bluuebunny/crossref_metadata_2025 huggingface dataset:
Pairwise correlated generalized valence bond model of electronic structure. VII. The b3∑ state of H2
Authors: Nyden Marc R. , Petersson G. A.
Published: December 2004

A modification of the overlap approximation for triplet pair correlation energies is presented. The modification allows the use of either the canonical absolute overlap or the minimum absolute overlap. When applied to the b 3∑ state of H2, this approximation reproduces the observed correlation energy to within 0.0002 hartree (or ±3%) for all internuclear distances from 1.3 bohr to infinity.
Monte Carlo simulation of water solvent with biomolecules: Serine and the corresponding zwitterion
Authors: Romano Silvano , Clementi Enrico
Published: December 2004

Monte Carlo simulation results are reported for clusters consisting of 250 water molecules surrounding serine, both in the neutral form and in two zwitterionic conformers (in order to gain some insight into conformational effects). Calculations were carried out at 300 K and using two‐body potentials obtained by means of quantum‐mechanical calculations. The spatial dependence of the average interaction energies was investigated. The solvation structure was investigated by means of radial distribution functions and probability density maps, which showed a few water molecules directly solvating the hydrophilic groups and, beyond them, a more or less rich and complex hydrogen‐bonded network of solvent molecules.
Ab initio calculations on large molecules using molecular fragments. Generalization of the molecular fragment basis at the minimum basis set level
Authors: Spangler Dale , Christoffersen Ralph E.
Published: December 2004

By determining basis set parameters in molecular environments using other criteria than total energy, it is shown that a generalization of the molecular fragment basis can be obtained in which calculated geometric and electronic structural properties are predicted substantially better than with other basis sets of similar size. As a first step in the development of a series of basis sets having successively greater flexibility and accuracy, several single‐zeta basis sets are created, using a two‐Gaussian contraction for each basis orbital. The best of these basis sets produced calculated geometric and electronic properties for a series of molecules that model a wide variety of organic molecules that are of better accuracy than the corresponding STO‐2G basis, and similar in most cases to STO‐3G. In addition, the basis set is shown to be applicable in either a Cartesian Gaussian basis or a floating spherical Gaussian basis.
Electron correlation and Hund's rule
Authors: Warner J. W. , Bartell L. S. , Blinder S. M.
Published: December 2004

It is suggested that simple electronic shielding effects induced by wave function antisymmetrization tend to govern the energy ordering of singlet and triplet terms within a two‐electron atomic configuration. This approach gives rise to the following alternating rule: For the term of greatest orbital angular momentum within a configuration, the triplet lies below the singlet. The energy ordering reverses for the term of next highest angular momentum, and continues to alternate with each change of one unit in the orbital angular momentum until the term of lowest angular momentum is reached. In an examination of over 600 energy levels of the elements and their ions, the alternating rule reliably orders singlet–triplet energy levels in some 90% of the cases.
Transferable integrals in a deformation density approach to crystal orbital calculations. IV. Evaluation of angular integrals by a vector‐pairing method
Authors: Avery John , ørmen Per‐Johan
Published: December 2004

A general method for performing angular integrations is presented. The method depends on the fact that the integral must be invariant under rotations of the coordinate system, and it also makes use of combinatorial analysis. In most cases the method presented is computationally much faster than alternative methods of angular integration using Condon–Shortley coefficients. Applications to charge density analysis and Fourier transforms are discussed, and a general formula for the action of angular momentum projection operators on functions of the Cartesian coordinates is derived. A general angular integration formula for an m‐dimensional space is also given.
Graph‐theoretical analysis of molecular properties. Isomeric variations in nonanes
Authors: Randić Milan , Wilkins Charles L.
Published: December 2004

Paths of length two and three appear to dominate variations in isomers of alkanes when various physical and chemical molecular properties are compared. The regularities previously observed for octanes have been fully examined for the set of 35 nonane isomers C9H20. Such examinations are facilitated by construction of appropriate grid graphs with paths of length two and three, respectively, representing molecules and connecting such points along the grid axes. By ordering structures in the two‐dimensional coordinate plane, various trends and regular changes in the relative magnitudes for the selected thermodynamic properties have been traced to molecular connectivity and topology.
Hohenberg‐Kohn theorem
Authors: Kryachko Eugene S.
Published: December 2004

The Hohenberg–Kohn theorem on the definition of the ground‐state energy of a system of fermions is discussed.
On Löwdin orthogonalization
Authors: Aiken John G. , Erdos John A. , Goldstein Jerome A.
Published: December 2004

It is shown that the Löwdin orthogonalization gives the unique minimum for the functional ϕ measuring the least squares distance between the given orbitals and the orthogonalized orbitals. Furthermore a much stronger result is obtained, namely that ϕ has only one local minimum, which is attained at the Löwdin orthogonalization and which is global. This justifies certain computer programs that compute Löwdin orthogonalization via minimization procedures. Finally there is a discussion of replacing the least squares metric by other metrics. The Löwdin orthogonalization turns out to be optimal with respect to all the commonly encountered norms.
Improved transformation algorithm of two‐electron integrals from atomic orbital basis to a symmetry orbital basis
Authors: Takada Toshikazu , Sasaki Fukashi
Published: December 2004

