bluuebunny/crossref_metadata_2025 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

The 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

We 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

Molecular 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

It 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

The 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

A 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

Calculations 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

MINDO/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

Several 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

Ab 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

The 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

A 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

An 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

Unitary 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

The 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

Use 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

Monte 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

The 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

Recently, 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

The 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

For 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

The 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

We 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

In 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

Ab 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

We 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

The 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

A 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.
A theoretical study of tautomerism: 2‐ and 4‐oxopyrimidine and some of their derivatives
Authors: Leś A. , Ortega‐Blake I.
Published: December 2004

Here we present a detailed study of the theoretical approach to the tautomerization processes considering 2‐ and 4‐oxo‐pyrimidine and several of their derivatives. We look into molecular relaxation, suitability of semiempirical methods, and the effect of basis sets size in pseudopotential ab initio calculations. We found that no semiempirical method is suited for studying the relative stability of the tautomers, even ab initio calculations with minimal basis sets. On the other hand MNDO appears to be very useful for molecular relaxation and can be used, as well as Ab initio calculations, for reasonable estimates of relative tautomerization. We also considered the quality of prediction of other parameters, in particular the ionization potentials. We considered the correlation of experimental and theoretical values as a means to adjust the theoretical results to obtain more reliable predictions.
N‐Representability conditions generated by a one‐particle grassmann factor of an antisymmetric function
Authors: Grudziński Hubert
Published: December 2004

N‐representability conditions for a two‐particle density operator implied by positive‐semidefiniteness of the projection operator PN+1(ϕ1 Λ ΨN) are derived and discussed. The operator PN+1(ϕ1 Λ ΨN) projects onto an (N + 1)‐particle antisymmetric function ϕ1 Λ ΨN, the Grassmann product of a one‐particle factor ϕ1 and an N‐particle factor ΨN. The polar subcone 𝒫2N(g, q) to the set of N‐representable two‐particle density operators 𝒫2N which corresponds to these conditions is found. It is shown that its extreme rays belong to two orbits for the action of the unitary group of transformations in one‐particle Hilbert space. The facial structure of the convex set 𝒫2N exposed by elements of 𝒫2N(g, q) is analyzed. An example of the operator that changes the structure of its bottom eigenspace when the number of fermions N surpasses a certain value is noted. A new approach to the diagonal conditions for N‐representability is found. It consists of the decomposition of the N‐particle antisymmetric identity operator onto the mutually orthogonal projection operators.
A constant‐denominator perturbation theory using circulant orbitals
Authors: Chen Min‐Bo , Parr Robert G.
Published: December 2004

A constant‐denominator perturbation formalism is developed employing a basis of circulant orbitals and a projected Møller–Plesset partitioning of the Hamiltonian operator. A formal justification for the classical Unsöld approximation is thereby provided. A calculation of correlation energy in the beryllium atom is carried out, and the results are compared with results obtained by the full configuration interaction method and conventional Møller–Plesset perturbation theory.
Correlated electron propagator theory and applications for open‐shell atoms and molecules
Authors: Born Gregory
Published: December 2004

A unitary group reformulation of electron propagator theory is used to derive the second‐order and 2p – h Tamm–Dancoff self‐energy approximations for open‐shell applications. A highest weight representation of the reference state is chosen in order to facilitate matrix element evaluation, but two special cases precluded by this choice are also discussed. Detailed numerical calculations are described for the lithium atom, oxygen molecule, and the amidogen radical.
Supplement to spherical tensor theory of long‐range interactions between two molecules
Authors: Piecuch Piotr
Published: December 2004

We simplify a recently obtained approximate formula for the third‐order interaction energy between two molecules expressed in terms of irreducible spherical polarizabilities and multipole moments of interacting systems. Similarly, we can simplify analogous higher‐order expressions. Then we briefly examine the magnitudes of the various third‐order contributions in comparison with the second‐order categories of long‐range interactions for some specific systems.
Spectral polynomials of systems with general interactions
Authors: Balasubramanian K. , Randíc M.
Published: December 2004

