bluuebunny/crossref_metadata_2025_split huggingface dataset:
Time‐dependent quantum theory III. Model for vibrational relaxation in crystals
Authors: Schurr J. Michael 
Published: December 2004

AbstractA one‐dimensional model consisting of a “diatomic” spring attached on one side to a rigid wall and on the other side to a linear array of mass‐springs is proposed as a model for the vibrational relaxation of small solute molecules in host lattices. A modification allowing a change in the equilibrium internuclear extension of the diatomic spring is also incorporated. The Hamiltonian divides naturally into pure diatomic, pure linear crystal, and the two mixed perturbation terms, one giving rise to stepwise vibrational cascade damping accompanied by phonon emission, and the other process, lattice relaxation, giving rise to phonon emission without any change of the quantum number of the diatomic spring. The cascade damping rate for a diatomic spring with a frequency less than the the maximum frequency of the linear crystal is calculated to second‐order, and it is shown that the perturbation series converges in this range.An upper bound to the cascade damping rate for a diatomic spring with a frequency greater (i.e., 4.5 ×) than the cut‐off frequency of the linear crystal is determined to be very small, λ ≦ 104 sec −;1.The rate for the lattice relaxation process corresponds to a line‐width λ = 6 cm −1 at 0K.An explanation for the thermal quenching of the low‐temperature luminescence of SO2 is based upon induced cascade‐phonon emission.
On the energy difference between the lP and 3P states of the beryllium isoelectronic sequence
Authors: Tatewaki Hiroshi , Taketa Hirosiji , Sasaki Fukashi 
Published: December 2004

AbstractWave functions of the 1S (ground state), 3P and 1P states for the beryllium isoelectronic sequence have been obtained in various approximations.The HF 2p orbitals for the 1P and 3P states are similar except for Be, where the 2p orbital is quite diffuse for the 1P state.The difference between the experimental E(1P) – E(3P) and the HF E(1P) – E(3P) is 0.62 eV for Be and 1.17 ∼ 1.40 eV for B+ ∼ F5+. The disagreements are attributed to the correlation effects between the 2s and 2p electrons. This is confirmed by ci calculations.It is shown that a limited basis SCF calculation reproduces the above feature of the HF results if we treat the orbital exponents as the variational parameters. The use of the Slater values for the orbital exponents is shown to be inadequate especially for the Be 1P state.The conclusions of this paper will be useful for discussing the V–T separations of H2 and C2H4.
Origin of the irrational part contained in the angular numerical factors of matrix elements of the Coulomb operator
Authors: Sureau A. 
Published: December 2004

AbstractBy means of second quantization formalism and angular momenta coupling techniques, we show the reason why the irrational part of the coefficients of the Slater integrals Rk(ab, cd) in the expression \documentclass{article}\pagestyle{empty}\begin{document}$ (\Psi |\sum\limits_{i < j} {e^2 /r_{ij} |\Psi } ') $\end{document} is common to all values of k, a, b, c, d, and depends only on (Ψ∣ and ∣Ψ′).
A self‐consistent variation‐perturbation theory for open shell atomic systems: Calculation of polarizabilities and shielding factors
Authors: Mukherjee P. K. , Moitra R. K. , Mukherji A. 
Published: December 2004

AbstractIn this paper a fully coupled variation‐perturbation theory has been introduced for handling open‐shell atomic systems in the presence of static perturbations. The static dipolar and quadrupolar polarizabilities and shielding factors for Li, Be+, B2+, B, C+, Na and Al have been calculated and compared with available results. Important sources of discrepancies in previous calculations of shielding factors have been noticed and critically examined. The dipolar shielding factors calculated in this paper show satisfactory agreement with the theoretical N/Z ratio. In the absence of any theoretical test for the quadrupolar shielding factor, the accuracy of the calculations of γ∞, should be judged in the light of the accuracy of the corresponding β∞ values.
Continuous degeneracy and energy‐localization of molecular orbitals
Authors: England Walter 
Published: December 2004