The transformation of two‐electron integrals from an atomic orbital basis to a symmetry orbital basis is a straightforward procedure, but becomes a time‐consuming process when the system has high symmetry. In the conventional transformation algorithm, the number of multiplications is proportional to the fifth power of the basis size. To reduce the computer time, a new transformation algorithm is proposed. In this method, the number of multiplications for the transformation is proportional to the fourth power of the number of atomic orbitals in an equivalent orbital group. A new transformation program has been completed and tested against the conventional n5 method. The present method may be regarded as extension of Almlöf's method to any molecular point group. The program cuts the CPU time for the transformation to one‐third in calculations for C4H8 and NiF6. This reduction is quite significant for large systems having high symmetry.
Inclusion of hydrogen p orbitals in the semiempirical calculation of NMR parameters. I. Influence on the FPT INDO spin–spin coupling constants
Authors: Facell J. C. , Contreras R. H.
Published: December 2004

Hydrogen 2p orbitals have been introduced into the basis set to calculate the Fermi contact term of spin–spin coupling constants using the FPT INDO method. Different coupling constants show different sensitivity to these hydrogen polarization functions. Some improvements are found for molecules containing N or F. Calculations of proton‐proton geminal coupling constants give more negative results than those of FPT INDO, yielding a better agreement with experimental values. The π‐transmission mechanism is notably exaggerated.
Average fock operators
Authors: Carbó Ramon , Domingo Llorençl , Gregori Josep
Published: December 2004

Average procedures of SCF methods are discussed. Although average operators are known from early Hartree–Fock times, some remarks against indiscriminate use of such operator forms may still be useful. In general, unless a very particular set of average structures is chosen, a dependence of final results on the SCF starting vectors is a troublesome fact. Consequently, energies, populations and molecular parameters in general may show unpredictable behavior under various trial vectors. It is shown that variationally coherent operator forms are given by state parameters with equal values for all the active MO's used in the construction of Coulomb and exchange terms throughout the SCF cycles.
Theoretical study of substituent effects on the acidity of the methyl group: Structure of anions CH2X−
Authors: Hopkinson A. C. , Lien M. H.
Published: December 2004

Geometries have been optimized using molecular‐orbital calculations (a) with a 4‐31G Gaussian basis set for carbanions CH2X− where X = H, CH3, NH2, OH, F, CCH, CHCH2, CHO, COCH3, CN, and NO2; and (b) with an STO‐3G basis set for methyl acetate and acetyl deprotonated methyl acetate. All the carbanions containing unsaturated substituents are planar, with a considerable shortening of the CX bond. Carbanions containing saturated substituents are pyramidal with the out‐of‐plane angle α increasing with the electronegativity of the substituent. Double‐zeta basis set calculations give proton affinities over the range 449 (for CH3CH2−) to 355 kcal/mol (for CH2NO2−), with all unsaturated anions having smaller affinities than saturated anions. The correlation of proton affinities with 1s binding energies, and with charges on both the carbon of the anion and on the acidic proton of the neutral molecule are examined.
Vibrationally inelastic scattering and relaxation times in gaseous HF
Authors: Gianturco F. A. , Lamanna U. T. , Battaglia F.
Published: December 2004

A numerical fit to computed ab initio points of the HF–HF potential energy surface is here employed in its simplest spherical form to solve the corresponding close‐coupling equations that yield vibrationally inelastic collision cross sections for the V/T process in the gas phase. The existence of a deep potential well in the interaction is examined here for its effect on near‐threshold cross section behavior and evidence is found, through the present calculations, for the relative importance of several (orbiting) shape resonances that contribute to the Q1←0 cross sections at low collision energies (≤0.4 eV). The bearing of such lengthened interaction times on the corresponding low temperature relaxation times is shown in the ensuing calculation of pτ in the T range between 300 and 4000 K. In spite of the simplicity of the present model, quite good agreement is in fact found with experiments in the low‐ T region, while the lack of V, R/T coupling explains the departure of the computed pτ, above 1000 K, from the experimental findings.
Algebraic structure of fermion density matrices. I
Authors: Dyadyusha G. G. , Kryachko E. S.
Published: December 2004

In this paper we define the algebraic structure of a reduced fermion density matrix. We relate the algebraic structure to certain symmetry properties of the reduced density matrix.
Analysis of molecular orbital wave functions in terms of valence bond functions for molecular fragments. I. Theory
Authors: Hiberty P. C.
Published: December 2004

A method of expansion of molecular orbital wave functions into valence bond (VB) functions is extended to molecular fragments. The wave function is projected onto a basis of mixed determinants, involving molecular orbitals as well as fragment atomic orbitals, and is further expressed as a linear combination of VB functions, characteristic of structural formulas of the fragment but whose remaining bonds are frozen. Structural weights for the fragment are deduced from this expression. Delocalized molecular orbitals are used as a startpoint, as they are after an ordinary SCF calculation. Wave functions of medium‐sized molecules may be analyzed with reasonable storage requirements in a computer.
Mapping between local potentials and ground state densities
Authors: Katriel J. , Appellof C. J. , Davidson E. R.
Published: December 2004

