bluuebunny/crossref_metadata_2025_split huggingface dataset:
Two‐electron theory of non‐interacting surface and impurity states
Authors: Davison S. G. , Tan W. K. 
Published: December 2004

AbstractSome earlier results in the Davison‐Cheng two‐electron theory of surface and impurity states are corrected. Although the surface spin state findings are only slightly modified, it is found that the inner and outer impurity spin states no longer always occur separately, but can in fact co‐exist. After discussing the connection between the two‐electron theory of monatomic crystals and the one‐electron theory of diatomic crystals, the paper concludes by briefly outlining the recent developments in the one‐electron theory of surface and impurity state interaction.
SCF perturbation theory and intermolecular interactions
Authors: Basilevsky M. V. , Berenfeld M. M. 
Published: December 2004

AbstractA self‐consistent perturbation theory is derived in the framework of Roothaan's MOLCAO procedure for closed shell systems. Contrary to previous investigations which have considered only one particle perturbations, two particle perturbation operators are considered. Expressions for the first‐order density matrix and first‐ and second‐order energy corrections are obtained. A diagram formulation of the complete perturbation expansion is presented.The results are applied to the treatment of the intermolecular interaction problem. The interaction energy is represented as a sum of several contributions: Coulomb, exchange, resonance, polarization and exchange repulsion. A semi‐empirical version of the theory is suggested which explicitly involves all the physically significant energy terms and may be useful for the investigation of complex systems.
PCILON. perturbative configuration interaction using localized orbitals and numerical integration. I. Numerical integration techniques for the calculation of Hamiltonian matrix elements between localized orbitals
Authors: Daudey J. P. , Diner S. 
Published: December 2004

AbstractModern techniques for multidimensional numerical integration, Korobov's and Sobol's formulas namely, are used for the direct computation of matrix elements between the localized molecular orbitals needed for a configuration interaction calculation by a perturbation method. A minimal orbital basis of Slater functions is used for formaldehyde and ethylene taken as example. The resulting precision is satisfactory.
Direct minimization of the energy functional in LCAO–MO calculations
Authors: Kari R. , Sutcliffe B. T. 
Published: December 2004

AbstractIn this paper we obtain formulae useful in methods for the direct minimization of the energy functional in the LCAO‐MO‐MC‐SCF approach. The formulae are appropriate for dealing with variations in both the linear and nonlinear parameters. We include formulae for the usual closed‐ and open‐shell problems as special cases.
A study of the AMO method as applied to the lithium metal. I. Review, results, and discussion
Authors: Calais Jean‐Louis , Sperber Gunnar 
Published: December 2004

AbstractThe total electronic energy per atom in the lithium metal has been calculated for three different Fermi surfaces as a function of the internuclear distance. In each case the optimized AMO energy as well as the total energy corresponding to doubly filled molecular orbitals (MO) has been calculated. For densities around the equilibrium density the spherical Fermi surface yields the lowest energy whereas a cubic Fermi surface is preferred for low densities. For densities around the equilibrium there is no band splitting: the AMO energy coincides with the MO energy. The computations have been carried out within an LCAO approximation with overlap and multicenter‐integrals calculated accurately.
A study of the AMO method as applied to the lithium metal. II. The first‐order density matrix and the shape of the fermi surface
Authors: Sperber Gunnar , Calais Jean‐Louis 
Published: December 2004

AbstractAlternant molecular orbitals for the lithium metal are constructed in different ways. The corresponding first‐order density matrix is calculated for different shapes of the Fermi surface. Numerical methods to calculate the first‐order density matrix are described.
A note on Löwdin orthogonalization and the square root of a positive self‐adjoint matrix
Authors: Scofield D. F. 
Published: December 2004

AbstractA quadratically convergent process using a continued fraction method for finding the square root of the overlap matrix used in Löwdin orthogonalization is presented. The continued fraction method is compared to several other methods for finding the square root of a matrix. The method is found to be more efficient than the other methods when high accuracy is desired.
Decoupled Hartree‐Fock methods. II. Calculation of the potential curves of diatomic molecules
Authors: Náray‐Szabó G. 
Published: December 2004