AbstractThe energy‐localization method is examined for continuous degeneracy using a grouptheoretic approach. Conditions for the degenerate orbitals are obtained and an enumeration of symmetry groups where continuous degeneracy may occur is given. It is found that the orbitals may be equivalent under operations not contained in the total symmetry group. An alternative explanation for the free rotation of the lone pairs in F2 is offered.
Long range interaction energies using Gaussian basis sets and a one center method
Authors: Singh T. R. , Bukta J. F. , Meath W. J. 
Published: December 2004

AbstractA one center method, based on the work of Karplus and Kolker, is discussed and used to calculate the induction energy, through O(R−8), for the H(ls) – H+ interaction employing two types of Gaussian basis sets constructed from functions of the form {rje−αr2}. The effective hydrogen atom excitation energies and transition multipole moment matrix elements generated in these calculations are used to calculate the dispersion energy for the H(ls) – H(ls) interaction, through O(R−10), and the R−9 triple dipole energy corresponding to the interaction of three H(ls) atoms. The results indicate that Gaussian functions can form good basis sets for obtaining long range forces for a variety of multipole interaction energies.
Self consistent calculation of dynamic multipole polarizabilities and excited state wave functions of open shell ions: Li sequence
Authors: Moitra R. K. , Mukherjee P. K. 
Published: December 2004

AbstractA variational formulation of the Hartree–Fock–Roothaan (HFR) theory for open shell ions in presence of time dependent perturbations is presented. The theory has been used to calculate the dynamic polarizabilities of the first three ions of the Li sequence. The polarizability values, extrapolated to zero frequency, show good shell by shell agreement with the corresponding static results. The polarizability graphs display resonance behaviour at the transition frequencies of the ions, and a study of these points leads to analytic HF wave functions for their low lying excited states. The calculated transition frequencies are in excellent accord with the experimental values. The calculated oscillator strengths for the 2s → np transitions are in reasonable agreement with the extensive multiconfiguration calculations of Weiss and the available experimental results.
Internal symmetry groups of non‐rigid molecules
Authors: Gilles J.‐M. F. , Philippot J. 
Published: December 2004

AbstractHougen has established, for quasi‐rigid molecules, the relationship between permutationinversions acting on the molecular Hamiltonians written in Cartesian co‐ordinates and permutation‐rotations (perrotations) of symmetry acting on nuclear equilibrium configurations. We extend these relations to the case of non‐rigid molecules. For this, we introduce kinetic perrotations which act on nuclear equilibrium configurations in the same way as do Altmann's isodynamic operators. We show that isodynamic operators do not always form a group. Moreover, their action cannot be extended to the electrons. They cannot be used for the classification of molecular wave functions. This classification is achieved by using the group of Longuet‐Higgins and the group of the corresponding feasible perrotations.
On the representations of the rotation group
Authors: Corio P. L. 
Published: December 2004

AbstractThe matrices of the irreducible representations of the 3‐dimensional rotation group are shown to be related to Krawtchouk's orthogonal polynomials of a discrete variable x = j – m', whose degrees are given by n = j + m. The relation follows directly from the recurrence formulas satisfied by the matrix elements and permits a concise development of the formal properties of the rotation matrices. In particular, an asymptotic relation for large j is developed that generalizes a formula first discussed for a special case by Wigner.
Coupled Hartree–Fock calculation of the electric dipole hyper‐polarizabilities: He sequence
Authors: Bhattacharya A. K. , Sengupta S. , Mukherji A. 
Published: December 2004

AbstractThe variation perturbation method in the coupled Hartree‐Fock (HF) scheme has been used to calculate the fourth‐order energies of He, Li+ and Be2+ ions subjected to a uniform external electric field. The hyper‐polarizabilities γh which are related to the fourthorder energies have been calculated neglecting intra‐atomic correlation. For He the observed value is γh = 53.6 ± 4.0 a.u. The present estimate in the coupled and uncoupled HF schemes yield 36.2 and 45.3 a.u. respectively. The other calculations using correlated ground state wave function gave values in the range 42‐44 a.u. The discrepancies between our result and those of others have been discussed.
An expansion for four‐center integrals over Slater‐type orbitals
Authors: Salmons Lydia S. , Ruedenberg Klaus 
Published: December 2004

