bluuebunny/crossref_metadata_2025_split huggingface dataset:
Transferable integrals in a deformation density approach to crystal calculations. I. Crystal harmonics and their properties
Authors: Avery John , Ørmen Per‐Johan , Chatterjee Ibha 
Published: December 2004

AbstractThe term “crystal harmonic” is introduced to denote a symmetrized plane wave in the special case where the wave vector is a reciprocal lattice vector. Crystal harmonics, thus defined, have the translational symmetry of the lattice, and they also have the transformation properties of the irreducible representations of the crystal's point group. An expansion is derived expressing crystal harmonics in terms of spherical Bessel functions and in terms of the functions 𝒴𝓁,ξ (eigenfunctions of L2 which are also basis functions for IRS of the crystal's point group). A sum rule for the functions 𝒴𝓁,ξ is derived. Methods are given for expanding periodic functions of special symmetry in terms of crystal harmonics. Methods are also presented for calculating matrix elements of the potential in a crystal using crystal harmonics as a basis and for transforming to a STO basis. It is shown that the invariant component of the product of two crystal harmonics can be expressed as a sum of a few invariant crystal harmonics, and expressions for the coefficients in the sum are derived. Orthogonality with respect to summation over networks of points and normalization are also discussed. The properties mentioned above are illustrated in detail in the case of cubic crystals with point group Oh.
Stability and bonding of disilyne and its isomers: A generalized valence bond‐effective potential study
Authors: Snyder Lawrence C. , Wasserman Zelda R. , Moskowitz Jules W. 
Published: December 2004

AbstractWe have employed an effective potential and a single‐zeta basis in SCF–MO computations to estimate the relative stability of linear disilyne HSiSiH and five isomeric structures defined in earlier all‐electron ab initio SCF–MO computations. The effect of electron correlation has been estimated by generalized valence‐bond (GVB) computations for the five valence electron pairs of these structures. All our computations indicate that linear disilyne is the least stable structure and that H2SiSi, the silicon analog of vinylidene carbene, is the most stable structure. In these structures silicon occurs in divalent and tetravalent states. The nature of silicon bonding in these valence states is illustrated by contour diagrams of the GVB orbital pairs.
Novel graph‐theoretical approach to estimating the relative importance of individual Kekulé valence structures. III. Nonalternate and nonbenzenoid hydrocarbons
Authors: El‐Basil Sherif 
Published: December 2004

AbstractMolecular connectivities of submolecules [H. Joela, Theor. Chim. Acta 39, 241 (1975)] corresponding to Kekulé structures of nine nonalternate hydrocarbons and four nonbenzenoid hydrocarbons containing four‐membered rings are correlated with their Kekulé indices. In the latter class of compounds it was observed that the corresponding submolecules contain cut vertices and bridges in contrast to submolecules of benzenoid hydrocarbons which are devoid of such bridges. It was observed, furthermore, that the branching index goes up with the number of bridges in the submolecule. The results present an application to the abstract relation [D. Cvetković, I. Gutman, and N. Trinajstić, J. Chem. Phys. 61, 2700 (1974)] between resonance and MO theories.
Feenberg scaling and higher‐order invariants in Rayleigh–Schrödinger perturbation theory
Authors: Bhattacharyya Kamal 
Published: December 2004

AbstractIt is shown that the determination of a unique scaling parameter, based on scale‐invariant forms for energy in the scaled zero‐order Hamiltonian approach of Feenberg, is not possible because the higher‐order invariants themselves are nonunique.
Variational marginal amplitudes
Authors: Hunter Geoffrey , Tai Chin Chiu 
Published: December 2004

AbstractThe theory by which a wave function may be factorized into conditional and marginal amplitudes is extended to the domain of approximate wave functions. The approximate conditional and marginal factors are well defined, and the marginal factor satisfies a variation principle that is equivalent to a reduced Schrödinger equation having the same form as that derived in the case of exact wave functions. Of the two ways of calculating the effective potential in the reduced Schrödinger equation (which are equivalent in the case of exact wave functions), the integral method is demonstrated to be intrinsically more accurate than the differential method. The variation principle for the marginal amplitude leads to a technique for improving approximate wave functions within a subspace of the whole configuration space. These concepts are illustrated by calculations on the ground state of the helium atom.
Method for constructing isomerization reactions
Authors: Balasubramanian K. 
Published: December 2004

