bluuebunny/crossref_metadata_2025_split huggingface dataset:
Adiabatic perturbation theory for the degenerate case. I. Perturbation of isolated degenerate or quasidegenerate levels
Authors: Dmitriev Yuri 
Published: December 2004

AbstractAdiabatic formulae for secular operators and contracted Hamiltonians in an arbirary combination of degenerate or quasidegenerate subspaces are derived. A detailed consideration of the adiabatic limit in the power series is given, and “stability” of proper linear combinations with respect to a transformation produced by the Sα‐matrix is proved.
Energy of interaction of two hydrogen atoms using contracted Gaussian type valence‐bond wavefunctions
Authors: Olson Mark L. , Konowalow Daniel D. 
Published: December 2004

AbstractValence‐bond type wavefunctions based on contracted Gaussian atomic orbitals afford an adequate description of the potential of the ground 1Σ state of H2 for a wide range of internuclear separations. Semiempirical techniques for scaling the potential curve are evaluated. An efficient method for optimizing non‐linear variables in the wavefunctions is explored.
Iterative introduction of integral approximations with error bounds in SCF calculations
Authors: Jafri J. A. , Whitten J. L. 
Published: December 2004

AbstractAnother possible application of a previously reported approximation theory for electron repulsion integrals using rigorous error bounds is considered by incorporating the electron density matrix in the approximation scheme. Error bounds are set on the contribution of a given integral to the total energy for a given molecular wave‐function; the wave‐function is then refined cyclically and additional integrals are computed exactly if necessary until convergence is achieved.
Relativistic molecular spinors by generalized multiple scattering theory
Authors: Cartling Bo G. , Whitmore Douglas M. 
Published: December 2004

AbstractA molecular one‐electron Dirac equation is derived by variation of a total energy density functional, whereby the one‐electron energies are ascribed a physical meaning. The multiple scattering formalism for molecular systems is relativistically generalized for the determination of molecular four‐component spinors. Optimal spinors and one‐electron energies for a finite basis set are derived by variation of a functional. The form of the secular equation is very similar to the nonrelativistic form. Using scattering theory, the quantities appearing in the secular equation are interpreted.
Perturbation theory with an approximate perturbation: The effect of charge overlap on interatomic interactions
Authors: Deal Walter J. , Young Ralph H. 
Published: December 2004

AbstractThe evaluation of interatomic interactions at large separations (R) typically involves neglecting electron exchange, treating the Coulomb interaction between atoms as a perturbation, neglecting third‐ and higher‐order energy contributions, and approximating the Coulomb interaction by a short expansion in spherical harmonics and, usually, powers of R−1. This last approximation, using an approximate perturbing Hamiltonian to evaluate a second‐order perturbed energy, is examined here; error bounds and a simple correction are introduced. Three illustrative applications to the HH+ interaction are given: the error incurred by truncating the spherical‐harmonic expansion is bounded, the R−1 expansion is corrected for the overlap of the “atomic” charge distributions, and the R−1 expansion is analyzed to see why it works as well as it does.
Singlet and triplet excited state electric dipole polarizabilities of conjugated hydrocarbons
Authors: Trsic M. , Sanhueza J. E. , Espinoza Ll. 
Published: December 2004

AbstractFirst excited singlet and triplet electric dipole polarizabilities are reported. The π polarizability is calculated by means of a modified Rayleigh–Schrödinger perturbation theory and an SCF‐LCAO basis. The σ contribution is included by an additive scheme. The polarization of the σ electrons is partially accounted for through an empirical correction. Results compare satisfactorily with a configuration interaction perturbation calculation.
Comparative study of unconventional 1s basis functions for the 1Σ ground state of H2 and He
Authors: Leclerc Jean‐Claude 
Published: December 2004

AbstractWe investigated various nonstandard 1s basis functions (generalized Slater‐Gaussian, ellipsoidal Gaussian, floating spherical and ellipsoidal Gaussian, rational function, Hulthén approximation, two‐Slater‐type orbital, generalized Guillemin–Zener function, and various noninteger‐n elliptical orbitals) for approximating the 1Σ ground state of H2 and He2++. A CI trial wave‐function including Σg‐type MO's is adopted and molecular integrals are evaluated numerically. The energy improvement on the 1s STO is small except for noninteger‐n orbitals which closely approach the “SCF limit”.
Analysis of the half‐projected Hartree–Fock function: Density matrix, natural orbitals, and configuration interaction equivalence
Authors: Smeyers Yves. G. , Delgado‐Barrio G. 
Published: December 2004