The mapping between the local one‐body potential and the ground state density is discussed. The role of degenerate ground states, which form a set of measure zero in potential space, is shown to be amplified by the unitary transformation between degenerate densities, forming a space filling set in density space. A numerical experiment demonstrating these features is carried out. No indication of non‐V representable densities is encountered.
New finite‐difference method for solving the pair radial equations of the many electron perturbation theory
Authors: Ischenko S. Ya. , Pavlov‐Verevkin V. B.
Published: December 2004

A new convenient and efficient finite‐difference (FD) method is developed for solving the pair radial equations (PRE) of many electron perturbation theory (MPT). This method can be interpreted as the FD analog of the well‐known Fourier method. The method is used to solve PRE arising in the second order of MPT based on the hydrogenic and Hartree–Fock (HF) zero approximations. Being very simple programmed our method gives results comparable with the most accurate variational calculations.
Approximate exchange and electrostatic interaction energies of deformed ions
Authors: Gutowski Maciej , Kąkol Małgorzata , Andzelm Jan , Piela Lucjan
Published: December 2004

Computation of exchange‐polarization and electrostatic‐polarization interaction energies between ions is the most expensive step in ab initio investigations of the properties of perfect and imperfect ionic crystals. In the present paper approximate formulas are proposed for these quantities. They save about 95% of the computation time and give these values with an error less than 0.2 kcal mol−1 as compared to ab initio results. The formulas for the exchange‐ and electrostatic‐polarization energies involve the generalized overlap integral between the one‐determinantal wave functions of the deformed ions. The approximations are tested in the calculations of the interactions of deformed ions in LiF and NaF crystals.
Generation of generalized branching diagram spin functions by Schmidt orthogonalization of spin‐paired functions
Authors: Ruttink Paul J. A.
Published: December 2004

The generalized branching diagram (GBD) spin representation is defined as the method of sequentially coupling together a number of subsystem spin eigenfunctions using the general rules of angular momentum coupling. It is shown that any GBD representation may also be obtained by Schmidt orthogonalizing a set of cannonical spin–paired (SP) functions, provided the SP basis is suitably ordered. The ordering procedure used is well suited to computer implementation. This is a generalization of results known in the literature for the Yamanouchi–Kotani and for the Serber spin representations.
Improved CI formula evaluation: Elimination of the phase determination at the determinant level for arbitrarily coupled CSFs
Authors: Bauschlicher Charles W. , Lengsfield Byron H.
Published: December 2004

The amount of work needed to evaluate the matrix elements in a configuration interaction calculation can be very large. This is especially true if the phase associated with bringing determinants into maximum coincidence is evaluated at the determinant level. A method is presented which allows the phase to be determined at the occupation level for arbitrarily coupled configuration state functions.
Effective potential theory of atom–diatom scattering in the presence of “intermediate” reactive channels
Authors: Varracchio E. Ficocelli
Published: December 2004

A field‐theoretical formalism is applied to the problem of atom–diatom scattering, in the presence of “intermediate” reactive channels. This leads to an integral equation formulation for elastic processes and to a numerical quadrature problem for inelastic vibro–rotational transitions. The key quantity of the theory is represented by an effective potential that contains full information on the dynamics of the process. A closed equation is obtained for this quantity, along with an approximation scheme of the second order in the system interaction potential. A diagrammatic technique is introduced and the physical interpretation of the approximate form of the effective potential considered.
Self‐Consistent APW–k · p method. I. Theory
Authors: Lima I. C. Da Cunha , Da Silva A. Ferreira , Parada N. J.
Published: December 2004

A first principles method based on an APW–k · p band structure calculation is derived in order to obtain the self‐consistent eigenenergies, crystal potential, and electronic density. The simplicity and extensions of the method are discussed, including comparison with the results obtained by the use of the Chadi and Cohen special points technique.
Uniform quality gaussian basis sets for molecular calculations. III. Charge optimized basis sets
Authors: Poirier R. A. , Daudel R. , Csizmadia I. G.
Published: December 2004

Gradient optimized constrained (2s ≠ 2p) and unconstrained (2s ≠ 2p) Gaussian 3G basis sets are reported for the first‐row atoms and ions XO, for Q = −2 to +4. Analytic equations have been fitted to the logarithm of the exponents as a function of the nuclear charge Z and formal charge Q. Consequently only two parameters Z and Q have to be specified in order to completely define a basis set.
Importance of the concept of bond and binding in the physical chemistry of solids
Authors: Lafourcade L.
Published: December 2004

The nature of problems connected with binding which arise in the everyday work of experimental physicists and material scientists is illustrated by reference to two different experimental studies. (i) Sliding in crystals of group V elements is found to take place not only along planes cutting the quasimetallic bonds, but also along planes apparently cutting their “covalent” bonds, thus suggesting that a more elaborate picture of the two types of bonds and of their interrelation is necessary. (ii) The physisorption of linear pentatriacontane on alkali chlorides indicates alignment of the paraffin molecules along the [110] directions. This may be associated with polarization of methylene groups by ions in the substrate. This hypothesis must be substantiated by suitable quantum‐theoretical calculations, which in turn must be based on an adequate description of the adsorption bond.
From molecular crystals and organic polymers to chemisorption processes: Importance of local interactions
Authors: Seel M.
Published: December 2004

