bluuebunny/crossref_metadata_2025 huggingface dataset:
Alternative derivation of perturbation expansions in the projection operator formalism
Authors: Timoneda J. Juanós I
Published: January 2005

The perturbation‐theoretic expansions obtained from Löwdin's projection operator formalism are derived in a new way, using Kato's formulation of perturbation theory. Kato's approach provides a convenient alternative to diagrammatic techniques for obtaining eigenvalues and eigenvectors. Different normalization criteria imposable on the wave function are easily visualized in terms of the operator that yields the perturbed state vector when it acts upon the unperturbed wave function.
Water‐Chain intervention in the ketonization of vinyl alcohol. An ab initio study
Authors: Lledós A. , Bertrán J. , Ventura Oscar N.
Published: January 2005

The ketonization of vinyl alcohol in aqueous solution has been studied by means of ab initio calculations, using the STO‐3G basis set. The intervention of a chain of two water molecules reduces dramatically the potential barrier. This result agrees with experimental facts.
Spin and charge densities from Hiller–Sucher–Feinberg identities. Test calculations for He, B, C, N, O, and F atoms and H2O, N2, and CH3 molecules
Authors: Ishida Kazuhiro
Published: January 2005

Spin and charge densities for several atoms and molecules can be calculated by the use of the Hiller–Sucher–Feinberg identities in the Hartree–Fock (HF) or the unrestricted Hartree–Fock (UHF) level with Gaussian basis sets. Previously presented formulas for the necessary integrals are improved for rapid computations when the d‐type Gaussian functions are added to the basis set. For charge density, a reliable description is obtained even for the HF or the UHF wave function, despite the use of the noncusp basis functions. The lack of the cusp in the Gaussian functions can be overcome also for spin density.
Accurate SCF computations on hydrogen bonds: Role of polarization functions on the bridge hydrogen atom
Authors: Seel M. , Del Re G.
Published: January 2005

For Hartree–Fock calculations, the limited basis 6–31G(*), with p functions on the bridge proton as the only polarization functions, is shown to be better balanced than the larger 6–31G* basis with d polarization functions on the heavy atoms and is therefore, a more suitable basis for the Hartree–Fock description of hydrogen bonds in large systems.
Theoretical study of lithium‐fluoride and lithium‐chloride ion pairs in aqueous solution. An SCF‐CNDO/2 approach including continuum solvent effects
Authors: Gómez‐jeria J. S. , Contreras Renato R.
Published: January 2005

SCF‐CNDO/2 calculations, including solvent effects via an extended version of the Generalized Born Formula (GBF), have been performed for LiX(H2O) species (n = 1,2; X = F, Cl). Several minima in the free energy surface, representing intimate and solvent‐separated ion pair structures, have been analyzed. Qualitative results show a preferential stabilization of the intimate forms with respect to the solvent‐separated ones. The results are discussed on the basis of a convenient partition of the total solute‐solvent free energy. The interaction of the ionic species with the bulk solvent neglected in previous studies appears to be responsible for the preferential stability of the intimate forms.
Ab initio exchange‐correlation parameter in the Xα method
Authors: Nagy Á.
Published: January 2005

The method of statistical exchange‐correlation parameter is presented. It has been shown that there is only a small difference between the self‐consistent, the statistical, and the αHF parameters. We suggest using statistical exchange‐correlation parameters in molecular calculations.
Bohr orbit theory revisited. II. Energies for 1S, 2P, 3D, and 4F states of helium
Authors: Harcourt Richard D.
Published: January 2005

