bluuebunny/crossref_metadata_2025 huggingface dataset:
On formulas in closed form for Van Vleck expansions
Authors: Gora Edwin K.
Published: December 2004

Canonical transformations have been widely used to simplify Hamiltonians and other operators. In molecular and in solid state theory, the so‐called Van Vieck expansion is usually employed for this purpose while in theories of particles interacting with fields a combination of canonical transformations in closed form with Van Vleck type expansions has been found effective. For some of the transformations used in applications formulas in closed form are well known. It will be shown here that such formulas can be derived whenever the transformation function is bilinear in the canonical variables, and further that the use of matrix operators makes it possible to simplify these derivations substantially. The Cayley‐Hamilton theorem is then used to express the expansions for the matrix operators in closed form. The number of separate operator terms appearing in the formulas thus obtained is the same as the rank of the matrices used. To calculate the coefficients of these operator terms a new type of special functions is introduced. The resulting linear canonical transformations include generalized rotations in both ordinary and phase‐space. Explicit results have been obtained for several two‐ to four‐dimensional problems.
The symmetrized powers of group representations
Authors: Boyle L. L.
Published: December 2004

Tables of symmetrized powers of the irreducible representations of point groups are presented together with a derivation of the formula used to obtain them. It is shown how these tables may be applied to various quantum‐chemical problems.
Decoupled Hartree–Fock methods. I. Calculations for atoms with orthogonalized orbitals
Authors: Náray‐Szabó G.
Published: December 2004

By a proper approximation of the interaction term in a many‐electron Hamiltonian the Hartree‐Fock equations are decoupled. Making use of this simplification one obtains a good initial guess for the wave function with minimal computational work. Refining the procedure, the exact HF limit can be achieved. Total energies, ionization potentials and excitation energies for light atoms are calculated.
One‐Electron properties from approximate LCAO‐SCF wave functions
Authors: Bendazzoli G. L. , Dixon M. , Palmieri P.
Published: December 2004

Approximate and ab initio molecular wave functions are obtained using Gaussian expansions of different length for the Slater orbitals. The expectation values of several one‐electron operators are obtained and the accuracy of different wave functions discussed.
Slater orbital molecular integrals with numerical fourier transform methods. I. (coplanar) multicenter exchange integrals over 1s orbitals
Authors: Graovac Ante , Monkhorst Hendrik J. , Zivkovic Tomislav
Published: December 2004

Slater orbital r12−1 integrals are calculated with a numerical Fourier‐transform method based on a formulation first given by Bonham, Peacher and Cox. Spherical wave expansions are introduced that decouple the Feynman integrations for the charge distribution Fourier transforms. The Feynman integrals are evaluated semianalytically, and their properties are analyzed in detail. The final computational step involves a numerical integration over charge distribution quantities. Results for (coplanar) multicenter exchange integrals over 1s orbitals are given. As long as the charge distributions are overlapping considerably, the method gives good results, even when these distributions are highly asymmetric. The method as presently implemented fails when highly disconnected charge distributions are involved.
Simple test of the utility of modified Hartree‐Fock orbitals: The He atom
Authors: Palting Pancracio , Sanders William A.
Published: December 2004

A method proposed recently for the generation of modified Hartree‐Fock virtual orbitals has been tested by performing a simple configuration‐interaction calculation for the ground state of the He atom. A very compact truncated basis set was constructed by using an a priori criterion based on the probability density within the region of the occupied orbital. The best results were obtained by making the virtual orbital energies more positive.
A double perturbation theory for molecular complexes
Authors: Beretta E. , Vetrano F.
Published: December 2004

Consideration is given to the problem of interactions between molecular systems (magnetic couplings being neglected) by highlighting the fact that the main difficulty of a perturbation theory that takes into account the exchange effects, resides in the differentiated symmetry of the unperturbed state and of the state of interaction (at an overlap other than zero). This difficulty has been overcome by choosing for the Schrödinger equation of the interacting systems a particular representation on the set of unperturbed functions and by reversing the symmetry properties onto the operators. This will lead to a new equation no longer presenting any difficulties for the symmetry interconnection. This equation is used for a double perturbational expansion both in Coulomb and in exchange terms, thus obtaining general perturbation equations. Explicit solutions are provided (up to the second total order) which are briefly discussed.
Bounds for Hartree‐Fock perturbation theory
Authors: Burrows B. L.
Published: December 2004