Some aspects of studies on organic solids, polymers, and solid surfaces are discussed in connection with the suggestion that local interactions can constitute an important common feature of these quite different systems, which allows a common treatment of certain properties in cluster‐type calculations. The examples of molecular crystals, of the influence of different side groups bound to the backbone of a regular polypeptide, and of the interactions of fluorine and chlorine atoms with a silicon surface are treated in order to illustrate this thesis, with special emphasis on the reduction of a variety of bonding situations to local interactions rather than on details of computations.
Metal–metal bonds
Authors: Serre Josiane
Published: December 2004

In this survey paper the main properties of metal–metal bonds are summarized. The results of several calculations on compounds containing such bonds are analyzed.
Nonempirical analysis of unusual chemical bonds. II. AlH2BH4 and AlH2C3H5
Authors: Barone Vincenzo , Lelj Francesco , Russo Nino
Published: December 2004

Ab initio computations have been performed on the compounds AlH2BH4 and AlH2C3H5 in order to achieve a better understanding of the peculiar characteristics of the metal to ligand bond. Our results suggest a bidentate coordination for the tetrahydroborate complex and an η3 coordination for the allyl complex. Due to the nonrigidity of the BH and allyl complexes, possible interconversion paths between different coordination modes have also been analyzed.
Convergence problem in ab initio crystal orbital calculations
Authors: Karpfen Alfred
Published: December 2004

The various computational procedures for treating the problem of lattice summations in ab initio crystal orbital calculations are briefly reviewed and the cutoff problem is discussed. Several numerical examples are presented for demonstrating the fast convergence of the total energy per unit cell with respect to the inclusion of further neighbors' interactions, in case reasonable cutoff procedures are applied. The importance of electrostatic considerations for the interpretation of long range effects is stressed.
Some thermodynamic parameters for hydroxy amino acids: Bicine and tricine
Authors: Soni M. L. , Kapoor R. C.
Published: December 2004

pK values of N,N‐dihydroxyethylglycine (bicine) and N‐[tris(hydroxymethyl)methyl]‐glycine (tricine) have been determined by the Irving‐Rossotti method in an aqueous medium at 25, 30, 35, 40, 45, and 50°C and at different ionic strengths (I = 0.1, 0.5, and 1.0). Plots between pKa(NH) and 1/T for various ionic strengths have been obtained and the values of slopes have been used to calculate the ΔH, ΔS, and ΔG for the dissociation reactions of bicine and tricine. The ΔH, ΔS, and ΔG values for bicine were found to be 10.6 ± 0.6 kcal mol−1, −1.9 ± 1.8 e.u., and 11.1 ± 0.06 kcal mol−1, respectively, and for tricine 11.2 ± 0.6 kcal mol−1, 1.6 ± 1.6 e.u., and 10.7 ± 0.06 kcal mol−1, respectively. The pKa(NH) values decrease with rise in temperature but the influence of ionic strength is not significant.
Theoretical studies of photo‐oxidative cleavage reactions of nitrogen‐activated CC double bonds of enamines, indoles, and tryptamines
Authors: Yamaguchi Kizashi
Published: December 2004

The ab initio MO and semiempirical multireference (MR) CI calculations were carried out to elucidate the energy differences between peroxy 1,4‐diradical (DR) and 1,4‐zwitterionic (ZWI) intermediates, which play crucial roles in photo‐oxygenation reactions of nitrogen‐activated CC double bonds of enamines, indoles, and tryptamines. It is found that ZWI is more stable than DR in the case of electron‐rich enamines. Protic solvents such as methanol are highly effective for the stabilization of ZWI by hydrogen bondings. From the present theoretical results, it is concluded that tryptophane undergoes the photooxidative cleavage reaction to give formylkynurenine under a specific condition, where polar solvents or catalysts sufficiently stabilize the ZWI state for the species.
Interaction of the mutagenic base analogs O6‐methylguanine and N4‐hydroxycytosine with potentially complementary bases
Authors: Psoda Anna , Kierdaszuk B. , Pohorille A. , Geller M. , Kusmierek J. T. , Shugar D.
Published: December 2004

Infrared spectroscopy has been employed to study possible base pair interactions, in nonpolar media, between O6‐methylguanine and uracil, cytosine and adenine; and between derivatives of N4‐hydroxycytosine and adenine. The association constants of O6‐methylguanine with uracil, cytosine, and adenine are well below 1M–1, whereas those for interaction of 1‐methyl‐N4‐methoxycytosine and its 5‐methyl derivative with adenine are identical, K = 14M–1. The significance of the latter finding is discussed in relation to the conformation of the exocyclic N4‐methoxy group. Quantum chemical calculations, with the aid of the perturbation method, were carried out for the interaction of O6‐methylguanine with uracil, cytosine, and adenine, to establish the most energetically favoured configurations for interactions of the free bases, and of the same base pairs in the B form of DNA. The role of the conformation of the exocyclic —OCH3 group in O6‐methylguanine is discussed. The relevance of both the experimental and theoretical results to mutagenesis by O6‐methylguanine and N4‐hydroxycytosine is examined.
Construction of hydration shells for the tautomeric forms of heterocycles based on electrostatic potentials
Authors: Hofmann Hans‐Jörg , Peinel Gustav , Krebs Christine , Weiss Cornelius
Published: December 2004