AbstractApplying an extended form of the Mulliken approximation and a monopole approximation for the Coulomb integrals the Hartree‐Fock nonorthogonal energy expression is decoupled. Thus, the total energy splits into a sum of one‐electron increments. The increments are minimized directly with respect to the linear coefficients and orbital exponents. Further, the ZDO approximation is used in the decoupled energy expression to avoid difficulties arising in connection with the evaluation of multicenter integrals. “Rigid core” calculations were carried out for the valence electrons of first‐row diatomics. In case of nonpolar molecules good results are obtained for equilibrium distances and force constants. The method fails for molecules with atoms having very different nuclear charges.
Representable reference density matrices induced by information theory
Authors: Larson Everett G. 
Published: December 2004

AbstractA class of reference full density matrices and their reduced density matrices is presented. These density matrices are designed to be of value as references from which to describe and measure the effects of electron correlation in atoms, molecules, and solids. A given reference full density matrix is constructed to contain the least possible information consistent with having the (recognized) symmetry properties of—and reducing to the 1‐matrix of—a given “true” full density matrix (which in a typical application is constructed from a correlated variational wave function). Therefore, the reduced density matrices derived from are representable and depend only upon the 1‐matrix of and the (recognized) symmetry properties of for their construction. Furthermore, the property of containing the least possible information consistent with the given constraints makes these reference density matrices ideally suitable as references from which to describe the electron correlation contained in the “true” full density matrix magnified image.
Détermination des Orbitales Moléculaires par Minimisation Directe de L'Energie de L'Etat Fondamental et des Etats Excités des Molécules
Authors: Benard Marc , Julg André 
Published: December 2004

AbstractUn procédé de minimisation directe de l'énergie d'une molécule par rapport aux coefficients des orbitales atomiques des fonctions moléculaires est utilisé en vue de déterminer les fonctions de l'état fondamental et des états excités. L'orthogonalité entre les divers états est obtenue par des conditions moins restrictives que celles de Roothaan, si bien que l'énergie obtenue pour la première transition électronique est abaissée: de 0,1 à 0,2 eV pour les transitions π → π* des polyènes.
A configuration interaction study of the spin dipole‐dipole parameters for formaldehyde and methylene
Authors: Langhoff Stephen R. , Elbert Stephen T. , Davidson Ernest R. 
Published: December 2004

AbstractThe electron spin dipole‐dipole contribution to the zero field splitting has been evaluated for the 3A2 (n → π*) and 3A1 (π → π*) states of formaldehyde using a CI wave function constructed from contracted Gaussian‐lobe functions. The values D = 0.539 cm−1 and E = 0.031 cm−1 were obtained for the 3A2(n → π*) state and D = −0.588 cm−1 and E = 0.058 cm−1 were obtained for the 3A1 (π → π*) state using the CI wave function constructed from SCF orbitals of the respective parent configurations. An analysis of the effect of CI on the parameters is given for the 3A2 (n n → π*) state of formaldehyde and the 3B1 ground state of methylene. Numerical results are given which show that internally consistent self‐consistent field orbitals (ICSCF) are superior to canonical SCF orbitals as a starting point for a CI calculation. Our CI wave function for the 1A1 ground state gave an energy of −114.13658 hartrees which is significantly lower than any previously reported energy calculation. This wave function gives a dipole moment of 2.22 Debye (C+O−) in good agreement with the experimental value of 2.33 ± 0.02 Debye.
Symmetry in the Heitler‐London method. II. The determination of the allowed molecular multiplets
Authors: Ledovskaya E. M. , Petrashen M. I. 
Published: December 2004