General structures represented by graphs with unequal interactions (weighted edges) are considered and their characteristic polynomials (spectral polynomials) are obtained. It is shown that the procedure based on pruning terminal vertices previously developed by one of the present authors (K.B., Ref. 1) can be generalized to more common graphs in which nonuniform interactions (unequal couplings) occur. Special cases of the present approach are Möbius graphs, signed graphs, directed graphs, multigraphs, and pseudographs (i.e., graphs with multiple connections and graphs with loops, respectively). Weighted graphs (with general weights) are applicable to a variety of chemical problems such as problems of chemical kinetics, analysis of NMR spectra, the study of simple molecular orbitals, and molecular vibrations.
Length dependence of the optical transition energies of the exactly solvable Hubbard model for linear polyenes
Authors: Hashimoto Katsufumi
Published: December 2004

Some accurate results on the length dependence of the excitation energies from the ground state to ionic excited states in the Hubbard model of linear polyenes are obtained based on the method of Lieb and Wu. To this end, it is first shown that singly ionic excited states with “plus” alternancy symmetry in the Hubbard model are described by the wave functions in which the two electron operator [∑(−)nCC] is acted on (N − 2)‐electron covalent eigenstates. Then by solving the Lieb‐Wu equations the exact excitation energies of the lowest ionic state, which corresponds to the E state in this model, are calculated for systems with up to 50 electrons. The result, together with a correction for the end effect, indicates that the excitation energies do not decrease as 1/N but converge to the limiting value more rapidly when the number of electrons N becomes large.
Energetics of proton transfer between carbon atoms (H3CH  CH3)−
Authors: Latajka Zdzisław , Scheiner Steve
Published: December 2004

Ab initio calculations were carried out to study the potential energy surface of (H3CHCH3)−. The 6–31G* basis set is supplemented by a set of diffuse p functions on both C and H (with a range of exponents for the latter). The binding energy of CH4 and CH3− to form the (H3CHCH3)− complex is about 2 kcal/mol, much smaller than for comparable ionic H‐bonded systems involving O or N atoms. Nearly half of this interaction energy is due to correlation effects, computed at second and third orders of Møller‐Plesset perturbation theory. Correlation is also responsible for substantial reductions in the energy barrier to proton transfer within the complex. This barrier is computed to be 13‒15 kcal/mol at the MP3 level, depending upon the exponent used for the H p functions.
Energy levels of paramagnetic ions: Algebra. V. Weak‐field models
Authors: Kibler Maurice , Grenet Geneviève
Published: December 2004

We explore a generalized weak‐field model for the description of the electronic properties of a partly filled shell(S) ion in a crystalline field. Such a model corresponds to the one developed, in parts III and IV of this series, for dN and fN ions in cubical symmetry except that the constraint relations are relaxed. This leads to a fourteen‐parameter weak‐field model for dN ions in octahedral symmetry and to a 33‐parameter weak‐field model for fN ions in octahedral symmetry. The latter two models are completely equivalent to the corresponding strong‐field models as developed by Griffith and by Tanabe, Sugano, and Kamimura. The constraint relations of parts III and IV are further discussed. In particular, the role they play in fitting procedures is examined. As a conclusion, the weak‐field model of III and IV appears as a phenomenological version of the generalized weak‐field model introduced in this paper.
The bonding properties of MoFes clusters
Authors: Chunwan Liu , Jianmin Hua , Zhida Chen , Zhenyang Lin , Jiaxi Lu
Published: December 2004

In this paper the electronic structure of a series of MoFeS cluster compounds (from dinuclear to nonanuclear) are calculated by using the MAD‐SCC and EH methods. The MO character, bonding property, as well as some other physicochemical properties are discussed. Some common regularities of these cluster compounds have been revealed. An extensive electron delocalization has been found in all these types of cluster compounds. There exists a certain degree of MM bonding in each type of the clusters. The Mülliken bond order of the MM bond are found to be as follows: MoMo > MoFe > FeFe, and for remaining bonds: MoL > MoSb > FeSb > FeL > MM. The chief contribution to the formation of stable MoFeS clusters is found to arise from the bonding interaction between the inorganic sulfur S* and metal atoms. The calculated results show that the magnified image rhomb is the basic structural unit in the MoFeS clusters. It is suggested that in the process of spontaneous assembly, the electron can be transported from the S* to the M atom, therefore the bridging effect of the S* plays an important role in this process.
Prediction of new materials and properties of solids
Authors: Cohen Marvin L.
Published: December 2004

