bluuebunny/crossref_metadata_2025_split huggingface dataset:
Variable ζ calculation for self‐consistent screening parameters in ab initio molecular theory
Authors: Selsby R. G. 
Published: December 2004

AbstractA resolution of Roothaan's HF–SCF–LCAO–MO equations is proposed in which atomic orbital exponents (ζ) are made dependent on the molecular charge distribution and included in the self‐consistent scheme. Screening parameters so obtained are self‐consistent with the molecular orbital coefficients and compare closely to optimum orbital exponents found by other methods.The technique is applied to the ground, lowest positive, and lowest negative ion states of the hydride series LiH, BH, and HF. Calculated potential curves are used to define purely theoretical values for the vertical and adiabatic ionization energies and electron affinities. Predictions are compared to experimental values where available.
Dispersion relations and spectral densities
Authors: Brändas Erkki , Hehenberger Michael , McIntosh Harold V. 
Published: December 2004

AbstractWeyl's eigenvalue theory for ordinary second‐order differential equations is discussed for the case of a continuous spectrum. It is demonstrated that the spectral density function obtained from a suitably averaged Green's function, equal to the Weinstein function, can be directly related to the Weyl–Titchmarsh m‐function. The explicit connections with scattering theory are derived and it is found that the Weyl and Jost solutions are proportional; the proportionality factor being the reciprocal value of the latter at the origin. The physical interpretation of the complex poles of the spectral density is discussed in relation to Gamow's exponentially growing functions. The advantage of using a formulation that allows for a “perturbation” of boundary conditions is pointed out.
Potential surface crossings for diatomic molecules
Authors: Berrondo M. , Rojas D. H. 
Published: December 2004

AbstractWe study the nonradiative processes in diatomic molecules produced by a potential surface crossing in terms of a generalized optical potential containing an absorptive and a resonant part. The theory is applicable to inelastic atomic scattering, predissociation, accidental predissociation and collisionally induced dissociation. The coupling term between the electronic surfaces (in the diabatic representation) is evaluated semiclassically in terms of the “inelastic action” s. While the Landau–Zener formula is obtained from a linearized function of s, a more realistic form is proposed as a rational fraction in s.
Combined CI–HY studies of atomic states. II. Compact wave functions for the be ground state
Authors: Sims James S. , Hagstrom Stanley A. 
Published: December 2004

AbstractCombined CI–HY method techniques have been employed in obtaining a 57‐term CI–HY wave function with an energy of −14.66632 a.u. A method due to Brown has been adopted for obtaining this wave function and various shorter expansions. A 44‐term expansion with an energy of −14.66606 a.u. is analyzed in terms of various pair effects, and qualitative arguments are presented for understanding these effects.
Effect of approximate linear dependence on the solution of the eigenvalue problem: A study by means of the super‐secular equation
Authors: Nordling J. O. 
Published: December 2004

AbstractUsing the super‐secular equation, as defined by Löwdin, this study gives a numerical illustration of the difficulties involved in the solution of the Schrödinger equation with approximate linear dependence in the basis set. The harmonic oscillator is chosen as the model problem and the main part of the study is made for Gaussians as basis set. For comparison some calculations are also reported for another basis set, exponentials. The results show that, with the numerical precision available on present computers, the numerical accuracy for the calculated eigenvalues is critically small also for rather small orders of the basis set—and that the accuracy decreases rapidly with increasing order.
Electronic structure and collective excitations of long molecules with conjugation in the main chain
Authors: Misurkin I. A. , Ovchinnikov A. A. , Vinodgradov G. A. 
Published: December 2004

AbstractElectronic structure and collective excitations of long molecules with conjugated bonds in the main chain (linear polyene, cyclic polyene, polyphenylacetylene (PPA)) are considered. The electronic structure of these polymers is investigated by the generalized Hartree–Fock method. The first triplet collective excitations are derived using the compact technique of the Green's functions. This approach is shown to be equivalent to the random phase approximation. The problem of the triplet collective excitations in long cyclic polyenes is solved analytically and good agreement with the exact results is found. The effects of the free ends in a linear polyene are considered. The approach developed for PPA and polyene may be applied to an investigation of any polymer molecule with equivalent unit cells.
Selected stable states in large quantum systems
Authors: Hatch Dorian M. 
Published: December 2004