AbstractIn the framework of the Heitler‐London method, a method for determining the allowed molecular multiplets is proposed. The method is based on the connection of the total molecular spin with the permutation symmetry of the coordinate wave function and on the isomorphism of the molecular point group with a certain subgroup of the electron permutation group. The method does not depend on the approximation in which the molecular ions are considered.
Symmetries of n‐electron wave functions under various spatial groups
Authors: Gallup G. A. 
Published: December 2004

AbstractA new method is used to arrive at Kotani's formula (vide infra) for the character of the representation of the group of spatial symmetry provided by functions which are eigenfunctions of the total spin operator. An alternative form involving determinants of the symmetric functions is also given. The results are applied to some cases which were untreated before and have particular interest in valence‐bond calculations. The problem of the construction of bases functions of the given symmetry is also discussed, and a solution with a wide range of applicability is given.
A variational perturbation treatment of the hydrogen molecular ion using the green function method on the united atom
Authors: Corsaro Felicia A. , Solenberger Françoise R. , Hameka Hendrik F. 
Published: December 2004

AbstractWe calculated the second‐order perturbed energy and the first‐order perturbed wave function of the hydrogen molecular ion by the Green function method based on a united atom with effective nuclear charge, Z. Since the perturbation is given by (Z/r) — (1/rA) — (1/rB), its magnitude depends on the parameter Z. We obtain an analytical expression for the second‐order perturbed energy as a function of Z and the internuclear distance R. We discuss a variety of methods to determine the best values for Z and to derive the potential energy curve and the force constant for H; these methods vary in the accuracy of their results.
Spin projected EHF method: Calculations for a four‐electron model system
Authors: Mayer I. 
Published: December 2004

AbstractThe spin projected extended Hartree‐Fock equations for successive optimization of the orbitals are derived for the four‐electron case and applied to butadiene in the PPP approximation. The method shows an excellent convergence and gives 91.4% of the correlation energy for the given model‐Hamiltonian.
The self‐consistent symmetrized OPW method with an application to crystalline selenium
Authors: Boehm Juhani Von , Krusius Peter 
Published: December 2004

AbstractA review of the nonrelativistic self‐consistent symmertrized orthogonalized‐plane‐wave (SCSOPW) method used for determining electronic energy bands in periodic solids is given. Working equations based on the full use of group theory at all stages are presented for elemental crystals. As an example the method is applied to the trigonal selenium crystal.
Spin‐orbit interaction in polyatomic molecules: Ab initio computations with Gaussian orbitals
Authors: Bendazzoli G. L. , Palmieri P. 
Published: December 2004

AbstractStandard sets of Gaussian atomic orbitals (STO‐3G, STO‐4.31G) are used to evaluate spin‐orbit coupling constants in linear molecules (CO, NNN) and spin‐orbit effects on singlet–triplet transition intensities in formaldehyde. All spin‐other orbit effects have been included. In all cases spin‐other orbit interactions form a large fraction of the matrix elements. Simple formulae to evaluate spin‐orbit one‐ and two‐electron integrals over atomic orbitals are presented. Standard molecular integral programs can be used for the computation of spin‐orbit integrals.
Corrections to coupled Hartree–Fock theory: the rearrangement effect
Authors: Bhattacharya A. K. , Moitra R. K. , Mukherji A. 
Published: December 2004

AbstractIn this communication we discuss a method of incorporating corrections to the coupled Hartree–Fock (CHF) formalism by introducing the so‐called “rearrangement effect.” In this we take account of the relaxation of the core orbitals when excitations from a starting Hartree–Fock wave function occur. The magnitude of this correction numerically is found to be quite significant for the polarizabilities of two‐electron atomic systems, results for which are reported.
Comparison between the point‐charge electrostatic model and the angular overlap model: The general case
Authors: Kibler Maurice R. 
Published: December 2004