AbstractA method is formulated for enumerating and constructing isomerization reactions of molecules exhibiting large amplitude nonrigid motions. This method not only enumerates the isomers of nonrigid molecules and the corresponding rigid molecules but also the symmetry species spanned by the equivalent structures whose representative is an isomer. Consequently, using the method of correlating the symmetry species of a group to the symmetry species of its subgroup the splitting patterns of isomers of nonrigid molecule to those of rigid molecule are obtained. This provides an elegant method for both enumerating and constructing reaction graphs. The method is illustrated with examples.
Ab initio molecular calculations with pseudopotentials: Calculations of double‐zeta quality on ethylene, acetylene, and water
Authors: Gáspár R. , Gáspár R. 
Published: December 2004

AbstractCalculations with pseudopotentials of double‐zeta quality have been performed on ethylene, acetylene, and water molecules. A description of the carbon–carbon double and triple bonds is presented in the framework of the pseudo‐FSGO method. A possible model of the oxygen lone pairs has been established and its functioning has been proved by calculations on the water molecule.
MO study of flavin reduction
Authors: Teitell Murray F. , Fox J. Lawrence 
Published: December 2004

AbstractMINDO/3 calculations have been performed on semiquinone and fully reduced lumiflavins and on hydroperoxy adducts of lumiflavin. Frontier orbital indices were calculated. Reduction of the flavin was studied in bent and planar flavin rings. The results suggest that the planar reduced flavin has a smaller ionization potential than the bent reduced flavin. This could account for the low redox potential of protein‐bound reduced flavins.
Theoretical investigation of the electrophilic attack. IX. Ab initio study of the C2H4 · HF molecular complex
Authors: Volkmann D. , Z̈rawski B. , Heidrich D. 
Published: December 2004

AbstractSeveral configurations of the C2H4 · HF molecular complex were studied using the 4–31G basis set. The most stable configuration was found to be the π hydrogen bonded complex. For this structure the interaction energy was computed employing a double‐zeta basis plus polarization functions. The changes in electronic properties of the components C2H4 and HF due to complex formation were discussed.
STO‐3G study of uracil, thymine, 5‐fluorouracil, 5‐methoxyuracil, and their 4‐hydroxytautomeric forms
Authors: Zielinski Theresa Julia 
Published: December 2004

AbstractAb initio molecular orbital calculations with an STO‐3G basis have been performed to investigate the energetics and electronic properties of some 5‐substituted uracils and their 4‐OH tautomer forms with R including F, CH3, and OMe. In all cases, the diketo form is more stable. An excellent linear correlation between the calculated and experimental ionization potentials was found.
Molecular inversion in the nπ* states: A theoretical investigation of some model systems in a semiempirical molecular orbital framework
Authors: Banerjee Manas , Bhattacharyya Sankar Prasad 
Published: December 2004

AbstractThe considerations of Walsh rules are extended to rationalize the loss of planarity in the 1,3nπ* states of simple carbonyl and thiocarbonyl molecules. The role of Fermi correlation in shaping the differences between conformations in the singlet and the triplet state is emphasized. The role played by the π* orbital is also considered.
Characterization of bond and current correlation structures in a molecular many‐electron wave function
Authors: Fukutome Hideo , Hashimoto Katsufumi 
Published: December 2004

AbstractA method has been developed to analyzed the bond and current correlation structures of a molecular many‐electron wave function. It is shown that the second order density matrix contains information about the bond and current correlations in its off‐diagonal components with respect to the indices of orbital basis functions. We break down the off‐diagonal correlation functions into five kinds: charge, spin scalar, spin quadrupole, charge spin, and spin polar correlation functions. For a real wave function, the four correlation functions, except for the spin polar one, have only symmetric–symmetric and antisymmetric–antisymmetric components. The former components give site–bond and bond–bond correlations of charges and spins, while the latter components give current–current correlations of charges and spins. The spin polar correlation function has only symmetric–antisymmetric components that give site–current and bond–current correlations of spins. The five off‐diagonal correlation functions are expressed in terms of the off‐diagonal components of the second order density matrix. The linked off‐diagonal correlation functions are defined in that they give dynamical bond and current correlations. The method is applied to the analyses of the bond and current correlations in the low lying exact eigenstates of the PPP Hamiltonian of benzene.
Density matrix equation for crystals
Authors: Frishberg C. , Massa L. 
Published: December 2004