AbstractThe utility of an infinite number of degrees of freedom is examined in the context of quantum systems. Such systems are known to allow inequivalent representations of the commutation relations, qualitative differentiation (spontaneously broken symmetries) arising from cooperative effects, and superselected stable states. This freedom is discussed and then used in an exactly soluble model of the measurement process.
The “seniority” classification of spin hamiltonian and states of complexes and molecules in approximation of one‐centered plethysms
Authors: Men B. A. , Leschinsky M. L. , Men A. N. 
Published: December 2004

AbstractA modification of the concept of “seniority” for the classification of the permitted terms and the effective operators in complexes and molecules is presented. Tables of the states of complexes of impurity orbital nondegenerate ions (N = 3, 4) with spin S (\documentclass{article}\pagestyle{empty}\begin{document}$ S = \frac{1}{2} - \frac{7}{2} $\end{document}) and the corresponding tensorial operators are given.
A generalized formula for the energies of alternant molecular orbitals. I. Homonuclear molecules
Authors: Tyutyulkov N. N. 
Published: December 2004

AbstractUsing the method of alternant molecular orbitals (AMO) it is shown that the energies ofAMO's (Ek), for any alternant homonuclear molecule having a singlet ground state, are connected with the energies of theMO's (ek) obtained by the conventional Hartree–Fock (HF) method by the formula\documentclass{article}\pagestyle{empty}\begin{document}$ E_{k\alpha (\beta )} = \pm \sqrt {\Delta ^2 + e_k ^2 } $\end{document}, where Δ is the correlation correction. The formula is applicable in the semiempiricalLCAOform used in the Pariser–Parr–Pople theory, by Hubbard's approximation of γ integrals.
Electric field gradient calculation in V2O5
Authors: Lazukova N. I. , Gubanov V. A. , Pletnev R. N. 
Published: December 2004

AbstractThe electric field gradient at the 51V nucleus in V2O5 has been calculated by the Mulliken–Wolfsberg–Helmholtz method. In contrast to the results obtained from crystal field theory, covalency effects in the MO method are shown to give rise to a valence contribution comparable with the lattice contribution. The total electric field gradient correlates with NMR experiments and confirms the adequacy of the method of calculation used.
Variational principles for discontinuous wave functions and the independent particle model of electronic structure
Authors: Ludeña Eduardo V. 
Published: December 2004

AbstractUsing the variational method advanced by McCavert and Rudge, we obtain the independent particle model variational principle for loge localized discontinuous wave functions. The transformation of the variational expressions into matrix form when the loge localized discontinuous orbitals are expanded in finite basis sets is discussed. The simplifications brought about by this new method in the evaluation of molecular integrals are indicated.
Alternant molecular orbitals (amo's) for some organic semiconductors: Ion radical salts from 7, 7, 8, 8‐tetracyanoquinodimethane (TCNQ) and chloranil/ para‐phenylenediamine (PDC) charge transfer complex
Authors: Dugay M. , Thomas J. 
Published: December 2004

AbstractWe report an attempt of ab initio computation for the ground‐state wave‐function of a few organic semiconductors (namely TCNQ salts and the PDC charge transfer complex) for which we show that electrical conduction appears to look strongly like that of a band‐gap semiconductor.
The use of single exponential orbitals in one‐center molecular orbital calculations
Authors: Combs L. L. , Miller Carl P. 
Published: December 2004

AbstractSingle‐exponential Slater type orbitals of the form ψ1 = (1 + L1(r, θ) + L2(r, θ) +…︁+ Ln(r, θ)) exp (− αr) are examined for their potential use as one‐center molecular orbitals. These are then to be used as molecular fragments in a LCMO study. The system examined is HeH+ + with calculated energies and dipole moments being compared to the exact values. These functions behave best in the region of chemical interest (the bonding region) and thus demonstrate a possible usefulness in LCMO calculations and in the field of one‐electron diatomics.
Matrix elements for an approximate ab initio π‐electron theory
Authors: Pilkington Phillip W. , Neely Stanley C. 
Published: December 2004