The total‐energy pseudopotential method is described, and some applications are presented with emphasis on the predictive nature of the approach. For several applications, silicon is used as a prototype material, and the successful predictions related to structure and superconductivity at high pressure are discussed.
Generalized 1/Z expansion for heteronuclear molecules
Authors: Pucci R. , March N. H.
Published: December 2004

We have first studied empirical regularities in various series of heteronuclear diatomic molecules between the energy E, the total number of electrons N, the equilibrium distance Re and Z̄ = (Z1Z2)1/2 where Z1e and Z2e are the nuclear charges in the diatom. In particular, for various alkali halide series, Re2|E|/N5/3 is shown to correlate rather simply with Z̄Re3. Some theoretical basis is afforded by generalizing the 1/Z expansion used early by the writers in work on homonuclear diatomics. Finally, when Z2/Z1 → ∞, a model is presented which predicts a finite asymptotic bond length and this prediction is confronted with available experimental data for both heteronuclear diatoms and for the polyatomic series CH4 to SnH4.
Construction of orbital angular momentum eigenfunctions for many‐particle systems by harmonic projection
Authors: Avery John , Larsen Peter Sommer
Published: December 2004

Formulas are derived which allow the direct construction of total orbital angular momentum eigenfunctions for many‐particle systems without the use of Clebsch–Gordan coefficients. One of the equations is closely analogous to Dirac' identity for the total spin operator. This equation describes the action of L2 on a function of the particle coordinates in terms of a class operator of the symmetric group and a "contraction operator." A general projection operator for constructing symmetric eigenfunctions of L2 is presented.
The use of inner projections of the polarization propagator to study different contributions to the magnetic shielding tensor. I. Proton deshielding by steric compression
Authors: Ferraro M. B. , Natielo M. A. , Contreras R. H.
Published: December 2004

A new method for studying different contributions to the magnetic shielding tensor is proposed. These contributions come from different molecular fragments, which are defined through a localization procedure. They are obtained by means of inner projections of the polarization propagator onto the subspace defined by the chosen molecular fragment. To illustrate the utility of this method, results are presented for the proton desheilding effect of steric crowding. Different degrees of approximation both in the polarization propagator formalism and in the ground state wave function can be used. Results presented in this paper were obtained at the INDO level, within the CHF scheme. Good agreement with experimental values is obtained.
On the stability of single‐ and double‐stranded DNA helices: The application of the PPT‐MCF method on large fragments of DNA
Authors: Otto P.
Published: December 2004

The pseudo‐polarization tensor mutually consistent field (PPT‐MCF) method recently introduced [1] has been applied to study the stacking interactions between the nucleotide bases in large periodic B‐DNA fragments. The effects on the global and local binding properties caused by replacing one base in the periodic sequence by another base are investigated.

The increase in the stability for comparable fragments owing to this base substitution is further enforced in the case of periodic alternating helices. The most important results are that the stacking interaction between two bases is slowly converging with the interbase distance and that the average contribution per base to the binding energy is repulsive.

Furthermore, the energetical properties of double helix models in B‐ and Z‐DNA configurations, respectively, consisting of up to five base pairs have been compared. It turns out that the G C G C sequence in Z‐DNA is significantly more stable than either in periodic or periodic alternating B‐DNA. In these cases the average energy contribution of a single Watson–Crick‐type base pair is predicted also to be positive. From the calculations it follows that the double helix is not stabilized owing to the hydrogen bonding between the bases belonging to both strands, in contradiction to most other investigations.
Application of the Green's function theory to the calculation of ionization potentials of model oligomeric systems
Authors: Deleuze Michaël , Delhalle Joseph , André Jean‐Marie
Published: December 2004

The vertical ionization potentials of model hydrogen chains have been calculated, in the framework of STO‐3G and 4‐31G bases, at the second‐order level of the many‐body Green's function theory. Compared to the second‐order many‐body perturbation theory, this approach provides a qualitative description of trends observed with orbital relaxation, pair removal, and pair relaxation effects when studying oligomeric systems of increasing size with varying bond length.
Finite‐size dimensional analysis of the superconducting vibronic interaction
Authors: Tachibana Akitomo
Published: December 2004