AbstractThe half‐projected Hartree–Fock function for singlet states (HPHF) is analysed in terms of natural electronic configurations. For this purpose the HPHF spinless density matrix and its natural orbitals are first deduced.It is found that the HPHF function does not contain any contribution from odd‐times excited configurations. It is seen in addition, in the case of the singlet ground states, this function is approximately equivalent to two closed‐shell configurations, although the nature of the excited one depends on the nuclear geometry. An example is given in the case of the LiH ground state. Finally, the application of this model for studying systems of more that two atoms is criticized.
A density matrix variational calculation for atomic Be
Authors: Garrod Claude , Fusco Mario A. 
Published: December 2004

AbstractThe ground‐state energy of the beryllium atom is calculated using a variational procedure in which the elements of the two‐body reduced density matrix (particle–particle matrix) are the variational parameters. It is shown that, for this problem and with the limited number of spin‐orbitals used, the trace condition and the simultaneous nonnegativity conditions on the particle–particle, the particle–hole, and the hole–hole matrices form a complete solution to the N‐representability problem.The energy obtained is – 14.61425 a.u., practically identical to the value given by a configuration interaction calculation which uses the same states. The effects of weakening the nonnegativity conditions on each of the matrices in turn were also explored.
Spin‐free quantum chemistry. XVII. The Hückel–Hubbard theory and the Woodward–Hoffmann rules
Authors: Matsen F. A. 
Published: December 2004

AbstractWe have developed a many‐body version of Woodward–Hoffmann theory which is capable of rapid computation of π‐electronic surfaces. This theory, called the Hückel–Hubbard theory, employs Hückel parameters as reaction coordinates and the Hubbard parameter for electron repulsion. We apply it to the cis‐trans isomerization of ethylene and to several pericyclic reactions.
Spin‐Free quantum chemistry. XVIII. The unitary group formulation of the many‐electron problem
Authors: Matsen F. A. 
Published: December 2004

AbstractThe representation of an N‐electron Schrödinger Hamiltonian on an orthonormal, spin‐free (freon) orbital product space is exactly modeled by a second‐degree polynomial in the infinitesimal generators of the unitary group. Symmetry adaptation of the orbital product space with respect to the symmetric group yields Gel'fand states which provide base for irreducible represntations of the unitary group. These exist in closed form as, in consequence, does the representation of the model Hamiltonian in this same basis. We retain as physical only those states characterized by tableaux with no more than two columns for which the spin labelling is one‐half the difference in the lengths of the two columns. The unitary group formulation is equivalent to standard, number‐conserving, second‐quantized, many‐body theory.
Radial moment analysis of isovalent hybridization in N2
Authors: Aldrich Haven S. , Aiken John , Cusachs L. Chopin 
Published: December 2004

AbstractA radial moment analysis has been performed for the Hartree–Fock molecular orbitals of the nitrogen molecule. The objective of the analysis was to determine the extent of isovalent hybridization in even and odd sigma molecular orbitals. The radial moment analysis for the LC‐SCF‐AO fragments of the 2σg, 2σu, and 3σg molecular orbitals substantiates Mulliken's earlier conjecture concerning promotion into 3s atomic orbitals for the 3σg molecular orbital. The concept of free isovalent hybridization is discussed in terms of the atomic orbital shape defined by the extracted moments.
A comparison of different DODS methods when the number of electrons increases
Authors: Mayer I. , Kertész M. 
Published: December 2004

AbstractWe have performed RHF, UHF, UHF with subsequent spin projection, and EHF calculations for the π‐electrons of some polyene chains of different lengths in order to investigate the relations among these methods when the number of electrons increases. Special attention is paid to the importance of spin projection for different energetic quantities.
Molecular orbital interpretation of isomer shifts and quadrupole splitting of the mössbauer γ‐line in the compounds of Antimony and Tin
Authors: Kothekar V. 
Published: December 2004