Upper and lower bounds for the second‐order energy in both coupled and uncoupled Hartree‐Fock perturbation theories are derived. Using these bounds inequalities are derived for the error in the geometric approximation.
Application of Local Energy Method to the Estimation of the Correlation in Geminals
Authors: Lyast I. Ts. , Biktimirov A. Ya.
Published: December 2004

For an estimation of the pair correlation the interelectronic distance r12 in geminal ψk(12) is introduced. The calculations are carried out by the local energy method [1, 2]. The influence of other electrons are taken into consideration with the help of the one‐ and two‐electron integrals depending upon r1 and r2 as parameters. If the strong orthogonality condition is satisfied all two‐electron integrals and most of the one‐electron integrals vanish. All atomic orbitals are expressed in terms of Gaussian functions. A trial calculation is made for the beryllium atom.

POUR tenir compte de la corrélation, on introduit la distance interélectronique r12 dans la géminale ψk(12). Le calcul est réalisé par une méthode des énergies locales [1, 2]. L'influence des autres électrons est décrite par des intégrales à un et deux electrons, dépendantes de r1 et r2 comme paramètres. Dans les conditions de l'orthogonalité forte, toutes les intégrales à un électron et la plupart des intégrales à deux électrons disparaissent. Pour simplifier l'algorithme du problème, toutes les orbitales sont exprimées par les fonctions de Gauss. Le calcul est réalisé sur le modèle de l'atome Be.

Für Berechnung der Korrelation wird der Interelektronenabstand r12 in Geminal ψk(12) eingeführt. Die Berechnung wird mit der Lokalenenergiemethode durchgeführt [1, 2]. Die Einwirkung der anderen Elektronen wird durch 1‐ und 2‐Elektronenintegrale berücksichtigt, die von Parametern r1 und r2 abhängen. Bei Erfüllung der starken Orthogonalitätsbedingung verschwinden alle 2‐Elektronen‐ und die Mehrzahl der 1‐Elektronenintegrale. Alle Orbitale werden durch Gaussfunktionen ausgedrückt. Eine Berechnung für das Atom Be wird durchgeführt.
Computations on Heisenberg Spin Models
Authors: Seitz W. A. , Klein D. J.
Published: December 2004

A computational approach for general Heisenberg spin Hamiltonians for a finite number of interacting doublet species is described. Maximum use of permutation and point group symmetry is incorporated in factorizing the secular equation. Associated problems in the computation of symmetric group characters, related frequencies, and selection of linearly independent kets from a large linearly dependent set are also solved.
A nearly free electron model for the dihydrides of the Alkaline‐Earth metals
Authors: Lindner P. , Berggren K‐F.
Published: December 2004

A simple, “nearly free electron” model for the dihydrides of Be, Mg, Ca, Sr and Ba is investigated. To zeroth order the valence electrons are assumed to form a free gas. Effects of band structure are included in second‐order pseudopotential perturbation theory. The stability of three probable crystal structures is investigated, and lattice parameters are calculated for two different choices of the pseudopotential.
On the accuracy of the many‐points local procedures
Authors: Majorino G. F. , Rubino C.
Published: December 2004

As until now proposed in the literature, in the local energy calculations we can distinguish “few‐points” procedures, in which the number M of configurational points is strictly related to the number N of trial functions used, and statistical “many‐points” procedures, in which the number M of points can be arbitrarily increased. In this paper we demonstrate that the energy errors resulting from a “many‐points” calculation M points/N functions (M > N) can be connected in a simple way with the errors of the (MN) partial calculations N points/N functions.

This suggests a possible approach for the problem of the choice of the configurational points to be introduced in the calculation, and leads to a simple interpretation of the numerical meaning of the error associated with the ordinary Ritz energy. Numerical examples on the hydrogen atom are reported.
Core model calculation of the electric field gradient: Projection operator formalism with application to NH3
Authors: Cook Earl C. , Ebbing Darrell
Published: December 2004