A formalism for the determination of the most favored sites of monohydration and the orientation of water molecules around a solute by means of electrostatic potentials is suggested. The results of this method may serve as starting point for explicit supermolecule calculations. The hydration schemes determined in this way for the tautomeric forms of 2‐ and 4‐hydroxypyridine can be used as a basis for the evaluation of the displacement of the lactam–lactim equilibrium under the influence of the water environment.
Study of predissociation resonances by the complex coordinate method
Authors: Moiseyev Nimrod
Published: December 2004

The complex coordinate method is applied to the predissociation resonances of two‐state model system. The stability of the resonance positions and their widths, as well as the affect of using real and complex basis sets are studied.
Molecular electrostatic potentials from PCILO wave functions
Authors: Lochmann R. , Peinel G. , Weller T.
Published: December 2004

The molecular electrostatic potentials for several small molecules were investigated using PCILO wave functions at different stages of the perturbation expansion. The utility of the localized picture within the PCILO framework can be shown, even at zeroth order only. For simplicity the approximation of fixed standard bond polarities could be introduced in order to reproduce shape and values of the potential with a sufficient degree of accuracy.
A new look at correlations in atomic and molecular systems. I. Application of fermion monte carlo variational method
Authors: Moskowitz Jules W. , Kalos M. H.
Published: December 2004

We are engaged in research directed toward the development of compact and accurate correlation functions for many‐electron systems. Our computational tool is the variational method in which the many‐electron integrals are calculated by Monte Carlo using the fermion Metropolis sampling algorithm. That is, a many‐fermion system is simulated by sampling the square of a correlated antisymmetric wave function. The principal advantage of the method is that interelectronic distance rij may be included directly in the wave function without adding significant computational complexity. In addition, other quantities of physical and theoretical interest such as electron correlation functions and representations of Coulomb and Fermi “holes” are very easily obtained. Preliminary results are reported for He, H2, and Li2.
MSXα method and transition‐state procedure
Authors: Murilo Oliveira P. , Maffeo B.
Published: December 2004

Theoretical aspects of the MS Xα method are analyzed. It is shown that real field self‐consistency is not achieved in an MS Xα calculation and some consequences of this fact are discussed. The approximations involved in the use of the transition‐state procedure to evaluate ionization and excitation energies from a MS Xα calculation are presented in some detail and commented.
A posteriori symmetry analysis of polymer electronic band structures
Authors: Božović I. B. , Delhalle J. , Damnjanović M.
Published: December 2004

In an attempt to illustrate how to apply abstract line group theoretical results to electronic structure polymer calculations, an a posteriori symmetry analysis is carried out on the extended Hückel energy band structures of two model chains of H2 molecules, whose symmetries are respectively characterized by the 𝕃;312 and 𝕃;63/mcm line groups. The symmetry quantum numbers have been assigned to the bands, and the compatibility relations and selection rules for direct optical absorption are derived.
Connections between perturbation theory and the unitary transformation methods of deriving effective Hamiltonians
Authors: Westhaus Paul
Published: December 2004

The connections between open shell Brillouin–Wigner perturbation theory and the Van Vleck unitary transformation formalisms for generating effective Hamiltonians are explored. An explicit expression is obtained relating the generator Ŝ of the unitary transformation eiŝ with the amplitudes to be found from perturbation theory. The “renormalization effects” needed to produce the explicit “orthogonal‐Hermitian” form of the effective Hamiltonian in perturbation theory are related directly to the generator of the unitary transformation. The conclusions reached previously by Jørgensen and Brandow regarding the identity of the effective Hamiltonians of the formalisms are explicitly verified for the case that the generator Ŝ satisfied the Kemble condition. The procedure suggests how the powerful techniques of perturbation theory can be used within the unitary transformation framework to guarantee properly renormalized wave functions.
Cluster expansion of the wave function. Electron correlations in singlet and triplet excited states, ionized states, and electron attached states by SAC and SAC–CI theories
Authors: Nakatsuji Hiroshi , Hirao Kimihiko
Published: December 2004

The symmetry‐adapted‐cluster (SAC) and SAC–CI theories reported previously have been applied to the study of electron correlations in ground state, singlet and triplet excited states, ionized state, and electron attached state. Formulas for calculations of one‐electron properties and transition properties from the SAC and SAC–CI wave functions are given. Calculations were carried out for the ground and Rydberg excited states of water and its positive and negative ions, with the use of the simpler computational scheme than the previous one. The results compare well with experiments.
Internal stresses and chemical binding in the H molecule
Authors: Bamzai Anjuli S. , Deb B. M.
Published: December 2004