AbstractThe electronic parameters in the Mössbauer spectroscopy, electric field gradient (EFG), and change in the charge density at the nucleus site Δψ2(0) are evaluated on the basis of the CNDO/II method for various compounds of antimony and tin and compared with experimental data. The correlation between the isomer shift adn the quadrupole splitting with these electronic parameters is used to evaluate δR/R and Q and compared with the results of other workers. Different methods for the theoretical interpretation of the Mössbauer parameters are discussed. It was found that Molecular Orbital (MO) methods give quite reliable results for antimony and tin compounds and can be used for elucidating the bonding mechanism in these compounds.
Stability, continuity, and symmetry of variational wave‐functions
Authors: Moiseyev N. , Katriel J. 
Published: December 2004

AbstractInterrelations between the local and the global aspects of the stability, continuity, and symmetry properties of variational wave‐functions are discussed. The spherical limit of one‐electron diatomic molecules and the Hartree–Fock approximation of the ground state of the two‐electron atom are shown to exhibit the various concepts involved in an ab initio, yet sufficiently simple, manner.
Halogénures Alcalins: Un Modèle Incluant une Délocalisation à Courte Distance Application à la Stabilité Relative des Divers Arrangements Cristallins
Authors: Marinelli Andre Julg Et Francis 
Published: December 2004

AbstractThe introduction of symmetry‐adapted hybrid atomic orbitals on the metallic atoms allows us to divide the crystal into elementary cells which contain 8 valence electrons each. These cells are described by linear combinations of the halogen valence shell s and p orbitals and the hybrid orbitals of the nearest metallic atoms which point to the halogen. The electronic delocalization of the halogen ions is very weak (⩽0.02) for: LiF, NaF, KF, LiCl, NaCI, and KCI. The cell energy in the crystal is obtained by using a first‐order perturbative treatment. In agreement with experiment, the f.c.c. type is found more stable than the b.c.c. or the blende type.
A study of Löwdin's criterion for completeness of basis sets
Authors: Leopold J. G. , Cohen M. , Katriel J. 
Published: December 2004

AbstractLöwdin has formulated a useful criterion for testing the completeness of an expansion basis set. From this criterion one may obtain an incompleteness coefficient for a truncated (finite) basis set. We have investigated the significance of this incompleteness coefficient for some of the basis sets we have used in our recent calculations of bounds to quantum mechanical properties. The similarity of the convergence properties between our bounds and the incompleteness coefficient suggests that Löwdin's criterion is likely to be useful in practice.
Errors in molecular integrals: An influence on RHF energy values
Authors: Stepanov Nikolaj F. , Pupyshev Vladimir I. 
Published: December 2004

AbstractThe influence of errors in molecular integrals on the calculated RHF energy values is considered for two models which correspond to round‐off and shift errors. The energy variations induced by errors in elements of one‐ and two‐electron matrices and the overlap matrix are represented in a quadratic approximation and the same degree of accuracy is maintained for mean values and standard deviations. The formulas given point out that mean values are less than zero when some of the errors are non‐shifted. Special care is required when Gaussian lobe functions are used.
Cubic harmonics in Cartesian coordinates
Authors: Kwiatkowski T. , Olszewski S. , Wierzbicki A. 
Published: December 2004

AbstractA full set of harmonics which are at the basis of all irreducible representations of the cubic point group and having order l ⩽ 16 has been calculated in terms of Cartesian coordinates. Due to their complication, former calculations of harmonics in Cartesian coordinates for half of the irreducible representations did not exceed l = 6. The method presented in this paper is a modification of that originally given by Von der Lage and Bethe; it can be readily applied to the calculation of harmonics of arbitrary order for any irreducible representation of the cubic point group.
Reduced local energy as a criterion for the accuracy of approximate H2 wave‐functions
Authors: Javor Frank , Thomas Gerald F. , Rothstein Stuart M. 
Published: December 2004