A modified Bohr orbit procedure is used to calculate the energies for the 1S ground state and the 2P, 3D, and 4F excited states of the helium atom. The energies are calculated from \documentclass{article}\pagestyle{empty}\begin{document}$ {{\int\limits_0^\pi {E\left(\Phi \right)P\left(\Phi \right)d\Phi } } \mathord{\left/ {\vphantom {{\int\limits_0^\pi {E\left(\Phi \right)P\left(\Phi \right)d\Phi }} {\int\limits_0^\pi {P\left(\Phi \right)d\Phi } }}} \right. \kern-\nulldelimiterspace} {\int\limits_0^\pi {P\left(\Phi \right)d\Phi } }} $\end{document}, in which E(ϕ) is the Bohr orbit energy for angle ϕ between the position vectors \documentclass{article}\pagestyle{empty}\begin{document}$ \vec r_1 $\end{document}
r1 and \documentclass{article}\pagestyle{empty}\begin{document}$ \vec r_2 $\end{document}
r2, and P(ϕ) is a probability function for this angle. Numerical procedures are used to evaluate the integrals. Energies that range between −2.9082 and −2.9054 au are calculated for the 1S state (cf. −2.9037 au, exact). The Bohr energies for the excited states are −2.1318, −2.1240, −2.0562, −2.0555, −2.0314, and −2.0312 au, which are generally close to the exact energies of −2.1332, −2.1239, −2.0557, −2.0557, −2.0313, and −2.0313 au for the 23P, 21P, 33D, 31D, 43F and 41F states. Some relationships that exist between the Bohr theory and the Schrödinger local energies are discussed. Approximate Bohr orbit estimates for the energies of the 2P states of He, Li+,…,Ne8+ are reported.

The invariance of the two‐electron Bohr hamiltonian with respect to the interchange of the electron coordinates leads to two classical probability functions when the orbit quantum numbers for the two electrons differ.
A simple introduction to colored symmetry
Authors: Coxeter H. S. M.
Published: January 2005

The problem of systematically coloring periodic patterns has interested textile designers, artists, and crystallographers since 1935. The classification of possible procedures has been seen to depend on space groups and their subgroups and factor groups. Crystallographers naturally worked in Euclidean three‐space before generalizing to two, and then four, dimensions. The present treatment deals with the one‐dimensional case in a manner that can easily be extended. Avoiding the crystallographers' customary emphasis on translations, among the various kinds of symmetry operations, allows the classification to be readily adapted to non‐Euclidean geometries.
Integral processing in beyond‐Hartree‐Fock calculations
Authors: Taylor Peter R.
Published: January 2005

The increasing rate at which improvements in processing capacity outstrip improvements in input/output performance of large computers has led to recent attempts to bypass generation of a disk‐based integral file. The “direct” SCF method of Almlöf and co‐workers represents a very successful implementation of this approach. The present work is concerned with the extension of this general approach to CI and MCSCF calculations. After a discussion of the particular types of MO integrals for which — at least for most current generation machines — disk‐based storage seems unavoidable, it is shown how all the necessary integrals can be obtained as matrix elements of Coulomb and exchange operators that can be calculated using a direct approach. Computational implementations of such a scheme are discussed.
Implementation of the complex coordinate method for resonances and photoionization cross sections by means of matrix element extrapolation
Authors: Froelich Piotr , Sangfelt Erland , Weiner Brian
Published: January 2005

A new implementation of the complex coordinate method for calculation of molecular resonances and photoionization cross sections is presented. The method originates from the idea of analytic continuation of stabilization graphs, but instead all matrix elements are numerically continued. Exterior scaling is invoked in conjunction with the use of dilationally adapted basis sets. It is operationally equivalent to the bivariational method in the Feshbach‐partitioned manifold of complex basis functions, but no complex integrals are calculated. Instead, the complex eigenvalue problem arises from the analytical continuation of the realvalued matrix elements pertinent to any atomic or molecular structure code in its standard (real) form. That includes the possibility of using numerical basis sets. Since the method does not require modification of existing numerical codes, it can serve as a complement to any large scale CI or MCSCF molecular structure calculation.
The peri effect in aromatic hydrocarbon carcinogenesis: An empirical force field examination
Authors: Seybold Paul G. , Lipkowitz Kenny B.
Published: January 2005

