of fragments of membrane‐active complexons
Authors: Kryachko Eugene S. , Kruglyak Yuri A. , Dalton Bryan J.
Published: December 2004

The nonrigid molecule symmetry group for methylamine is determined as a set of permutations and permutation inversions for two situations. In the first case the internal rotations of the methyl group and NH2 group are included and the second case the transition of a hydrogen atom from the methyl group to NH2 group is also included. In both cases the energy level splitting of the rigid model of the methylamine is found, nuclear statistical weights of the split levels are calculated, and sections rules for the allowed dipole transitions are given.
Stable and efficient algorithms for Xα multiple scattering calculations
Authors: Case David A. , Yang Cary Y.
Published: December 2004

Solutions to some practical problems that arise in multiple scattering calculations on large molecules are discussed. (1) Numerical instabilities near the zero of energy can be removed by rescaling the secular matrix. (2) The calculation of structure factors can be made much more efficient by the application of symmetry projection operators. (3) An energy search procedure is described that ensures that no states are inadvertently neglected. Test calculations incorporating these changes illustrate the improved numerical stability, and show decreases in computation time of 30–60%, when compared to previous codes. The procedures suggested here are applicable to both relativistic and nonrelatitistic calculations.
Self‐consistent approximation to the polarization propagator
Authors: Weiner Brian , Goscinski Osvaldo
Published: December 2004

A theorem is presented that characterizes approximate states and truncated operator manifolds associated with self‐consistent approximate propagators. This theorem establishes a natural relationship between Hermiticity, stationarity, nonredundance and completeness of operator manifolds, model time evolution, and the vacuum condition. For the case of the polarization propagator we describe algorithms by which we can construct states and manifolds that satisfy this theorem and the vacuum condition.
High accuracy wave functions and eigenenergies for the vibration–rotation states of diatomic molecules by factorization method
Authors: Mohammad S. Noor
Published: December 2004

A solution of the wave equation for the nuclear motion of a diatomic molecule with an exponential potential function and the rotational term included has been performed by the Schrödinger‐Infeld‐Hull factorization method. Two different procedures have been followed for the factorization of the wave equation, and in each of them, as type‐B factorization is incapable of producing wave functions, it has been transformed to type‐C factorization, and a complete set of wave equations have been obtained. Of the two procedures, although the former appears to be more direct, the latter is the more accurate and generalized one.
Nonempirical calculations on diatomic transition metals. II. RHF investigation of lowest closed‐shell states of homonuclear 3d transition‐metal dimers
Authors: Wolf Andreas , Schmidtke Hans‐Herbert
Published: December 2004

Potential‐energy curves of the 3d dimer series Sc2 through Cu2 are calculated for the lowest closed‐shell states within the nonempirical RHF formalism using limited basis sets of minimal to near‐double‐zeta–plus‐polarization size. Calculated spectroscopic constants are compared to semiempirical results as well as to experimental estimates. The possibility for closed‐ or open‐shell ground states is discussed for each dimer. For diatomic Sc and Cu a detailed study of basis set effects on calculated molecular constants is carried out.
Effective potential model for calculating the energy shift in the ground state of two‐electron atoms
Authors: Jolly Pratibha , Sane Kamalni , Sane K. V.
Published: December 2004

An effective operator for the electron–electron interaction derived earlier has been shown to be successful for calculating the ground‐state energy shift values for 10 members of the helium isoelectronic sequence in terms of a single free parameter. Some possible applications of the modified interaction operator for semiempirical calculations are suggested.
Direct configuration interaction with a reference state composed of many reference configurations
Authors: Siegbahn Per E. M.
Published: December 2004

The configuration interaction method where a single reference state is composed of a linear combination of reference configurations is analyzed in detail. In this method single and double replacements are constructed by applying annihilation and creation operators on the reference state. The analysis is based on the recently derived factorization of the direct CI coupling coefficients into internal and external parts. Using the internal coupling coefficients the integrals are transformed to new entities which are used in the diagonalization step. This two‐step procedure differs significantly from the usual straightforward one‐step direct CI procedure. A number of operations analysis shows that calculations with the present method should be feasible even with a large number of reference configurations in the reference state. Based on first‐order perturbation theory the accuracy of the method is predicted to be close to the accuracy obtained with the usual CI method with many reference configurations.
Biological response as a function of conformation, chirality, and electronic characteristics: A catecholamine study
Authors: Scharfenberg Peter , Sauer J.
Published: December 2004

The hypothesis is introduced, that nonrigid drug molecules interact with biological receptors in a well‐defined but unknown conformation that need not belong to an energy minimum. A verification of this assumption has to include a match of conformation and chirality. Even the different action of pairs of nonrigid enantiomers allow one to recognize uniquely the important role of conformations because flexible molecules are partially able to avoid wrong attachment to the receptor. According to a simple model, a monotonic relation between biological activity and rotational barriers (and/or torque constants) can be expected and, by means of rank correlation analysis of adrenergic activities, has been found, too. In order to apply the latter method, particularities concerning quantitative structure–activity analyses of nonrigid and/or chiral molecules are worked out. We optimized conformations by means of analytically calculated first partials of the energy and a quasi‐Newton method. Using a convenient numerical method, it was shown that coplanar conformations of catecholamines are generally unstable. Moreover, CNDO/2 proved to be a reliable method for conformational studies, in which rotations about conjugated bonds [1] are not considered.
CNDO/INDOformalism forfblock elements
Authors: Fanning M. O. , Fitzpatrick N. J.
Published: December 2004

The intermediate and complete neglect of differential overlap (INDOandCNDO/2) molecular‐orbital theories are developed for molecules withfblock elements in both the open‐ and closed‐shell configurations.
Padé algorithm for the computation of static and dynamic second‐order properties by large‐scale CI expansion
Authors: Bendazzoli G. L. , Evangelisti S. , Ortolani F.
Published: December 2004

By introducing a finite basis, the inhomogeneous equations of perturbation theory are approximated by systems of linear equations. We present and discuss a Padé‐type algorithm suitable for large‐order systems and having better convergence properties than the classical Jacobi procedure.