AbstractA new expression is given for the electron repulsion integral over Slater‐type orbitals on four different centers. It is based on the asymptotic expansion derived from the bipolar expansion of a previous paper. The expression has the form

where qp = {np, lp, mp}. Both F and σ are closed expressions. The quantity F is a combination of incomplete gamma functions, Laguerre polynomials and spherical harmonics. It depends upon the relative coordinates of a point P on the AB axis and a point Q on the CD axis. The functions σnlm(A, B) depend on the charge distribution (χAχB); they have the character of overlap integrals and are of the form
The generalized separated electron pair model. III. An application to three localization schemes for CO
Authors: Robb M. A. , Csizmadia I. G. 
Published: December 2004

AbstractThe separated electron pair (SEP) model (strongly orthogonal geminals) and methods for its systematic extension have been applied to three different localization schemes for CO. The optimum SEP wave function is obtained for the particular localization scheme that involves three equivalent bent bonds. The major corrections to the SEP model arise from one‐electron transfer terms. Two‐electron transfer terms were important only for those pairs that were not well localized. It was found that the separate definitions of the total intrapair and interpair correlation energies did not depend strongly on the choice of localization scheme.
An economic storage and processing method for two‐electron integrals in LCAO‐MO calculations
Authors: Billingsley Frank P. 
Published: December 2004

AbstractAn economic algorithm for storing and processing two‐electron integrals arising in LCAO‐MO calculations is presented. The integrals are sorted prior to the SCF iterative scheme, classified according to equivalences in the orbital indices and finally stored on separate files that contain only integrals of one type. The novel approach of physically separating the integrals according to category is shown to be more efficient than random storage. Actual computing times for the new technique are tabulated for a representative number of molecular systems and compared with times obtained using previously reported methods.
Theoretical studies of diamagnetic properties of the hydrogen molecule ion. I. Approximate variation‐perturbation calculation
Authors: Garrett Thomas B. , Zeroka Daniel 
Published: December 2004

AbstractA variation‐perturbation method, analogous to a technique devised by Das and Bersohn for the study of the hydrogen molecule, is developed for calculation of the diamagnetic susceptibility χ and magnetic shielding σ and is applied to a study of the hydrogen molecule ion. Two approximations are investigated–in a first approximation, χ = −0.37814α2a and σ = 1.112 × 10−5 c.g.s. units and in a second approximation, χ = −0.37569α2a and σ = 1.128 × 10−5 c.g.s. units.
Calculation of molecular quadrupole moments and a demonstration of the importance of overlap densities in the theory of polyatomic molecules
Authors: Rabinowitz James R. , Rein Robert 
Published: December 2004

AbstractA computational method for calculating quadrupole moments from molecular wave functions in a Slater orbital basis set is described. Using both IEHT and CNDO wave functions quadrupole moments for a series of polyatomic molecules are calculated. They are compared with experimental results and the IEHT wave functions are found to give agreement with experiment while CNDO wave functions do not. The importance of bicentric densities (overlap densities) in the calculation of multipole moments is shown. This is followed by a discussion of the usefulness of these wave functions for a quantitative characterization of the electronic structure of large molecules.
The Renner effect in four‐atomic molecules
Authors: Petelin A. N. , Kiselev A. A. 
Published: December 2004

AbstractThe theory of the Renner effect in X2Y2 and X2YZ linear molecules is considered. The Renner equations are obtained with the help of the Born‐Oppenheimer method. It is shown that these equations contain two Renner parameters for an X2Y2 molecule and three Renner parameters for an X2YZ molecules. Assuming these parameters to be small enough, an approximate solution of the Renner equations is obtained with the help of perturbation theory. Some general qualitative results are obtained in the first order of the perturbation theory; the second order calculations are made for some specific cases. The theoretical results are used to consider experimental data concerning the vibrational structure of the 1IIu ‐ 1Σ electronic transition in C2H2 and C2D2 molecules. The frequencies of the bending vibrations and the Renner parameters are calculated for the electronic 1IIu‐state mentioned.
The n‐electron problem and matrices representing the symmetric groups
Authors: Gallup G. A. 
Published: December 2004

AbstractThe application of the representation theory of symmetric groups to the solution of quantum chemical problems is discussed. This is done using matrices which do not represent Sn in the normal sense, but which are much simpler to calculate than the Yamanouchi‐Kotani representation. A complete discussion of the calculation of these matrices is given.
Le champ autocoherent non hermitien
Authors: Gouyet J. F. 
Published: December 2004