Following an interpretive formalism presented earlier, chemical binding in the H molecule has been studied in terms of the variations, with respect to R, of electrostatic field and stress components at five selected points on the interuclear axis. At three points phenomena analogous to those recorded earlier for H2 have been observed. In particular, the existence of extremal relationships for the difference density field and the total field, as well as for the corresponding stresses, at R ≃ Req for certain specific points on the internuclear axis has been confirmed. As in the case of H2, chemical binding in H occurs due to local variations of electrostatic pressure from point to point in such a manner as to cause the vanishing of either the total electrostatic force density or the difference force density at certain points on the internuclear axis.
Large order perturbation theory in the context of atomic and molecular physics—interdisciplinary aspects
Authors: Čížek Jiří , Vrscay Edward R.
Published: December 2004

The paper is introduced by a description of the role of divergent series in mathematics and their particular use in quantum mechanics. It is emphasized that there is a formal similarity between divergent series in nonrelativistic quantum mechanics and those series occurring in quantum field theory. It is indicated that studies of divergent series in nonrelativistic quantum mechanics can be helpful in the verification of suminability techniques in quantum field theory. The general problems of the application of perturbation theory to the study of the hydrogen atom in external fields are discussed. It is shown how the problem of the continuous spectrum can be bypassed. Further it is shown that algebraic techniques are very useful for a transparent formulation of perturbation theory. The theory is applied to the study of the hydrogen atom in a magnetic field and in an electric field and also to the study of the hydrogen molecule ion. The results for the hydrogen atom in a magnetic field and the hydrogen molecule ion are discussed in detail and the large order behavior of perturbation terms is compared with analytic formulas. Finally the questions of the summability for the series corresponding to the quartic anharmonic oscillator and the hydrogen atom in a magnetic field are discussed. It is seen that large order perturbation theory can be built into a continued fraction representation of a divergent perturbation series. Numerical results are presented for the two perturbation series mentioned above.
Size consistency corrections for configurational interaction calculations
Authors: Brändas Erkki J. , Combs Leon L. , Correia Nestor S.
Published: December 2004

A size consistency error formula, correcting for the erratic dependence on the number of particles in a doubly substituted (or otherwise restricted) configurational interaction (CI) treatment, is derived. The formula is expressed in terms of the particle pair eneriges ϵk and the normalization integrals Δk of the corrections to the unperturbed normalized wave function. The theory as well as the results for the 1A1 ground state of H2O and the 2B1 state of H2O+ show close agreement with the coupled electron pair approach (CEPA).
Spectra of chemical trees
Authors: Balasubramanian K.
Published: December 2004

A method is developed for obtaining the spectra of trees of NMR and chemical interests. The characteristic polynomials of branched trees can be obtained in terms of the characteristic polynomials of unbranched trees and branches by pruning the tree at the joints. The unbranched trees can also be broken down further till we obtain a tree containing just two vertices. This effectively reduces the order of the secular determinant of the tree we started with to determinants of orders atmost equal to the number of vertices in the branch containing the largest number of vertices. An illustrative example of a NMR graph is given for which the 22 × 22 secular determinant is reduced to determinants of orders atmost 4 × 4 in just the second step of the algorithm. The tree pruning algorithm can be applied even to trees with no symmetry elements and such a factoring can be achieved. Methods developed here can be elegantly used to find if two trees are cospectral and to construct cospectral trees.
General linear group approach to bivariational problems
Authors: Weiner B.
Published: December 2004

A bivariational scheme based on the general linear group of spin orbital space is presented, with the aim of obtaining approximations to the spectra of complex rotated Hamiltonians.
Variational solutions of a first‐order perturbation equation
Authors: Hamano Hidekazu
Published: December 2004

The variation‐perturbation method for solving a first‐order equation of Rayleigh‐Schrödinger perturbation theory is presented. The method consists of the combination of variational procedures and successive approximations. The recurrence formulas generate successively the higher‐order approximations of the variational solutions. It is possible to obtain the almost exact solution within a few steps. The method is applied to the calculations of the polarizabilities of a one‐dimensional harmonic oscillator and of the hydrogen atom, and the dipole‐dipole interaction energy of two hydrogen atoms.
Novel graph‐theoretical approach to estimating the relative importance of individual Kekulé valence structures. II. Benzenoid systems having four to seven fused benzene rings: “Pseudodegenerate” states
Authors: El‐Basil Sherif
Published: December 2004

Kekulé structures of 10 nonlinear acenes comprising 83 graphs are studied through the use of connectivities [M. Randić, J. Am. Chem. Soc. 97, 6609 (1975)] of their corresponding submolecules [H. Joela, Theor. Chim. Acta 39, 241 (1975)]. In certain rare cases states were identified to have identical branching indices but different Kekulé indices [A. Graovac, I. Gutman, M. Randić, and N. Trinajstić, J. Am. Chem. Soc. 95, 6267 (1973)]. Such states are termed pseudodegenerate states. A method is described to forecast and another to remedy such situations. The method emphasizes the relation between VB (resonance) and MO theories using graph‐theoretical concepts.
CNDO/2 calculations of relaxation and reconstruction of diamond and silicon [111] surfaces
Authors: Ĺszló I.
Published: December 2004