A core model approach to the calculation of deuteron quadrupole coupling constants is investigated using NH3 as an example. First the deuteron quadrupole coupling constant is calculated from a CNDO wave function. This result is subsequently improved by recomputing the N—D bond orbital by means of a variational calculation using the CNDO function to construct a core potential for the bond Hamiltonian. In order to simplify integrations a single‐center basis is chosen to represent the variational wave function. A projection operator formalism is used as a computational scheme to maintain orthogonality of the bond orbital to core orbitals. Excellent agreement with experiment is obtained. The procedure is applicable to more complicated molecules.
An Ab Initio calculation of the spin dipole‐dipole parameters for methylene
Authors: Langhoff Stephen R. , Davidson Ernest R.
Published: December 2004

The electron spin dipole‐dipole interaction in CH2 has been calculated as a function of bond angle with configuration‐interaction wave functions built from contracted gaussianlobe basis functions. The values D = 0.781 cm−1 and E = 0.050 cm−1 were obtained for the spin dipole‐dipole contribution to these parameters for the best CI wave function at the equilibrium geometry. The angular dependence of D shows that the assumption of perfect orbital following is not valid. Based on previous estimates of the spin‐orbit contribution to D, the total D is estimated to be 0.9 ± 0.1 cm−1 which is higher than the current experimental value 0.76 ± 0.02 cm−1.
Hydrogen‐like relativistic corrections for electric and magnetic hyperfine integrals
Authors: Pyykkö P. , Pajanne E. , Inokuti Mitio
Published: December 2004

Expressions are derived for the n‐dependent, hydrogen‐like relativistic corrections to the magnetic dipole and electric quadrupole radial hyperfine integrals of an arbitrary atomic state.

Good agreement has been obtained earlier between these corrections and the relativistic Hartree‐Fock results for s1/2 states. The agreement remains good for the p1/2 states. For the p3/2 states in heavier atoms the hydrogenic corrections still reproduce the Hartree‐Fock trend. For the higher l values the agreement is poor. Numerical tables are given for 1 ≤ Z ≤ 100 for the s1/2, p1/2, and p3/2 magnetic dipole cases and the p3/2 quadrupole case.
Perturbative ab initio calculations of intermolecular energies. II. The He ··· He problem
Authors: Daudey J. P. , Malrieu J. P. , Rojas Olivia
Published: December 2004

The ground state energy of the He2 system is calculated according to the techniques described in Paper I around the van der Waals equilibrium, without assuming the constancy of the intraatomic correlation energies. The second‐order results do not present an attractive region; the S2 decrease of the intraatomic correlation correlation corrections is larger than the attractive interatomic correlation corrections. The further orders reverse progressively the situation and finally give a qualitatively correct potential curve after the fifth order. Reaching almost exact solutions in the considered basis, one can demonstrate that the intermolecular calculation of the system A + B in the union of the basis for A and B involves an energy decrease which simply represents the effect of the extension of the basis set; and that a proper intermolecular calculation must compare the A + B energy with the A and B energies calculated in conveniently extended basis sets including the vacant MO's of the partner.
Coupled Hartree Fock calculation of static dipole polarizabilities and shielding factors of open shell systems
Authors: Gupta A. , Bhattacharya A. K. , Mukherjee P. K.
Published: December 2004

Static dipole polarizabilities and shielding factors for the 2p open shell atomic systems are presented using coupled Hartree Fock theory in the framework of the Roothaan formalism. Calculations have been performed for the ground as well as for some valence excited states. A variational approach has been adopted for the determination of the first‐order perturbed functions. The results are compared with those obtained from the correlated calculations and other techniques. The shielding factor values are in excellent agreement with the theoretical N/Z ratio.
Convergence problems in the solution of SCF equations
Authors: Dement'ev A. I. , Stepanov N. F. , Yarovoi S. S.
Published: December 2004

Some problems connected with the convergence of iterative solutions of the Hartree‐Fock equations for the open shell systems are discussed. The nonuniqueness of the Hartree‐Fock operator form is used.

The method of iterating by the operator's power is developed for obtaining solutions of the Hartree‐Fock equations. Some particular results for the molecules Li, Li are presented.
Hammerstein integral equivalent of Riccati's equation
Authors: Pulfer J. D. , Whitehead M. A.
Published: December 2004

A transformation exists which allows the general Riccati equation

to be written in a simpler form:

The transformed equation has the equivalent nonlinear Hammerstein integral equation

if the kernel N(r, r′) satisfies three conditions:

and

and

A solution of the nonlinear integral equation is devised by repeatedly integrating the Hammerstein equation. During this procedure the kernel generates an equation that contains only coefficients of β(r)0 and β(r)1. As a result, after truncating at the end of the nth cycle, it is a simple matter to write down a Padé‐type approximation: all coefficients in this approximation are capable of being evaluated in terms of simple algebraic formulations of P(r), R(r), and integrals over P(r).