AbstractA theoretical study of the spin‐optimized self‐consistent field methods is given in a second quantization formalism using the occupation‐branching number representation and a biorthogonal basis treatment given by Moshinsky and Seligman. A diagrammatic presentation can then be introduced. Further investigation will be thus facilitated.
Effect of many‐body interactions on the stability of rare‐gas halides
Authors: Lombardi E. , Ritter R. , Jansen L. 
Published: December 2004

AbstractExchange perturbation theory of the Rayleigh‐Schrödinger type is applied, in first and second orders, to the problem of bonding in rare‐gas halides. The basic model is that of a four‐electron, three‐center system with one effective electron replacing the unpaired electrons of a halogen atom, and two spin‐paired electrons representing the closed shells of the rare‐gas atom. On the basis of exchange perturbation theory, the model verifies a direct parallelism between bonding in rare‐gas compounds and the phenomenon of super‐exchange in ionic solids with paramagnetic cations. It is found that the observed stability and specific geometric configuration of the xenon and krypton fluorides are readily reproduced by the model. In addition, the model explains why other dihalides cannot exist. The two principal components of the interaction energy are found to be indirect exchange between halogen atoms via the rare‐gas atoms (attractive in the stable configurations) and, in compounds with coordination higher than two, simultaneous interactions between three halogen atoms (always repulsive). The observed approximate constancy of the binding energy per bond in xenon fluorides with increasing coordination is accounted for.
Product of group‐function expansions for correlated wave functions
Authors: Mehler E. L. 
Published: December 2004

AbstractA theorem is proved which demonstrates the relationship between a product of group functions describing the correlated motion of a particular group of electrons in an N‐electron system and a wave function obtained from the exact wave function which describes the correlation of the same group of electrons. By considering such products of group functions as elements in a variational wave function, an expansion for correlated wave functions is suggested, which emphasizes the correlated motion of groups of electrons in the whole system.
Spin density distributions in some fluorinated radical cations
Authors: Kumari Usha , Ray N. K. 
Published: December 2004

AbstractA theoretical study of π‐electron spin density distributions has been made for a series of fluoro‐substituted hydrocarbon radical cations using unrestricted Hartree‐Fock theory. Although some of the predicted proton splittings are not in very good agreement with experiment, the overall agreement with experiment can be passed as fairly satisfactory considering the approximate nature of the theory used. The experimental fluorine splittings can be well predicted by using a one‐parameter relationship between the isotropic fluorine splitting (aF) and the π‐electron spin density (ρCC) on the attached carbon. It has been further shown that both ρCC and the proportionality constant (Qeff) in the linear relation, are fairly insensitive to the parameter choice.
On the dimerization of BH3 and the associated delocalization (resonance) energy
Authors: Edmiston Clyde , Lindner Peter 
Published: December 2004

AbstractSCF calculations utilizing a basis of all s‐type Gaussians have been performed to investigate the dimerization of BH3 to B2H6. Localized molecular orbitals and pseudonatural orbitals are calculated. The dimerization energy obtained (11.5 kcal/mole) supports the assumption that the non‐Hartree‐Fock interactions (electron correlation) play a dominant role (Exp = 40–60 kcal/mole).The energy of the principal type of resonance structure based on the SCF‐MO's of the magnified image separated‐but‐distorted BH3 systems is rigorously calculated and found to be 150 kcal/mole higher in energy than the SCF energy of B2H6. Thus, resonance stabilization (delocalization) is shown to be extremely important to the stability of the “three‐center” bonds in B2H6, as has been suspected for many years.
Technique d'optimisation de l'energie SCF en fonction des exposants de slater
Authors: Bouscasse L. , Phan‐Tan‐Luu R. , Vincent E. J. , Metzger Et J. 
Published: December 2004

AbstractWe describe a method to optimize simultaneously Slater orbital exponents. The procedure is based on Newton's method and requires the derivatives of the energy as a function of the exponents. The calculation of these derivatives is described explicitly. The method has been applied to the hydrogen molecule.
Molecular integrals of relativistic effects with gaussian‐type orbitals
Authors: Matsuoka Osamu 
Published: December 2004