CNDO/2 calculations have been performed on the clusters X4H9 and X4Y9 modeling the [111] diamond and silicon surfaces. The X is either carbon or silicon atom and the Y is a pseudoatom containing one sp3 hybrid orbital. It is shown that in the CNDO/2 approximation in the foregoing pseudoatom models, the charge distribution of the cluster is better than the hydrogen atom, because the electronegativity of the hydrogen differs significantly from the electronegativity of the sp2 orbital of the silicon atom. Using the CNDO/2 parametrization, the electronegativity of the hydrogen is very near to the electronegativity of the sp3 orbital of the carbon atom, thus the hydrogen can be used for the saturation of the carbon clusters.
Critical examination of approximate LCAOMO methods. I. Reasons for the failure of the CNDO and INDO methods in theoretical conformational analysis of conjugated compounds
Authors: Birner P. , Hofmann H.‐J.
Published: December 2004

It is well known that the CNDO and INDO methods fail in the field of theoretical conformational analysis of conjugated compounds. The NDDO approximation, however, can be applied very successfully to this problem. In this paper, a comparative analysis of these three approximations is performed to clarify the reasons for the failure of the former two methods. It is shown that the defects are inherent in their formalisms, and there is no reasonable possibility to compensate them (e.g., by reparametrization) at the level of the CNDO and INDO approximations. The central inadequacy is the oversimplified treatment of the two‐center exchange interaction. In the case of molecules containing heteroatoms with lone‐pair electrons the known defects concerning the description of Coulombic interactions of anisotropic charge distributions can additionally influence the results. To overcome these shortcomings, at least an extension of the formalism to the level of the NDDO method is necessary.
Calculation of relaxed orbital binding energies in atoms: Zinc and cadmium
Authors: Das M. P.
Published: December 2004

Relaxed orbital binding energies of electrons in zinc and cadmium are calculated using a relativistic local density functional theory. The discrepancy between our calculated binding energies and those from gas phase experimental data are attributed to inhomogeniety and many body effects.
Theory of the electron distribution in compressed atoms at high temperatures
Authors: Csavinszky P.
Published: December 2004

To calculate atom‐atom interactions at high temperatures, one needs the electron densities of the interacting atoms. The present paper outlines an approach by which the temperature‐dependent electron densities of compressed atoms may be obtained. The approach suggested makes use of the temperature‐dependent Thomas‐Fermi (TF) equation, and a variational principle by which this equation may be solved approximately.
Scaled one‐electron hamiltonian model for open‐shell LCAO–MO–SCF calculations: Comparison with the restricted open‐shell method of roothaan
Authors: Banerjee Manas , Bhattacharyya Sankar Prasad
Published: December 2004

The performance of a recently proposed scaled one‐electron Hamiltonian (SOEH) model is tested against parallel sets of restricted open‐shell calculations by the method of Roothaan. It is found that the energy calculated by SOEH model, in general, lies slightly higher than the energy computed by the restricted open‐shell method of Roothaan lending credibility to the application of variational argument to the scaled pseudoenergy functional (Eav) for deriving the SOEH model. The numerical stability of the converged SOEH energy with respect to changes in trial vectors indicates the reliability of the method. The SOEH model is shown to perform well in the calculation of geometries of radicals and ions. The convergence behavior of the SOEH model is compared with that of the restricted open‐shell method of Roothaan.
Permutation‐Group classification and description of the Feynman–Goldstone diagrams
Authors: Kvasnička V.
Published: December 2004

A systematic permutation‐group approach for both the classification and description of the Feynman–Goldstone diagrams is presented. It allows us to “algebraize” the topological concepts and notions of many‐body diagrammatic techniques, for example, the connectivity and disconnectivity of diagrams, the automorphism of a diagram, etc.
Long‐Range interaction coefficients between H, He+, He, and Li+
Authors: Easa S. I. , Yousif F. N.
Published: December 2004

Using the new expression for the dynamic multipole polarizabilities in terms of effective oscillator strengths and effective transition energies derived from the variational procedure based on the total energy expansion in terms of induced multipole moments, we have calculated the long‐range dispersion force coefficients and the leading relativistic correction to the long‐range potential between H, He+, He, and Li+. We have in addition calculated the oscillator strength sum rules for the above systems. Our results are comparable with those obtained using both a hydrodynamic model to quantum mechanics and double perturbation theory.
Electronic aspects of enzymatic catalysis
Authors: Ferreira Ricardo , Gomes Marcelo A. F.
Published: December 2004

Enzymes are large aperiodic structures and this hinders both ab initio molecular orbital and Bloch‐type band theory of calculations. A frontier orbital perturbation theory of catalysis is applied to enzymes. Reasons are given for proposing that the induced‐fit conformational changes, essential to enzymatic catalysis, leads to an increase in the electronic eigenvalue density at the active site, enhancing the necessary catalytic orbital perturbation.
Ab initio studies on the nonplanarity of a peptide unit: Calculations on model compounds
Authors: Sawaryn A. , Yadav J. S.
Published: December 2004