The zeroes of the denominator of the Padé‐type approximation define the points where singularities occur in β(r).
Equivalence‐restricted open‐shell SCF theory
Authors: Jackels Charles F. , Davidson Ernest R.
Published: December 2004

A method is presented for generating open‐shell equivalence‐restricted SCF orbitals in high‐symmetry situations using Roothaan–Hartree–Fock programs which are adapted for lower symmetry.
Half‐projected and projected Hartree‐Fock calculations for singlet ground states. II. Lithium hydride
Authors: Smeyers Yves G. , Delgado‐Barrio G.
Published: December 2004

The half‐projected Hartree–Fock function (HPHF) for singlet states is defined as a linear combination of two Slater determinants which contains only spin eigenstates with even spin quantum numbers. The possible uses of such an approach for determining molecular properties are investigated computing the potential energy curve, binding energy, force constant, and dipole moment variation corresponding to the lithium hydride ground state. Full projected and restricted Hartree–Fock calculations (PHF and RHF) are performed simultaneously for comparison purposes. It is found that the HPHF model yields very satisfactory results, very close to those of the PHF scheme. Both models predict properly the molecular behavior as a function of nuclear separation, whereas the RHF one fails. A discussion is given in terms of configuration equivalents. It is concluded that the HPHF scheme seems to be useful for determining molecular properties specially in the case of large systems in which the more sophisticated methods are unmanageable.
Virtual orbital transformation prior to configuration interaction with localized orbitals
Authors: Coffey Patrick
Published: December 2004

A virtual orbital transformation is proposed involving pairing of localized occupied orbitals with virtual orbitals. The virtual orbitals are transformed so that each virtual orbital is as “close” as possible to its occupied counterpart, where closeness is the inverse of the particular definition of localization. The appropriate transformation is derived for the special case of Foster–Boys localization, and an illustrative CNDO/2 calculation on HNO is presented. INDO CI results on the series N2, CO, BF indicate that use of this transformation may reduce the number of energetically significant configurations.
Density matrix expansions and their application in the theory of the many‐electron systems
Authors: Kamel M. A. , Labzowsky L. N.
Published: December 2004

A method of calculation of the correlation energy is proposed, which includes the superposition of configurations and the two particle approach. This method is based on the density matrix formalism. The approximate, but N‐representable expressions for the reduced density matrices are used. The correlation energy of the beryllium atom is calculated as an example.
Divergence of the R−1 expansion for the second‐order H–H interaction
Authors: Young Ralph H.
Published: December 2004

The conventional R−1 expansion of the second‐order intermolecular interaction energy (R = intermolecular distance) is shown to diverge for all R in the prototype case of two 1s hydrogen atoms.
A new integral transform basis function
Authors: Bishop David M. , Schneider Barbara E.
Published: December 2004

A new integral transform function:

where s(n) is a positive definite shape function, is proposed and investigated. A test on H shows that it does not suffer from the inadequacies of earlier integral transform functions, of the form:

where c(ζ) is a positive definite shape function.
Variable ζ calculation for self‐consistent screening parameters in ab initio molecular theory
Authors: Selsby R. G.
Published: December 2004

A 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

Weyl'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

We 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

Combined 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

Using 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

Electronic 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

The 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

A 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

Using 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

The 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.
On the solution of the least‐squares local energy variance minimization equations
Authors: Harriss D. K. , Solev I. G.
Published: December 2004

The convergence behavior of an iterative procedure proposed by Frost, Kellogg, and Curtis for solution of variance minimization equations is discussed. Use of particular sets of initial parameters in the iterative procedure is shown to yield rapid convergence.
Variational principles for discontinuous wave functions and the independent particle model of electronic structure
Authors: Ludeña Eduardo V.
Published: December 2004

Using 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

We 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.
A new approach to canonical orthonormalisation
Authors: Lathouwers Luc
Published: December 2004

The canonical orthornormalisation procedure is derived through an integral equation with a finite rank kernel. Its optimal properties in connection with the problem of approximate linear dependence are established.
The use of single exponential orbitals in one‐center molecular orbital calculations
Authors: Combs L. L. , Miller Carl P.
Published: December 2004