AbstractThis work involves the derivation of approximate forms for the matrix elements of an ab initio π‐electron molecular orbital theory. The result may be described as a complete neglect of differential overlap mathematical formalism plus σ‐π exchange. The basis set of π atomic functions for these derivations is a set of approximate Löwdin orthogonalized atomic orbitals (LOAO's) produced by successive pairwise orthogonalization. Using these functions, we derive approximate equations for the one‐electron integrals of molecular orbital theory, α and β, which, for the first time, show the effects of overlap‐coupling in a molecule. Many new methods of approximation enter the theory. There are approximate equations for π‐electron, nuclear attraction potentials and for π‐electron, σ‐core repulsion potentials, all approximations are compared to more accurate calculations where possible. A mechanism is also included for testing the effects of σ‐charge shifts upon the results of the π‐electron calculations.
Computation scheme for optimizing multiconfigurational wave‐functions
Authors: Kuprievich V. A. , Klymenko V. E. 
Published: December 2004

AbstractA computation scheme is proposed to determine the wave‐functions of molecular systems within the framework of the CMC SCF theory and the APSG SCF approach. The orbital optimization is carried out by the refined first‐order one‐electron Hamiltonian method. Explicit expressions of the first and second energy derivatives are obtained. In the suggested scheme all the calculations are based on using the matrices of the “partial” Coulomb and the exchange operators constructed over the orbitals at the current iteration cycle.
Generating functions for oscillator matrix elements
Authors: Witschel W. 
Published: December 2004

AbstractTwo general harmonic oscillator elements \documentclass{article}\pagestyle{empty}\begin{document}$$ \left\langle m \right|\hat x^s \hat p\left| n \right\rangle $$\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$$ \left\langle m \right|\exp \left[ { - \alpha \left( {\hbar /m*\omega } \right)\hat x^2 } \right]\exp \left( {\beta \hat x} \right)\left| n \right\rangle $$\end{document} are derived by a generating function method using operator techniques which contain practically all one‐ and two‐centre integrals with equal frequencies of chemical physics.
Generalized existence conditions for surface states of a semi‐infinite Kronig–Penney crystal
Authors: Roy C. L. , Tripathy S. K. 
Published: December 2004

AbstractA derivation of most general existence conditions for surface states of a semi‐infinite Kronig–Penney crystal is reported. They reduce to Steslicka's conditions under a subsidiary restriction and also indicate that the surface‐state energies may lie in the allowed bulk bands. Numerical computations supporting the qualitative conclusions are provided.
A theoretical study of the vibrational structure in the \documentclass{article}\pagestyle{empty}\begin{document}$\tilde{A}^{2}A_{1} - \tilde{X}^{2}B_{1}$\end{document} transition of PH2
Authors: So S. P. , Richards W. G. 
Published: December 2004

AbstractThe potential energy curves of the bending mode of PH2 in the ground 2B1 and the excited 2A1 states have been calculated using ab initio SCF‐MO wave‐functions. The radical is found, in agreement with experiment, to be bent in the two states. The calculated results clarify the interpretations of the anomalous behaviour of observed vibrational intervals, and offer an explanation of the ‘quasilinearity’; of the radical in the 2A1 state.
A variational method for calculating dynamic polarizabilities
Authors: Hameka Hendrik F. , Svendsen E. Nørby 
Published: December 2004

AbstractWe investigate whether or not a previously proposed variation‐perturbation method for calculating static polarizabilities can be used also to calculate dynamic polarizabilities. We find that the method can be used for frequencies below the first excitation frequency of the system. By amending and supplementing the procedures for solving the second‐order equations we can obtain the same accuracy for dynamic polarizabilities as in the previous procedure for static polarizabilities.
Additivity model for calculations of UHF spin densities and charge densities in some methyl‐substituted radical anions
Authors: Sharma K. K. 
Published: December 2004

AbstractThe additivity model as suggested by Moss et al. has been used for predicting spin densities in methyl‐substituted radical anions. Linderberg's relation has been employed for evaluating the core‐resonance integrals (βrs) and a heteroatom model for the methyl group has been used.
The AMO method at small internuclear distances
Authors: Chao K. A. , Oliveira F. A. , De Cerqueira R. O. , Majlis Norberto 
Published: December 2004