The nonplanarity of a peptide unit has been studied by the ab initio method (GAUSSIAN 76) considering both the pyramidal structure of nitrogen and the variation of the ω angle for the N‐methyl‐acetamide and N‐ethyl‐acetamide in their cis and trans conformations. Several semiempirical methods have also been used for the sake of completeness of this work. All methods except CNDO and PCILO support a nonpyramidal structure for the nitrogen. The distortions of the planarity of the peptide unit show for both cis and trans conformations of the model compounds a significant asymmetric shift of the minimum on the energy curve for the ω rotation.
Electrostatic effect on catalytic rate enhancement in serine proteinases
Authors: Náray‐Szabó G.
Published: December 2004

The hypothesis that an electrostatic effect of the buried aspartate side chain may contribute considerably to the extreme catalytic power of serine proteinases is presented. This statement is based on an analysis of environmental effects, due to amino acid residues in the vicinity of the Ser‐221…︁His‐64 couple and to hydration in subtilisin BPN'.
Self consistent field MO studies of the vinylguanidinium ion
Authors: Sapse A. M. , Snyder G. , Santoro A. V. , Herzig L.
Published: December 2004

Ab initio Hartree–Fock calculations are used to predict the effect of substituting one hydrogen on the guanidinium ion by a vinyl group. The results show no overlap between the π‐electron system of the guanidinium moiety and that of the vinyl group.
Convergence behavior of some orbital optimization procedures
Authors: Bhattacharyya Sankar Prasad , Mukherjee Debashis , Bhattacharyya Debendra Madhab , Khan Priyotosh
Published: December 2004

Sources of occasional convergence problems in our recently proposed algorithm for orthonormality constrained orbital optimization in SCF calculation, as well as in the partly equivalent orthogonal gradient method, are traced and remedial measures are suggested. A simple scaling technique for accelerating convergence in the related orthogonal gradient method is tested.
Bounds to atomic properties: Electric polarizabilities of lithium isoelectronic sequence ions
Authors: Muszyńska J. , Papierowska D. , Pipin J. , Woźnicki W.
Published: December 2004

Using the optimal wave functions obtained by means of the superposition of correlated configurations method, elaborated previously, static and dynamic polarizabilities and rigorous lower bounds to them have been calculated for the ground states of three‐electron atoms in the lithium isoelectronic sequence (Li I–C IV). The results can be treated with considerable confidence, especially for higher members of the sequence. Furthermore, the calculated rigorous lower bounds for static polarizabilities enable us to rule out several theoretical and experimental values obtained previously. The results obtained by us are then employed to evaluate the leading unknown terms in the Z−1‐type expansion for the polarizability, extending thereby our treatment to much higher members of the isoelectronic sequence.
Perturbation for a rigid rotator in an electric field
Authors: Requena A. , Peña R. , Serna A.
Published: December 2004

The behavior of a rigid rotor perturbed by an electric field is studied. An hypervirial calculation, to obtain the perturbation series without calculation of the perturbed wavefunctions, is used to determine the Stark‐shifted eigenvalues. A numerical estimation of the m equals; 0 → m = 1 transition for the lowest vibrational state (v = 0) and the first rotational state (J = 1) for the HF and DF molecules using Padé approximants is made.
AGP Propagator calculations
Authors: Aa. Jensen Hans Jørgen , Weiner Brian , Öhrn Yngve
Published: December 2004

The use of the antisymmetrized geminal power (AGP) consistent reference state for RPA polarization propagator calculations is explored. Illustrative applications to the three lowest electronic states (3B1, 1A1, and 1B1) of the methylene radical are reported with comparisons to other theoretical methods and experiment.
Comparative study of the Hartree–Fock and the Hartree–Fock–Slater method
Authors: Wagner A. J.
Published: December 2004

The Hartree–Fock method (standard Roothaan closed‐shell HF–LCAO theory) and the Hartree–Fock–Slater method (restricted HFS–LCAO–DV method developed by Baerends and Ros) have been compared with emphasis on the respective one‐electron equations and on the matrix elements of the respective Fock operators. Using the same STO basis in the two cases, the matrix elements of the Fock operators and of their separate one‐electron, Coulomb, and exchange contributions have been calculated for the same orbitals and density of the ground state of the diatomic molecule ZnO. The effects of methodical (exchange potential) and numerical (DV method, density fit) differences between the HF and HFS methods on the various matrix elements have been analyzed. As expected the methodical effect prevails and is responsible for the higher (less negative) values of the matrix elements of the HFS Fock operator compared to those of the HF Fock operator. Numerical effects are observable also and are caused by the difference in integration procedures (DV method), not by the density fit.
Two‐dimensional fully numerical solutions of molecular Schrödinger equations. I. One‐electron molecules
Authors: Laaksonen Leif , Pyykkö Pekka , Sundholm Dage
Published: December 2004

A two‐dimensional fully numerical relaxation approach is presented for the electronic Schrödinger equation of linear molecules. The method is tested on the lowest σ, π, δ, and ϕ states of H and HeH2+. About 10‐figure accuracy is obtained for the orbital energies. Seven‐point numerical formulas are given for first and second derivatives.