Methyl substitutents located peri to bay‐region benzo rings of polycyclic aromatic hydrocarbons generally reduce or eliminate carcinogenic activity, most likely because such substituents force the hydroxyl groups of dihydrodiol intermediates to adopt preferentially pseudodiaxial, rather than pseudodiequatorial, conformations. Empirical force field calculations have been employed to examine the influences of peri and other positional substituents on hydroxyl conformation, taking naphthalene, anthracene, and phenanthrene as model compounds. For the unsubstituted naphthalene and anthracene dihydrodiols, the pseudodiequatorial conformation is preferred. This preference is reduced by adjacent methyl substitution and reversed by peri methyl substitution. Because of steric crowding the phenanthrene bay‐region dihydrodiol preferentially adopts a pseudodiaxial conformation. The results are discussed in relation to recent experimental evidence.
Spectroscopic studies on some phenylethylamine drugs: Molecular orbital calculations
Authors: Abu‐Eittah R. H. , Hamed M. M. , Abdou M. M.
Published: January 2005

The electronic absorption spectra of some phenylethylamine drugs, namely, d‐pseudoepherine, l‐pseudoephedrine, l‐ephedrine, dl‐ephedrine dl‐norephedrine, phenylethylamine, methoxyphenamine, and l‐noradrenaline were investigated in polar and nonpolar solvents. The observed transitions were interpreted, and the role of σ‐π interaction was explored. Molecular orbital calculations were performed on representatives of the above group of compounds, namely, d‐pseudoephedrine, l‐ephedrine, and l‐noradrenaline using the INDO procedures and adopting the best conformer of the molecule. The transition energy, band intensity, and dipole moments were calculated and corresponded satisfactorily with the experimental values.
Cellular spin resonance inversion by ion‐induced dipoles
Authors: Pollock J. Kent , Pohl Douglas G. , Pohl Herbert A.
Published: January 2005

Cellular spin resonance (CSR) or electrorotation is the spinning of cells or other particulate matter in rotating electric fields. The spin rate of the (bio)particle varies markedly with the applied frequency and often is seen to have rather sharp maxima as the frequency is varied. In certain frequency ranges, living cells often are observed to undergo a striking inversion of their spin rate and then spin counter‐clockwise (CCW) while the direction of rotation of the applied electric field is clockwise (CW).

The CSR spectra are presumably due to dipolar interactions with the applied field, as are the spectra obtained by straightforward dielectrophoresis (DEP) techniques. The two spectra, however, differ radically in the low frequency ranges (below about 1 MHz). It is our objective to explain this apparently anomalous behavior.

We believe that the anomaly appears primarily because one is comparing rotational with translational force responses. In the DEP techniques, the simpler translational force arising from the comparative polarizability of cell versus medium (water) gives a straightforward measure of the differential polarizability owing to volume and surface effects pro forma. In the CSR techniques the spin rate reflects the torque on the cells and hence emphasizes polarization at the outer periphery of the cells rather than that of the average overall polarizability.

The problem is considered in terms of a living or dead cell rotating with an angular velocity Ω in a fluid medium of viscosity η when it is subject to an electric field rotating at angular frequency ω. It is observed in many experiments that Ω ≪ ω, and also that the sign of Ω for the same cell can change from CW to CCW and back to CW as the applied frequency ω of the CW electric field is increased. Moreover, the sign and magnitude of the CSR spectra differ for living and dead cells. All of these experimental results can be explained quantitatively by using Maxwell's equations and the dielectric properties of a lossy dielectric sphere in an ionically conductive dielectric fluid.
Direct calculation of the Hartree–Fock interaction energy via exchange–perturbation expansion. The He …︁ He interaction
Authors: Jeziorska Małgorzata , Jeziorski Bogumił , Čížek Jiří
Published: January 2005

The Hartree‐Fock (HF) equations for the (He)2 system are solved using a suitable exchange perturbation technique. The HF interaction energy is then obtained directly from a rapidly convergent iteration procedure. The method remains convergent for short interatomic distances, where the interaction energy surpasses the energy of intraatomic excitations. The fast convergence of the method is a result of the proper treatment of the exchange‐deformation effects. In the region of the van der Waals minimum, these effects account for 50% of the HF deformation energy.
“Non‐muffin tin” corrections of the SCF Xα‐SW Method. I
Authors: Rubin I. R. , Lobatch V. A. , Shulgin B. V.
Published: January 2005

The recently developed crystalline cluster method within the framework of the Johnson multiple scattering technique was successfully used in calculations of ionic cubic crystals and the defects with a cubic symmetry. In this paper a simple way of extension of the method to noncubic systems by a partial elimination of “muffin‐tin” approximation (MTA) is proposed.