AbstractThe AMO function of the hydrogen molecule ψ = ψc + η ψi, where ψc is the covalent part and ψi the ionic part, is investigated for small internuclear distances R. We found η → −1 as R →,−1 as R → 0, contrary to the intuitively expected limit η → 1. However, near R = 0 an analytical expression of ψ is derived, showing that ψ reduces to the helium ground state as R → 0. We have proved that the empirical concept „covalent and ionic character”︁ should be replaced by the symmetry argument in the case of small R.
Generalized Jansen's perturbation theory for exchange interactions between aroms or molecules
Authors: Suzuki Noboru 
Published: December 2004

AbstractThe theory for treating exchange interactions between atoms or molecules as a perturbation, which was first propoed by Jansen, is extended to general cases by the use of the group algebraic technique and a nonorthogonal basis set. As a result, a new expresion for the perturbation ket and energy of each order is obtained. A comparion of the expression with those presented by other investigators is made.
On the convergence of one centre partial wave treatments for diatomic molecules. H (1sσg) and coulomb versus electron exchange intermolecular forces
Authors: Ali M. K. , Meath William J. 
Published: December 2004

AbstractA semi‐analytical solution for the nucleus and the internuclear midpoint centred partial wave equations representing the Schrödinger equation for the H‐like molecule is discussed. Explicit proton and internuclear midpoint centred results for the interaction energy and the wave function for the 1sσg state of H are obtained as a function of the internuclear distance R and the number of coupled differential equation N N ≦ 14 used to represent the Schrödinger equation for the molecule. These, together with some energy optimized floating one centre results for the interaction energy, are used to (1) discuss the convergence of the partial wave calculation as a function of R,N, and the position of the expansion centre, (2) discuss the concept of Coulomb versus electron exchange interaction energies, and (3) discuss briefly the convergence problems of analogous one centre perturbation theory treatments for the ground state H molecule. The electron exchange H (1sσg) molecule provides a severe test for the uefulness of partial wave methods.
A study of molecular one‐electron properties in terms of localized molecular orbital components
Authors: Goddard John D. , Czizmadia Imre G. 
Published: December 2004

AbstractA number of molecular one‐electron progperties have been analyzed by partitioning their electronic components over energy localized molecular orbitals (LMO). The ammonia and ethane molecules, calculated in an Approximately double zeta qualtiy basis set, were considered. The partitioning of the electronic components of certain one‐electron properteies over LMO allows a quantitative rationalization of the sensitivity of certain properties to basis set effects due to the differeing degree of difficulty of accurately determining different LMO as measures of the molecular electron density.
Electronic‐structure studies of solides. V. Rigorous Hartree‐Fock treatment of metallic hydrogen using a plane‐wave basis
Authors: Kumar Lalit , Monkhorst Hendrik J. , Oddershede Jens 
Published: December 2004

AbstractWe have performed Hartree‐Fock calculations for simple cubic metallic hydrogen crystals using Bloch functions expanded in plane waves, All integrals were evaluated accurately including exchangeterms. Increasingly larger basis sets were used, and the total Hartree‐Fock energy obtained with the maximum number of plane waves (27) was −0.4770 hartrees/atom. This total energy is believed to be within a few millihartress of the Hartree‐Fock limit results. The deficiency of a plane‐wave expansion to represent the atomic cusps, however, makes it difficult to obtain the exact Hartree‐Fock limit with a plane‐wave expansion. When the correlation energy (calculated in the random‐phase approximation with Hartree‐Fock bands and functions as zeroth order states) is added, and upper limit of −0.501 hartrees/atom is found for the total energy of this system. The Fermi surface was found to touch the Brillouin zone boundaries around the X points due to an appreciable depression of the band energies in that part of the Brillouin zone. The equilibrium lattice spacing (a = 2.705 bohrs) was slightly smaller than that obtained earlier with an atomic orbital basis.
Convergence properties of generalized inner projections to dynamic polarizabilities
Authors: Ahlberg Ragnar 
Published: December 2004

AbstractGeneralized inner projections to dynamic polarizabilities, αA (iω), are shown to give bounds to dispersion coefficients, CAB, which are improved as the dimensionality of the projections is increased. Error bounds in the regular half‐planes of αA±(ω) are found from the maximum principle. Comparison with related approximations to polarizabilities is made.
The concept of fractional parentage for arbitrary molecular point groups
Authors: König E. , Kremer S. 
Published: December 2004