Single‐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

This 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.
On the solution of the N‐completeness problem
Authors: Kryachko E. S. , Kruglyak Yu. A.
Published: December 2004

A solution is given for the problem of N‐completeness which arises in practical calculations for many electron systems because of the necessity of employing a finite basis set of antisymmetric two‐particle functions.
Computation scheme for optimizing multiconfigurational wave‐functions
Authors: Kuprievich V. A. , Klymenko V. E.
Published: December 2004

A 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

Two 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.
The orthogonality problem in valence bond calculations
Authors: Raimondi Mario , Simonetta Massimo
Published: December 2004

The energy of the π‐electron system in benzene has been obtained by means of valence bond calculations using orthogonal and nonorthogonal basis orbitals at different levels of configuration interaction, which shows the influence of the orthogonalization procedures.
Electronic energies of the hydrogen molecule D′∏u and B″ Σ states
Authors: Ritchie A. G.
Published: December 2004

Calculations of the electronic energies and wave‐functions for the hydrogen molecule D'∏u and B″Σ states have been carried out at the estimated curve crossing distance of 1,5307 atomic units. The results show good agreement with previous calculations.
Generalized existence conditions for surface states of a semi‐infinite Kronig–Penney crystal
Authors: Roy C. L. , Tripathy S. K.
Published: December 2004

A 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

The 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

We 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

The 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

The 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

The 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

A 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

A 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

We 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

Generalized 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

The 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

MS‐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

Energy 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

An 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

The 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

The 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

A 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

Using 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.
Nonbonded interactions in membrane active cyclic biopolymers. II. Ion binding by valinomycin
Authors: Sundaram K. , Tyagi R. S.
Published: December 2004

A possible mode for the capture of a cation by the carrier molecule valinomycin has been simulated. The intramolecular nonbonded energy and the binding energy for a centrally located potassium ion at different stages in the capture process have been evaluated using a method proposed earlier. Contrary to intuitive expectations the open conformation of valinomycin is also found to have a strong affinity for K+. There appears to be a rather high potential barrier between the open and closed symmetric conformations.
Singer polymals. I. Evaluation of matrix elements
Authors: Poshusta R. D.
Published: December 2004

Hamiltonian matrix elements between pairs of explicitly correlated Singer polymals are derived. A new method for 1/r12 matrix elements is found which avoids the 6 by 6 matrix inversion required at each quadrature point in the old method. The new formula requires about half the computer time of the old one. The electron repulsion and nuclear attraction matrix elements are shown to be related to incomplete elliptic integrals. Simplified formulas are derived for the special cases of cylindrical symmetry, spherical symmetry, and single‐center expansions. An upper bound approximation formula for the purpose of neglecting matrix elements is derived. These bounds may be useful for single‐center expansions but are found to be too high for the general case.
Reduced density operators and the N‐particle problem
Authors: Coleman A. J.
Published: December 2004

An historical review of the theory of reduced density operators is given emphasizing the key role of the second order reduced matrix and related new concepts for understanding systems of many interacting fermions.
The role of model systems in the few‐body reduction of the N‐fermion problem
Authors: Percus J. K.
Published: December 2004

The problem of upper and lower ground state energy bounds for many‐fermion systems is considered from the viewpoint of reduced density matrices. Model density matrices are used for upper bounds to, first uncoupled, then coupled fermions. Model Hamiltonians are developed for lower bounds in corresponding fashion. Both mathematical and physical models are constructed for setting up universally valid inequalities on density matrices. These are joined by both inequalities and equalities in which the explicit form of the system at hand is used. A few illustrative examples are presented.
Inequalities for fermion density matrices
Authors: Garrod Claude , Hannon J. Michael
Published: December 2004

A partial trace over the occupation numbers of all but k states in the density matrix of an ensemble with an arbitrary number of single‐particle states is defined as the (reduced) k‐state density matrix. This matrix is used to obtain a complete, practical solution to the problem of determining the representability of the diagonal elements of the one‐ and two‐particle (reduced) density matrices. This solution is expressed as a series of linear inequalities involving the density‐matrix elements; the inequalities are identical with those derived previously by Davidson and McCrae by a different method. In addition, our method is used to obtain nonlinear, matrix inequalities on the off‐diagonal elements of the density matrices.