Even in a finite‐size system, the vibronic interaction acts as the attractive force to bind a pair of electrons. For small‐size systems, the electron repulsion overwhelms the vibronic attraction. As the size of the system becomes large, the electronic repulsion diminishes to zero in proportion to the volume of the system, whereas the vibronic attraction (1) grows to infinity for a one‐dimensional system, (2) converges to a finite value for a two‐dimensional system, and (3) diminishes to zero for a three‐dimensional system. Even for a three‐dimensional system, the vibronic attraction diminishes much slower than does the electronic repulsion. This brings about a concept of the critical size for an any‐dimensional system, over which size the vibronic attraction overwhelms the electronic repulsion, thereby creating purely attractive interaction for a pair of electrons, which may lead to superconductivity.
On the quality of basis sets
Authors: Sordo T. L. , Sordo J. A.
Published: December 2004

An analysis of the quality of a given basis set is presented in terms of the three fundamental parts of total energy. This analysis clearly displays three types of error occasionally present in the components of total energy. As an illustration of the application of these concepts, several STO and Gaussian basis sets for the Ni atom are analyzed.
Quantum chemical calculation of the barrier for tunneling of hydrogen in hydrogen abstraction from methane by methyl
Authors: Chandra Asish K. , Malar E. J. Padma , Gupta Debasis Sen
Published: December 2004

An adiabatic reaction path for hydrogen abstraction from methane by methyl is computed by quantum chemical methods and then symmetrized by properly defining the reaction coordinate. The theoretical barriers are then fitted with the barriers defined by the parabolic and Eckart functions. Rate constants for the hydrogen and deuterium‐abstraction processes via tunneling at low temperatures are then computed.
Localization of electron group functions
Authors: Zapol Boris P. , Puchin Vladimir E.
Published: December 2004

The requirements of variational freedom of electron group functions and their spatial separation are basic statements of the group functions method as they are necessary for taking into account the intragroup electron correlation while neglecting the intergroup one. But these requirements seem to be inconsistent with one another. This contradiction can be removed using the notion of antisymmetrical annulment of many‐electron functions introduced in the present work. The transformation of group functions (GF) by means of functions antisymmetrically annulling (ASA) other GF's is proposed that does not affect the whole system's wave function but can be used for localizing GF's. The problem of construction of a function \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \Phi $\end{document} ASA a given Φ can be reduced to solving a system of linear algebraic equations. A sufficient condition of existing of nontrivial \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \Phi $\end{document} is obtained.
Integral representation of a fundamental functional for the study of the zero‐point vibrational energy of hydrocarbons and the total Pi‐electron energy of alternant hydrocarbons
Authors: Arimoto Shigeru , Hall George G.
Published: December 2004

A further step is made in investigating the zero‐point vibrational energies En (or the total pielectron energies En for the case of alternant hydrocarbons) of lineraly extended system BAnB′ having n repeating identical moieties. By an approach using the aspects of form and general topology, an integral representation αint of a fundamental functional α, where α(φ) = limn→∞ (En(φ)/n), has been established, which enables one to treat these energies quantitatively in a unified manner.
Broken symmetry solutions of the extended Hubbard model
Authors: Ozaki Masa‐Aki
Published: December 2004

This paper describes a group theoretical classification of the unrestricted Hartree–Fock (UHF) solution of the extended Hubbard model including nearest‐neighbor repulsion and exchange interactions. We derived systematically all types of the broken symmetry solution with a single‐order parameter for the ordering vector Q = (π,π). It is shown that there are four nonmagnetic states: a charge density wave (CDW), a charge current wave (CCW), and two bond‐order waves (BOW), and five magnetic states: an ordinary antiferromagnetic state (AF), a spin current wave (SCW), two axial spin bond‐order waves (ASBOW), and an helical spin bond‐order wave (HSBOW). We showed that these phases can be derived naturally from the irreducible decomposition of the Fourier transformed interaction and the self‐consistent field (SCF) condition. Some numerical results are given for the half‐filled case.
Ab initio study of K adsorption on a Ag(100) surface
Authors: Gayen Sanjukta , Ermler Walter C.
Published: December 2004