AbstractThe method of fractional parentage is extended to the general case of mixed configurations in arbitrary nonsimply reducible groups, G ⊂ SO(3). Particular attention is devoted to the calculation of coefficients of fractional parentage (CFP) and expressions are provided for the matrix elements of F and G type operators between N electron functions.
MS‐Xα calculations of the electron affinities and ionization potentials of some heavy metals and their hydrides and fluorides
Authors: Preston Harry J. T. , Kaufman Joyce J. 
Published: December 2004

AbstractMS‐Xα calculations have been performed for the neutral species and the transition states for the positive and negative ions of the heavy metal atoms Mo, W, Re, Ir, Pt, and U and their diatomic hydrides and fluorides. Both nonspin‐polarized and spin‐polarized calculations were performed. The main purpose of this study was to gain insight into which negative ion species might be preferable to try to prepare for use in ion sources for tandem accelerators.
Vanadium monoxide energy‐spectrum calculation using the augmented‐plane‐wave and Green's function methods
Authors: Wolf G. V. , Farberov D. S. , Shirokovskii V. P. 
Published: December 2004

AbstractEnergy bands of VO are calculated by the augmented‐plane‐wave and Green's function methods. The results of calculations with different potentials are compared. The physical causes for differences in the bands are discussed.
Collision theory treatment of monomolecular and bimolecular gas reactions
Authors: Christov S. G. 
Published: December 2004

AbstractAn exact collision theory of unimolecular and bimolecular gas phase reactions is derived from a general quantum‐mechanical formulation of reactions rates based on the assumption that the reactants are in thermal equilibrium. In this way the quantum corrections to the classical collision theory expressions are rigorously defined. Approximate formulas for these corrections make it possible to determine well the temperature ranges within which the classical and the semiclassical approximations are valid. A comparison is made between the collision and the transition state theory with emphasis on some conceptual difficulties of the latter in treating the simple decomposition and recombination reactions. It is shown that in the classical (high temperature) limit these theories are incompatible except when the reaction coordinate is entirely separable (i.e., when the transition state theory is no longer useful).
Simple extended STO basis sets. Helium
Authors: Pellégatti Alain 
Published: December 2004

AbstractThe two‐parameter function, φ = (C1 + C2rn−1) exp (−ζr), (n = 2–5), has been used as a basis function to determine the independent particle model energy of two‐electron atomic systems in their ground state. The best energy is found for n = 3 (He—B3+) and for n = 4 (H−). Our energy values are significantly close to Hartree‐Fock results.
Perturbation treatment of the Hartree–Fock equations of 1s2p3s4Pθ state of the lithium isoelectronic sequence
Authors: Samanta S. R. , Ali M. A. 
Published: December 2004

AbstractThe first order Hartree–Fock equations of the 1s2p3s 4P0 state of the three‐electron atomic systems have been solved exactly. These solutions are used to evaluate Hartree–Fock energy up to third order with high accuracy. The third order Hartree–Fock energies for Li to Ne7+ are compared with those derived from experiment and other theoretical calculations.
Relationship between orthogonalization and orbital localization procedures
Authors: Lévy B. , Berthier G. 
Published: December 2004

AbstractA condition for the equivalence of the Löwdin orthogonalization method and various localization methods is derived, taking the matrix elements of the localizing operator into consideration. In the example of the π atomic orbitals of benzene, it is shown that the “ultralocalized” functions defined in the Anderson fashion with help of the Boys minimum‐fluctuation criterion do not fulfill this condition, in contrast with a Ruedenberg‐type localization.
An application of the method of conjugate gradients to the calculation of minimal basis set localized orbitals
Authors: Ryback W. , Poirier R. , Kari R. 
Published: December 2004

AbstractUsing an STO‐3G basis set, energy localized molecular orbitals (LMO) were determined for the ten electron series HF, H2O, NH3, and CH4 as well as for CH3OH and C2H2F2. The method of conjugate gradients is shown to be a viable alternative to other non‐eigenvalue methods. The characterization of the LMO in terms of first and second moment measures indicates that the STO‐3G basis set LMO may be accurately correlated to larger sp basis set LMO. Also, it is shown that the first and second moment measures display a good linear correlation with the classical concept of electronegativity.