AbstractThe aim of this paper is to explore in detail the mathematical connection between the point‐charge electrostatic model and the angular overlap model. More precisely, for any configuration nlx in any symmetry, the matrix elements, and therefore the energy levels, as given by the angular overlap model restricted to the antibonding effects λ (for any of the possible λ's), are deduced from an effective potential constructed according to the point‐charge electrostatic model. This allows us to give a mathematical proof of the equivalence between the point‐charge electrostatic model and the angular overlap model taking into account all the antibonding effects λ. Finally, the sum rules for the angular overlap model are examined in the light of the formulae connecting the two models considered. Numerical tables for obtaining the results as given by the angular overlap model restricted to any of the antibonding effects from those as given by the point‐charge electrostatic model are listed for the configurations nlx with l = p, d, f and g.
An alternative parametrization for the theory of complex spectra
Authors: Kibler Maurice R. 
Published: December 2004

AbstractThe aim of this paper is to investigate a new parametrization for the matrix, set up on the states of an open (nuclear or atomic) shell, of any two‐body interaction expandable in multipoles. Such a parametrization is particularly convenient for expressing the term energies in a simple form and for producing high degeneracies among the terms. Further, the parametrization considered allows the two‐body interaction to be decomposed into a Dirac interaction and a remaining part.
Spin densities in the Waller–Hartree spin‐free method
Authors: Lim T. K. 
Published: December 2004

AbstractSpin densities in the Waller–Hartree spin‐free method were found to be the same as in the spin‐projected Slater determinant method. The reduced spin projector Q is introduced and its relation with the spin projector P is discussed. An equation is obtained to show that a Sanibel coefficient can be expressed as a linear combination of N! products of Sanibel coefficients.
Dynamical screening by Σ‐electrons in π‐electron transitions: Treatment in the equations‐of‐motion method
Authors: Shibuya Tai‐Ichi , I'haya Yasumasa J. , McKoy Vincent 
Published: December 2004

AbstractDynamical screening in π‐electron systems is studied by the equations of motion method. By using a partitioning technique on the equations of motion we can obtain simple expressions for the effect of dynamical screening directly on the transition energies and transition moments in π‐electron systems. These results are used to study the effect of such screening in the N → V transition in ethylene. This procedure can be used to extend the equations‐of‐motion method to larger π‐electron systems.
Density matrix in the open shell theory
Authors: Mestechkin M. M. , Whyman G. E. 
Published: December 2004

AbstractAll the second‐order density matrix spin components for the spin‐projected Slater determinant are presented as expansions in direct products of powers of unprojected spin‐ and residual electron density matrices. Spin components of the second‐order transition density matrices between spin‐projected Slater determinants built of orthogonal orbitals are also obtained.
Effect of orbiting resonance on the elastic differential cross sections
Authors: Sheen S. H. , Skofronick J. G. , Mueller C. R. 
Published: December 2004

AbstractThe effects of orbiting resonances on elastic differential cross sections are investigated for the Lennard‐Jones (12, 6) model potential. The elastic differential cross section consists of three terms: a resonance term, a potential scattering term and an interference term. The interference term has a significant effect only at small angles of the differential cross section. The importance of the potential scattering term depends proportionally upon the orbiting resonance energy. For the low‐lying orbiting resonance states, the resonance term is the dominant term, but at higher energy it appears only in the backward differential cross sections. Generally, by fitting the large angle differential cross sections, the resonance orbital angular momentum can be estimated.
Nonadiabatic core polarization and penetration correction in alkali‐like atoms: Model computations on excited states of helium
Authors: Young Ralph H. , Deal Walter J. 
Published: December 2004

AbstractCorrelation between the motion of a highly excited outer electron and that of the remaining ionic “core” of an atom is generally treated in an adiabatic approximation, in which it is assumed that the outer electron affects the core in the same way as a stationary point charge. An alternative approach to this correlation problem which avoids the adiabatic approximation is tested here on the 1s2p, 1s3d, and 1s4f states of helium. The results provide the first accurate test of the adiabatic approximation and of a simple correction for the nonzero velocity of the outer electron. The approach used here is based on neglect, in the “correlation” part of the wave function, of the possibility that the outer electron comes closer to the nucleus than any core electron (“penetration”). A correction for this neglect is derived and tested on a version of the adiabatic approximation that likewise neglects penetration.
A density functional representation of quantum chemistry. III. Rigorous realization of the program in lattice space
Authors: Schleicher M. , Primas H. 
Published: December 2004