Ab initio Hartree–Fock calculations are reported for the chemisorption of K on Ag using three different types of clusters to model the system. Geometry optimization is done in 4 degrees of freedom. It is found that since there is an absence of complete charge transfer between the adsorbate and substrate, the interaction can be interpreted as being predominately covalent in nature.
Molecular mechanics study of the β‐spiral conformations of the Phe4, Tyr4, and Trp4 analogs of elastomeric poly(Val1–Pro2–Gly3–Val4–Gly5)
Authors: Luan Chi‐Hao , Urry Dan W.
Published: December 2004

The elastin‐derived polypentapeptide, poly(VPGVG), and analogs are becoming model systems for protein as well as forming a new class of biomaterials. The β‐spiral of poly(VPGVG) represents a new family of molecular structures in fibrous proteins. In particular for our interests here, aromatic amino acid residue substitutions at position four of poly(VPGVG) give rise to new polypeptides with interesting properties of increased elastic modulus, pressure sensitivity, etc. Molecular mechanics computations were carried out to answer the question, can the polypeptides with Phe, Tyr, and Trp substitution at position four of poly(VPGVG) form a β‐spiral structure like poly(VPGVG)? Employed in this study was a combination of conformational search using ECEPP/2 and the build‐up strategy and of molecular dynamics calculations using CHARMm. The results indicate that the VPGX Type II β‐turn structure appears to be the most prominent secondary structural feature for the three aromatic residues containing polypentapeptides, although there is more evidence for VPGFG and VPGVG to assume the VPGVG‐type structure than for VPGWG to do so. The study also shows that the aromatic side chains do not interrupt the β‐spiral structure, even in the case of tryptophan.
A general algorithm for computing Voronoi volumes: Application to the hydrated crystal of myoglobin
Authors: Procacci Piero , Scateni Riccardo
Published: December 2004

In this study is presented a general algorithm for computing Voronoi volumes of atoms of group of atoms in condensed phases. The method is essentially an extension of the Medvedev procedure to allow vertice determination for any Voronoi polyhedron, primitive or with degenerate vertices. The algorithm has been employed for computing time‐averaged volumes in the hydrated crystal of met‐myoglobin, using the data of a molecular dynamics simulation. The results, compared to previous volume determination in myoglobin, emphasize the fundamental role of solvent structure close to the protein surface in relation to the packing density properties of the residues. Relative volumes fluctuations of myoglobin residues have been found to be correlated to the corresponding mean square displacements from X‐ray diffraction studies and to the theoretical hydration energies.
The relative stability of the tautomers of α‐Hydroxytetronic acid
Authors: Bäucker Thomas , Klessinger Martin , Eckert‐Maksić Mirjana , Maksić Zvonimir B.
Published: December 2004

The relative stability of the four tautomeric forms of α‐hydroxytetronic acid was calculated with full geometry optimization at the STO‐3G, 3–21G, 6–31G*, and 6–31G** SCF levels. Correlation effects were estimated using the MP2 method. Intramolecular hydrogen bonds are found to be of primary importance for the relative stability of the various tautomers, and the same tautomer that in the case of L‐ascorbic acid is experimentally observed in the crystal as well as in solution is found to be the most stable one, if polarization functions on the hydrogen atoms are taken into account. It is concluded that even in the gas phase this tautomer predominates in α‐hydroxytetronic acid as well as in L‐ascorbic acid. © 1994 John Wiley & Sons, Inc.
Theoretical investigation of the enantioselective hydrogenation of α‐ketoesters over pt/alumina modified with cinchonidine
Authors: Schwalm O. , Weber J. , Minder B. , Baiker A.
Published: December 2004

Enantioselective hydrogenation of α‐ketoesters with cinchona‐modified platinum catalysts has been studied theoretically in order to rationalize the interaction between the chiral modifier and the substrate. The structure of the probable transition complex has been calculated for the system methyl pyruvate (substrate)–cinchonidine (modifier) using quantum chemistry techniques at both ab initio and semiempirical levels and molecular mechanics. The calculations indicate that crucial interaction occurs via hydrogen bonding of the quinuclidine nitrogen and the oxygen of the α‐carbonyl moiety of methyl pyruvate and confirm earlier experimental evidence that the quinuclidine nitrogen of the cinchonidine is involved in the interaction leading to enantiodifferentiation. The resulting complex, which resembles to a half‐hydrogenated state of the substrate, is shown to be a possible transition state for the enantioselective hydrogenation of α‐ketoesters. © 1994 John Wiley & Sons, Inc.