AbstractAn idempotent density matrix in which the orbitals are expanded in Bloch sums is used in the density matrix equation for ρ1(1,1′) to obtain an equation appropriate for a crystal. The general equation is presented as well as its simplification for the single‐cell approximation and the nearest‐neighbor approximation.
Lie groups and unitary transformations in ligand field theory
Authors: Sun Chia‐Chung , Han Yan‐De , Li Be‐Fu , Li Qian‐Shu 
Published: December 2004

AbstractUnitary transformations are performed with respect to three Lie group chains in quasispin schemes that are involved in the study of three different calculation schemes in ligand field theory. The unitary transformations hold true for either molecular or atomic orbitals being taken as the starting point. As a result, unitary transformations with respect to matrix elements are accomplished as well.
Ab initioMO investigation of the ethanolamine–formic acid complex
Authors: Šolmajer T. , Hodošček M. , Hadži D. 
Published: December 2004

AbstractThe title complex is considered a model for the interaction of catecholamine‐type ligands with anionogenic sites of receptors. It is usually assumed that the ligands interact in the protonated form, but there is no direct evidence of this. Model computations of proton transfer processes should contribute to the elucidation of this important problem. As a first step in this direction we have made computations in the STO‐4G base of the interaction energies, molecular electrostatic potentials, the proton potential curves, and the Mulliken population for three different arrangements of the acid and base molecules. Proton potential functions have also been computed for the complexes with two water molecules attached to the acid. The deeper potential well is nearer to the carboxylic oxygen in all cases examined.
General variation method for the relativistic calculations of atoms and molecules
Authors: Kagawa Takashi 
Published: December 2004

AbstractUse of the general variation method of Weinstein and MacDonald for the relativistic calculation of atoms and molecules is proposed. It is shown from the numerical calculations for hydrogenlike atomic systems that this method is useful in judging an accuracy of energies and wave functions obtained with a relativistic Hamiltonian whose spectra are not bounded. It is also shown that this method can be used to find spurious solutions such as 1p½ or 2d3/2 appearing in atomic systems. Problems in extending the method to many‐electron atoms and molecules are discussed.
Monte Carlo simulations of solid nitrogen in the isothermal–isobaric ensemble with an ab initioSCF–CI potential
Authors: Romano S. , Jönsson B. , Karlström G. 
Published: December 2004

AbstractMonte Carlo simulations in the isothermal–isobaric ensemble for the α phase of solid N2 have been carried out with two different pair potentials obtained from ab initio quantum chemical calculations. Comparison is made with data obtained from empirical potentials as well as with experimental data, and in general, the agreement with experiment is found to be good. It is also found that the differences between experiment and theory can largely be attributed to correlation effects, not considered in the quantum mechanical calculations of the pair potential.
Some new concepts on the nature of the covalent bond based on ab initio quantum‐chemical calculations
Authors: Pan Dao‐Kai , Niu Ze‐Fu , Gao Jian‐Nan , Liu San‐Lin 
Published: December 2004