AbstractThe goodness of the local fit of an approximate wave‐function, \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \psi $\end{document}, to the exact function, ψ0, is \documentclass{article}\pagestyle{empty}\begin{document}$ |\tilde \psi - \psi _0 | $\end{document}. From this quantity the global accuracy of \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \psi $\end{document} is defined and a “working supposition” is presented, which quantitatively relates the global accuracy to the accuracy of expectation values. Two criteria based on the accuracy of the reduced local energy and the density respectively, are presented as alternatives to \documentclass{article}\pagestyle{empty}\begin{document}$ |\tilde \psi - \psi _0 | $\end{document}. The relative global accuracies of eight wave‐functions for H2 are determined using the two criteria. The ‘working supposition’ is applied and predictions are made concerning the relative accuracies of the expectation values of the following operators: z2, r2, x2 + y2, 3z2 −; r2, ξ, r, r, and EL (the reduced local energy). The success rate is high (>90%) except for those operators which are sensitive to interelectron coordinates or derivatives of the wave‐function.
Discontinuous approximate molecular electronic wave‐functions
Authors: Stuebing Edward W. , Weare John H. , Parr Robert G. 
Published: December 2004

AbstractFollowing Kohn (reference 4), Schlosser and Marcus (reference 3), and Weare and Parr (reference 2), an energy functional is defined for a molecular problem which is stationary in the neighborhood of the exact solution and permits the use of trial functions that are discontinuous. The functional differs from the functional of the standard Rayleigh–Ritz method in the replacement of the usual kinetic energy operators T̂(μ) with operators T̂′(μ) = T̂(μ) + Î(μ), where Î(μ) generates contributions from surfaces of nonsmooth behavior. If one uses the ∇Ψ · ∇Ψ way of writing the usual kinetic energy contributions, one must add surface integrals of the product of the average of ∇Ψ and the change of ∇Ψ across surfaces of discontinuity.
A relationship between the sizes and energies of localized molecular orbitals. I. A study of selected first‐row hydrides
Authors: Daudel R. , Goddard J. D. , Csizmadia I. G. 
Published: December 2004

AbstractAb initio calculations have been performed on selected first‐row hydrides with a large Gaussian basis set. Energy localized molecular orbitals (LMO'S) were computed and analysed in terms of their sizes and shapes. The total molecular electronic energy was partitioned into components which may be associated with an MO, and the relationship between the sizes and energies of such orbitals was examined. It was found that a simple energy–size relationship exists for core LMO'S but only approximately holds for bond LMO'S.
A semi‐empirical MO theory for ionization potentials and electron affinities
Authors: Selsby R. G. , Machin C. , Hernandez M. L. 
Published: December 2004

AbstractA method for calculating the vertical ionization potentials and electron affinities according to their fundamental definition as differences between energies of the singlet ground and doublet ionized states is developed for cyclic hydrocarbons. The method adopts a new approach based on the central idea of a recent ab initio IP and EA calculation in which orbital exponents are optimized for both ground and ionized states. Hence, all the semi‐empirical parameters of the MO theory are written as functions of the effective nuclear charge which, in turn, is made self‐consistent with the molecular electronic charge distribution of the species. Although the MO theory is developed in the π electron approximation, the changes in the σ electron density, resulting from the loss or gain of a π electron, are explicitly considered in the calculation. The theory is compared to the earlier work of Hoyland and Goodman and tested against the first five polyacenes and on the condensed ring aromatics phenanthrene, pyrene, and perylene. Except for perylene, the results are in close agreement with the latest photoelectron spectroscopic measurements.
Accurate Thomas–Fermi–Dirac calculations for diatomic systems
Authors: Yonei K. , Goodisman J. 
Published: December 2004

AbstractThe Thomas–Fermi–Dirac equation for the electron density in a homonuclear diatomic system is solved numerically. The problems arising and methods of dealing with them are discussed and attention is given to the accuracy of the calculated energies. Comparisons are made to previously published work employing approximations, permitting a discussion of their utility.
Rotational invariance of INDO theories including d‐orbitals into the basis set
Authors: Figeys H. P. , Geerlings P. , Van Alsenoy C. 
Published: December 2004

AbstractIt is proved that in general the INDO approximation to the full Roothaan theory does not lead to expressions which are invariant under a rotation of local atomic axes. However, when only s‐ and p‐functions are used in the atomic basis set, the equations obtained are invariant due to the special properties of the p‐functions. When d‐orbitals are included into the basis set, rotational invariance is lost but can be restored if a supplementary approximation is introduced.
Atomic SCF loge localized wave functions
Authors: Ludeña Eduardo V. 
Published: December 2004