AbstractA mathematically rigorous reformulation of molecular quantum mechanics in terms of the particle density operator and a canonically conjugated phase field is given. Using a momentum cutoff, it is shown that the usual molecular Hamiltonian can be expressed in terms of the particle density operator and a rigorously defined phase operator. It is shown that this Hamiltonian converges strongly to the cutoff‐free Hamiltonian. In spite of the fact that this Hamiltonian is of second order in the phase operators, all hitherto published expressions are not correct. Unfortunately, the correct formulation destroys the intuitive appeal of using the particle density operator as a coordinate for the many‐body problems of quantum chemistry. Unless somebody provides an essential new and clever idea, we propose to resist the fascination of a local quantum field theory of molecular matter in terms of the particle density operator.
The electronic structure of molecules having arbitrary boundaries
Authors: Scheire L. , Phariseau P. 
Published: December 2004

AbstractIn this paper we discuss an extension of the standard multiple scattered wave method for molecular electronic structure calculations to the case of arbitrarily shaped molecules. A general theory is presented where the difficulties arising from the matching problem across an arbitrary boundary are avoided. The secular equation to determine the energy spectrum is obtained and the wave functions are calculated in all regions.
Semi‐quantitative and semi‐empirical versions in the quasi‐relativistic SCF‐MO‐LCAO methods: Numerical calculations for (PtCl6)2−
Authors: Bersuker I. B. , Budnikov S. S. , Leizerov B. A. 
Published: December 2004

AbstractQuasi‐relativistic (QR) versions of the CNDO and Mulliken–Wolfsberg–Helmholz (MWH) semiempirical methods based on the SCF‐QR‐MO‐LCAO method given earlier are worked out. For the CNDO method only the basic formulas and matrix element expressions are given, while for the MWH one, the parametrization as well as the basis functions and group spinor overlap integral calculation were discussed. (PtCl6)2− complex was chosen for a test calculation. The energy level values and LCAO coefficients were obtained and compared with the nonrelativistic calculations. One of the results was the occurrence of a very strong reduction of the spin‐orbit interaction due to covalency. The calculation proves the semi‐empirical versions of the QR‐MO‐LCAO method to be quite realizable in practice.
Quantum theoretical calculations of van der Waals interactions between molecules. Anisotropic long range interactions
Authors: Wormer Paul E. S. , Mulder Fred , Van Der Avoird Ad 
Published: December 2004

AbstractPresenting a relatively simple ab initio method to calculate full van der Waals interaction potentials between molecules, we give rules for the optimization of basis functions which permit the reliable evaluation of second order long range interactions. Closed expressions for the long range interaction energy are derived in which the orientational dependence is simplified to the utmost. Calculations show that even for molecules which have no dipole moment, such as ethylene, the strongly anisotropic electrostatic interactions are of the same magnitude as the dispersion interactions, but also that the anisotropic (“cross”) terms in the dispersion energy are about equal in size to the corresponding “quadratic” terms. Even though these anisotropic forces cancel to a large extent in the cohesion energy of the ethylene crystal, they can have important effects on some of the other crystal properties.
Variational localized‐site cluster expansions. VIII. Projection of spin symmetries
Authors: Klein D. J. , García‐Bach M. A. 
Published: December 2004

AbstractWe investigate the total spin structure of an approximate localized‐site wave function for a collection of paramagnetic sites interacting so as to favor a singlet ground state. As the number of sites becomes infinite we obtain the distribution of weights of the different symmetry components of the localized site wave function; further, although only a very small fraction of such nonsymmetric wave functions is actually singlet, we find that it generally yields the same bulk property expectation values as its singlet‐projected component.