AbstractThe ground states of eight molecules and some of their hole states are calculated. The calculations are performed on a medium‐size home‐made computer using self‐written programs. The basis set used is LEMAO‐3G, with scaling factors of the orbitals optimized by means of a method using orthogonal array and finding minima of fitted quadric curves. The conclusions are: (1) The LCAO‐MO method is the reflection of the interference effect due to the wave nature of electrons. (2) The mathematical methods of rescaling the orbital exponents is the reflection of the orbital contraction or diffusion occurring during the formation of MO. These conclusions are in agreement with the Virial theorem and the variation principle. They are also strongly supported by the photoelectron spectroscopy data. The calculated values of the energies of the valence orbitals are very near to those obtained by using some extended basis set, which are reported to be very close to the Hartree–Fock limits. From these results and discussions it may be concluded that the nature of the covalent bond should be considered as an interplay and mutual conditioning between the wave nature of the electronic motion on the one hand and the various attractive and repulsive factors on the other hand, among which the kinetic energy should be a very important repulsive factor. The mutual screening effects of the electrons in various MOS, which are different for different molecules, are also very important. This is perhaps one of the main causes of the differences in properties of different molecules.
Lower bounds to the Weizsäcker correction in statistical models for the Na atom with shell structure
Authors: Csavinszky P. , Vosman F. 
Published: December 2004

AbstractRecently, using the Na atom as an example, Csavinszky has introduced the shell structure into the Thomas–Fermi–Dirac energy‐density functional with the Weizsäcker and Hodges gradient expansion corrections to the kinetic energy term. Also recently, two rigorous lower bounds to the Weizsäcker correction in atoms of spherical symmetry have been derived by Gadre and Pathak. The present work investigates the magnitudes of the lower bounds in statistical models of the Na atom with shell structure.
Some applications of the Gel'fand–Levitan inverse method in atomic and molecular physics
Authors: Hron M. , Razavy M. 
Published: December 2004

AbstractThe Gel'fand–Levitan theory is applied to obtain the exact potential function for an atomic or a molecular system when the solution of the Schrödinger equation with a reference potential which is close to the actual potential is known. With this method one can construct bound state equivalent local potentials, or potentials which, for large quantum numbers, have spectra similar to that of the reference potential. In one‐dimensional problems the resulting potentials are not generally symmetric about the origin, even if one starts with symmetric reference potentials. This lack of symmetry is due to the presence of additional terms in the Hamiltonian which are of purely quantal origin, and therefore in any semiclassical treatment become negligible. This observation leads one to investigate the relationship between the spectrum of a given system and the symmetry of the underlying Hamiltonian. Examples are given to show that the dynamical symmetries usually associated with the spectral properties do not necessarily follow from the Gel'fand–Levitan inverse theory, but can be imposed as constraints on the solution. Additional constraints on the form of the two‐body wave function also arise from the observable transition rates for atom–molecule collisions and for the interaction of the charged particles in the system with an external electromagnetic field.
Unusual random walks
Authors: Randic Milan , Woodworth Wayne L. , Graovac Ante 
Published: December 2004

AbstractFor most structures (molecules, graphs, lattices) a count of random walks for nonequivalent sites will give different numbers, particularly for walks of many steps. Occasionally one finds the same count of walks for nonequivalent sites. These have been termed “unusual walks” and have been closely examined in the case of trivalent graphs. While it remains to be understood what structural factors are critical, some regularities have been observed and are discussed. Unusual walks within a single structure signal “isospectural” points in a graph. A number of structures possessing unusual walks have been displayed, and a few constructive steps which do not alter the “unusual” characteristics of selected vertices have been indicated.
The effect of an epoxide–nucleophile reaction upon hydrogen bonding involving the nucleophile
Authors: Bauer Joanne , Politzer Peter 
Published: December 2004

AbstractThe aim of this study has been to determine how the hydrogen bond between formaldehyde and ammonia is affected by the ring‐opening interaction of protonated ethylene oxide with the ammonia nitrogen. Our purpose is to gain insight into the possible effect of carcinogenic epoxides upon the hydrogen bonding within DNA base pairs; it is known that such epoxides react with nucleophilic sites in DNA, including amine nitrogens that are involved in hydrogen bonds to carbonyl groups. We have used an ab initio self‐consistent‐field molecular orbital procedure to compute optimized structures, interaction energies, and other properties of interest. The H2CO·HNH2 system and the protonated epoxide were found to form two stable complexes, with syn and anti orientations. Their formation is accompanied by a significant overall strengthening of the H2CO·HNH2 hydrogen bond, as indicated by both calculated force constants and bond lengths. An analysis of these and other properties, such as atomic charges, suggests that the interaction is leading to the formation of N‐protonated ethanolamine, which is linked to the formaldehyde through the proton on the nitrogen. If carcinogenic epoxides have a similar strengthening effect upon some of the hydrogen bonds in DNA, it could interfere in the replication and transcription processes.
Sur la theorie quantique des equations de hartree‐fock dependant du temps. III. Déatermination d'un ensemble unique de spin orbitales
Authors: Smet F. , Groenendael A. Van 
Published: December 2004