AbstractWe report in this work SCF atomic calculations for Li, Be, B, C, and Ne using a basis set of completely loge‐localized functions. For these second row atoms the total volume R3 was partitioned into a spherical loge of radius R and its volume complement. The loge‐localized basis functions were constructed as a product of Slater‐type orbitals and a cut‐off factor. The energy values obtained differ significantly from the Hartree–Fock ones indicating that the delocalization effects—not included in these calculations—are important.
Potential energy curves for NiH and NiH2
Authors: Guse M. P. , Blint R. J. , Kunz A. B. 
Published: December 2004

AbstractThe potential energy curves for the NiH and linear HNiH molecules resulting from the 3d84s2 and 3d94s configuration of nickel are calculated using the unrestricted Hartree–Fock and perfect pairing generalized valence bond methods. NiH bonding in the 3d84s2 configuration is by means of an sp hybrid orbital which comes from the 4s2 shell leaving a singly occupied nonbonding orbital free to bond to another hydrogen atom. The bond to the 3d94s configuration contains primarily the 4s orbital leaving an empty orbital in the nickel 3d shell which in turn bonds very weakly with another hydrogen. These results are compared to similar studies of the hydrogen atom on Sc, Mn and Cu and some implications for hydrocarbon catalysis are considered.
A study of the convergence in iterative natural orbital procedures
Authors: Thunemann K. H. , Römelt J. , Peyerimhoff S. D. , Buenker R. J. 
Published: December 2004

AbstractA series of five different Iterative Natural Orbital (INO) procedures are tested for the ground state of water and are compared on the basis of their respective convergence properties. The choice of configuration space employed in these methods is shown to be a key factor in determining the results of such calculations. If the CI space is generated by taking all single excitations with respect to a series of dominant or reference configurations, it is concluded that the practice of varying such generating species at each iteration is highly desirable. In general the choice of the configuration space is found to be much more important than the attainment of strict NO convergence, whereby experience indicates that inclusion of all singly and doubly excited configurations (or at least a select subset thereof) relative to a series of dominant configurations provides the most efficient means of approximating the true NOS of a given system within the general INO framework.
Two‐parameter ω‐technique for MO calculations
Authors: Mathur S. C. , Singh D. C. , Kumar B. , Mitra S. 
Published: December 2004

AbstractA two‐parameter ω‐technique for MO calculations is proposed. The parameters ω and ω′ are chosen empirically to obtain a good agreement between calculated and observed bond lengths. The method amounts to an inclusion of the effect of nearest‐neighbour electronic repulsion integrals into the conventional ω‐technique.
The pairwise correlated generalized valence bond model of electronic structure. II. A simple physical model for electron correlation
Authors: Petersson G. A. 
Published: December 2004

AbstractWhen electron pair correlations are incorporated into generalized valence bond wave functions, the necessary and sufficient wave functions for the quantitative description of chemical reactions are achieved. The resulting electron pair correlation functions are shown to be invariant; hence the generalized valence bond orbitals contain all the information in the correlated wave functions. In the case of pair correlation energies, this information is expressed through a simple function of the orbital overlaps. The resulting overlap approximation is applied to ground states, excited states, and transition states for chemical reactions. In all cases the exact energy is reproduced to within 0.5 kcal/mol (0.001 hartree). The pairwise correlated generalized valence bond method provides an opportunity to accurately predict reaction pathways for system of chemical interest.
Application of graphical methods of spin algebras to limited CI approaches. I. Closed shell case
Authors: Paldus J. , Adams B. G. , Čížek J. 
Published: December 2004

AbstractThe time independent diagrammatic technique based on the mathematical methods of quantum electrodynamics (second quantization, Wick's theorem, Feynman‐like diagrams) is combined with graphical techniques of spin algebras to derive general expressions for the matrix elements of spin independent one‐ and two‐particle operators between spin symmetry adapted ground, mono‐ and bi‐excited configurations of a closed shell system. Two coupling schemes are considered for bi‐excited states and their relative merits are discussed. Finally, the results are used to derive compact expressions for the coupling coefficients of the direct configuration interaction from molecular integrals (CIMI) method.