AbstractA mathematical analysis is presented of molecular integrals of relativistic interactions in molecules. The integrals are based on Gaussian‐type orbitals and include those arising from variation of electron mass with velocity, one‐electron Fermi contact interaction, electron spin‐same‐orbit interaction, electron spin‐nuclear spin interaction, electron spin‐spin contact interaction, electron spin‐other‐orbit interaction, electron spin‐spin dipolar interaction and electron orbit‐orbit interaction. The integrals are expressed in suitable forms for use in computer. It is also pointed out that the integrals are written essentially in terms of the overlap, nuclear attraction, electron repulsion, or field integrals.
A “Level–Shifting” method for converging closed shell Hartree–Fock wave functions
Authors: Saunders V. R. , Hillier I. H. 
Published: December 2004

AbstractA discussion of Hartree damping in closed‐shell Hartree‐Fock theory is given indicating when the method might force convergence of intrinsically divergent cases. An alternative, but closely related principle, “level shifting” is described, and the advantages of the latter procedure discussed.
An Ab Initio study of the permanganate ion
Authors: Mortola Albert P. , Basch Harold , Moskowitz Jules W. 
Published: December 2004

AbstractAn ab initio self‐consistent computation has been performed on the permanganate ion (MnO) in a large basis set of contracted gaussian functions. The ground state description as well as those of the first two excited states are discussed and compared with those obtained experimentally from photoelectron spectroscopy, ESCA, optical spectroscopy and magnetic circular dichroism.
Multipole structure of exchange polarization energy for H2+ Ion
Authors: Chałasiński G. , Jeziorski B. 
Published: December 2004

AbstractThe exchange polarization energy for the H2+ ion is expressed as an infinite sum of its angular components. At large internuclear distances R, a particular l‐component, referred to as induced 2l‐pole exchange energy, behaves asymptotically like

For larger R this suggests a rather slow l−4 rate of convergence of the series. However, as contrasted to the analogous expansion for the induction energy the convergence speeds up considerably with decreasing internuclear separation.It is also shown that at sufficiently large R a given induced 2l‐pole exchange energy can be computed with a high accuracy using a polarization function obtained with neglect of charge overlap effects. Near the bottom of the van der Waals minimum over 99% of the exchange polarization energy can be produced using this simplified form of the polarization function.
Application of the configuration‐interaction method and the random phase approximation to the Ab Initio calculation of electronic excitation energies of H2o
Authors: Truhlar Donald G. 
Published: December 2004

AbstractBy performing calculations on H2 O similar to the calculations of Dunning and McKoy on C2H4 and HCHO [1a], it is shown that the singlet excited states of the water molecule cannot be adequately represented by an ab initio calculation (no semiempirical elements) using a valence‐like basis set (either minimum basis or double zeta) of Slater‐type orbitals. The triplets which are the lowest states of their symmetry appear to be described more accurately than the other states, and the lowest four triplet excitation energies are calculated to be 8.1, 8.4, 9.5, and 10.3 eV. The implications for the applicability of simple molecular orbital theory of the type commonly applied are discussed.
Perturbative ab initio calculations of intermolecular energies. I. Method
Authors: Daudey J. P. , Claverie P. , Malrieu J. P. 
Published: December 2004

AbstractStarting from a knowledge of approximate wave functions of the isolated molecules (or atoms) A and B, a method is proposed to build up a zeroth‐order ground state and excited configurations for the complex AB in which the molecular orbitals keep their local significance. The standard Rayleigh‐Schrödinger perturbation in this basis provides a decomposition of the zeroth‐order interaction energy as a sum of the electrostatic and repulsion energy. In the second order, it is possible to identify the classical dispersion and polarization forces (modified by a term of order S2) and two additional contributions which are linked to the exchange possibility. The intramolecular correlation component is taken into account and compared with the correlation on the isolated molecules. It is moreover suggested that since we work in a rather limited basis set, the perturbed energy of AB must be compared with the unperturbed energies of A and B calculated in a basis including the vacant orbitals on their respective partner. Finally a possibility for going beyond the second order is described.