AbstractWe modify the matricial form of the TDHF equations we suggested in an earlier article, and impose a further constraint, called unicity constraint, to the equations' solutions. Indeed, this further constraint, combined with the orthonormalization conditions already taken into account, allows the TDHF equations a form accepting only one spin‐orbital set as a solution.
Vibrational predissociation of highly vibrationally excited van der waals molecules: A quantal close‐coupling calculation
Authors: Delgado‐Barrio G. , Villarreal P. , Mareca P. , Beswick J. A. 
Published: December 2004

AbstractIn this paper we present numerical calculations of close‐coupling equations to study vibrational predissociation of the T‐shaped He…︁I2(B) van der Waals molecule. In the region of high vibrational excitation of the I2 subunit, the vibrational predissociation rates are related to the widths of the resulting resonances for the He‐I2(B) collision. We apply a reasonable approximation to calculate the necessary background S matrix, i.e., the S matrix in absence of resonances. The rates of perpendicular vibrational predissociation, as a function of the initial I2 vibrational quantum number v1, show a maximum at v1 = 58 almost in agreement with the experimental data. However, an oscillatory and very interesting behavior of the rates in the region 60 ≤ v1 ≤ 65 is found.
Ab initio studies of F−(H2O)n and Cl−(H2O)n clusters for n = 1, 2
Authors: Sapse A. M. , Jain Duli C. 
Published: December 2004

AbstractAb initio Hartree–Fock calculations are performed on hydrates of the F− and Cl− ions using 6‐31G, 6‐31G**, and 6‐21G basis sets. Geometries and binding energies are obtained. An estimate of the correlation energy is provided by an MP2/6‐31G (Møller‐Plesset second‐order perturbation) calculation. Comparisons are made between the Cl−(SO2) and the Cl−(H2O) complexes.
A necessary and sufficient condition for the existence of real coupling coefficients for a finite group
Authors: Bickerstaff R. P. , Damhus T. 
Published: December 2004

AbstractWe establish a theorem which gives a necessary and sufficient condition for a set of matrix irreps of a finite group to admit real coupling (Clebsch–Gordan) coefficients. The proof is based on the method used by Feit to prove that a full set of coupling coefficients for a finite group determines the group up to isomorphism. A consequence of the theorem is that a finite group with real coupling coefficients is necessarily quasiambivalent. The theorem is used to demonstrate that real coupling coefficients do not exist for the point‐group hierarchies T ⊃ D2 and I ⊃ T or for the double‐group hierarchies I* ⊃ D3*, I* ⊃ D5*, and O* ⊃ D3*.
Usage de l'algégbre de lie su(n) dans l'étude des systémes quantiques á n états. IV. Geometrie du domaine des vecteurs de cohérence
Authors: Van Groenendael Augustin 
Published: December 2004

AbstractThe density operator of an n level quantum system is known to be a positive semidefinite, hermitian operator of trace one. In a previous article we have established, through su(n) algebras, a formalism where density operators are built from coherence vectors in a n2 − 1 dimension, real, Euclidean space. The last two conditions are then automatically satisfied. Being positive semidefinite means a restriction to the domain of coherence vectors. In this article we clarify this domain and obtain several equivalent tests to know if a given vector is part of it.
“Basis” lie algebra of electronic fock space: Application to evaluation of matrix elements of spin tensor operators
Authors: Panin A. I. 
Published: December 2004

AbstractA new set of generators of the operator algebra over the electronic Fock space is introduced. It is shown that with this set of generators the “basis” Lie algebra can be associated and that the operator algebra of the Fock space is the homomorphic image of the corresponding universal enveloping algebra. The algebraic structure revealed is used for deriving the reduction formulas for the elements of the simplest spin tensor operators between the Gelfand states.