bluuebunny/crossref_metadata_2025_split huggingface dataset:
Many‐electron problems III scaling of the density distributions and the potential fields
Authors: Gáspár R. 
Published: December 2004

AbstractThe Hellmann–Feynman theorem has been used to prove some energy relations. In this paper it is shown that in a scaled co‐ordinate system both the charge density and the potential field of neutral atoms may be scaled so that the corresponding scaled quantities are independent of the atomic number. In the proof the momentum theorem of real functions is used.
Optimized linear combinations of simple exponentials for atomic systems
Authors: Solomon C. E. 
Published: December 2004

AbstractHartree‐Fock wave functions for the He and Be isoelectronic sequences of ions are calculated using orbitals which are linear combinations of simple exponential functions. By a full optimization of the exponents and coefficients close approximations to the HartreeFock energies were obtained. To the same order of accuracy the resulting Hartree–Fock orbitals require fewer basis functions than used previously. A number of difficulties which arise in the numerical procedures as the size of the basis set is increased are analysed in detail. Similar results are obtained for the Li sequence using the Unrestricted HartreeFock method with and without projection.
The generalized separated electron pair model. II. An application to NH, NH3, NH, NH2− and N3−
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 has been applied to the series: NH, NH3, NH, NH2− and N3−. On going from NH to N3−, the SEP model, in its most general form, recovers 85–75% of the intrapair correlation energy and 60–55% of the interpair correlation energy obtainable with the given basis set. The best wave functions for each species recovered about 45–50% of the total empirical correlation energy which is expected to be very close to the basis set limit. It was apparent that the SEP model yields a set of one‐electron functions that are very useful for further improvement of the wave function. This fact apparently remains true even when the SEP model itself gives very poor energies.
Self‐consistent calculation of excited 3P state wave functions of atoms
Authors: Mukherjee P. K. , Bhattacharya A. K. , Mukherji A. 
Published: December 2004

AbstractA variation perturbation method in the Hartree–Fock scheme has been described to calculate excited 3P state wave functions of atoms. The starting wave functions are obtained from a study of the singularities in the dynamic polarizability calculation [1]. The 23P, 33P and 43P states of He, Li+, Be2+, B3+ and C4+ are studied. The results obtained are in satisfactory agreement with experimental values and with other accurate theoretical estimates.
Symmetry properties of one‐ and two‐electron molecular integrals
Authors: Brailsford D. F. , Hall G. G. 
Published: December 2004

AbstractThe maximum numbers of distinct one‐ and two‐electron integrals that arise in calculating the electronic energy of a molecule are discussed. It is shown that these may be calculated easily using the character table of the symmetry group of the set of basis functions used to express the wave function. Complications arising from complex group representations and from a conflict of symmetry between the basis set and the nuclear configuration are considered and illustrated by examples.
Ab initio calculation of electronic states of the ions H4+ and H5+
Authors: Kaplan I. G. , Rodimova O. B. 
Published: December 2004

AbstractElectronic state calculations for the ions H4+ (with symmetries D4 and C2v) and H (with symmetries D5 and D2d) are made using the valence‐bond method. All the configurations obtained from the given set of 1s‐functions of Slater type are taken into account. Space functions are used throughout the computation (“spin‐free quantum chemistry”). Preliminary quasidiagonalization of the secular equation is implemented by the construction of the multiplet eigenfunctions 2S+1Γ(α) from the initial variational functions. The results of the calculations are as follows: the ion H is unstable, the ion H is stable with equilibrium nuclear conformation of symmetry D2d and with the energy of dissociation into H and H2 near 4 eV.
On the nature of paramagnetism in macromolecules with conjugated cc bonds
Authors: Berlin A. A. , Vinogradov G. A. , Ovchinnikov A. A. 
Published: December 2004

AbstractThe paramagnetic properties of one‐dimensional macromolecules with conjugated CC bonds are discussed on the basis of low‐lying quasi‐homeopolar triplet excitations. A good agreement with the experimental results is shown.
Effect of methyl and hydroxyl substituents on the π‐electronic spectra and ionization potential of p‐benzoquinone
Authors: Mitra R. P. , Kapoor K. L. 
Published: December 2004

AbstractSCF‐LCAO‐MO‐CI semi‐empirical π‐electron calculations have been made of the first two singlet transitions and ionization potentials of hydroxy‐, methyl‐ and hydroxy‐methyl substituted p‐benzoquinone, using a modified Pariser‐Parr‐Pople method. The various molecules could be divided into two classes on the basis of their first π‐electron transition, namely, those in which the 3‐position was occupied and others where this position was vacant.
On the translation between MO and HL descriptions of co‐ordination compounds
Authors: Farberov D. S. , Men A. N. 
Published: December 2004

AbstractWave functions for impurities or local complexes in crystals are usually described within one of the two popular schemes furnished by the MO and the HL methods. The purpose of the present note is to draw attention to a set of tables which allow a translation between these two descriptions.
Structure electronique des complexes acide‐base de Lewis. I. Structure electronique et conformation moléculaire des molécules F3P·BH3 et F2HP·BH3
Authors: Labarre J.‐F. , Leibovici C. 
Published: December 2004

AbstractThe electronic structure and preferred conformations of F3P·BH3 and F2HP·BH3 are investigated in the framework of the CNDO/2 approximation. In complete agreement with microwave data, the staggered conformations are predicted to be the most stable ones. The barriers to internal rotation are in good agreement with experimental values (F3P·BH3: calc. = 3.03 kcal/mole, exp. = 3.24 ± 0.15 kcal/mole; F2HP·BH3: calc. = 3.63 kcal/mole, exp. = 4.05 ± 0.45 kcal/mole) and a bicentric energy partitioning shows that the variations of the total energy are completely reflected by the only variation of the interaction energy between phosphorus and H atoms bonded to boron. The analysis of the electron densities reveals the importance of the 3s(P) → 2px(B) transfer in the formation of the co‐ordination. Finally, the computed dipole moment value and direction agree with corresponding experimental data.
On formulas in closed form for Van Vleck expansions
Authors: Gora Edwin K. 
Published: December 2004

AbstractCanonical 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.
Decoupled Hartree–Fock methods. I. Calculations for atoms with orthogonalized orbitals
Authors: Náray‐Szabó G. 
Published: December 2004

AbstractBy 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.
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

AbstractSlater 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

AbstractA 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

AbstractConsideration 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.
Application of Local Energy Method to the Estimation of the Correlation in Geminals
Authors: Lyast I. Ts. , Biktimirov A. Ya. 
Published: December 2004

AbstractFor 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

AbstractA 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

AbstractA 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

AbstractAs 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

AbstractA 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

AbstractThe 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

AbstractExpressions 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

AbstractThe 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

AbstractStatic 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

AbstractSome 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

AbstractA 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).
Half‐projected and projected Hartree‐Fock calculations for singlet ground states. II. Lithium hydride
Authors: Smeyers Yves G. , Delgado‐Barrio G. 
Published: December 2004

AbstractThe 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

AbstractA 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

AbstractA 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.