The procedure suggested does reduce the intermediate integrals to the one‐dimensional ones, and they are calculated analytically. It is supposed that an approach of taking into account the nonspherical shape of the potential inside the “muffin‐tin” (MT) spheres will be effective in crystals with an ionic type of chemical bond.
Development and parametrization of sindo1 for second‐row elements
Authors: Jug Karl , Iffert Rüdiger , Schulz Joachim
Published: January 2005

The semiempirical MO method SINDO1 is extended to second‐row atoms from sodium to chlorine. The basis set has a provision to include d orbitals. To retain rotational invariance in a d orbital set, a number of hybrid integrals has to be included that invalidate the zero differential overlap (ZDO) assumption even in a symmetrically orthogonalized basis set. The inclusion of d orbitals rendered the set‐up of integral calculation of the original INDO method impractical. Instead of one subroutine for each integral, all explicitly calculated integrals (overlap, core, electronic repulsion) are now contained in a single subroutine under unifying aspects. The parametrization scheme includes pseudopotentials and adjusts the total energy under inclusion of zero point energies to experimental heats of formation of ground states. The vibrational frequencies for the calculation of zero point energies are obtained from calculated force constants and G matrix elements by a scaling procedure. The results for geometries, energies, and dipole moments are compared with MNDO data.
Exchange perturbation theories
Authors: Klein D. J.
Published: January 2005

Various earlier‐proposed perturbative approaches to the description of weakly interacting species are considered. It is argued that most of these perturbative approaches, including many of the so‐called exchange perturbation theories, exhibit a number of difficulties and limitations, which have not previously been emphasized. From these criticisms positive suggestions as to the nature of a general exchange perturbation‐like theory are made. Finally, a candidate for such a theory is outlined.
Method of local‐scaling transformations and density functional theory in quantum chemistry. II. The procedure for reproducing a many‐electron wave function from x‐ray diffraction data on one‐electron density
Authors: Kryachko Eugene S. , Petkov Ivan Zh. , Stoitsov Mario V.
Published: January 2005

The computational procedure for reconstructing a many‐electron wave function on the basis of x‐ray diffraction data of one‐electron density is proposed within the method of local‐scaling transformations.
Discrete spatial symmetries: Redundant coordinates and search for stationary points in reduced spaces
Authors: Banerjee Ajit
Published: January 2005

Given the invariance of an N‐body system under discrete operations of reflection, inversion, a rotation by 2π/n, and the corresponding relations among the derivatives of energy, we have constructed through an invertible transformation a set of active and redundant coordinates. Movement along the active coordinates preserves all symmetry relations. We show that algorithms for locating stationary points or for calculating reaction paths are exactly separable in these active and redundant coordinates. We further show that this formalism is equally applicable when equations of constraints among coordinates are specified for the movement of particles. This includes geometrical constraints on bond lengths, angles, substituent group internal rotations, etc. This formalism enhances the efficiency since (laborious) cartesian derivatives need to be calculated only for the active variables and that the problem is reduced in term of m(⩽3N) variables. We apply this procedure to obtain the equilibrium geometry of H2O molecule within the subspace of C2v symmetry configurations ab initio derivatives.
Ab initio studies on the catalytic mechanism of ester hydroloysis by serine proteases
Authors: Stamato Fulvia M. L. G. , Tapia O.
Published: January 2005

Some aspects of the catalytic mechanism of the serine proteases were submitted to ab initio RHF MO studies at a 3‐21G basis set level. Analytical gradients were used to optimize the geometry of the molecular partners and to sense the interactions among them when they make up for the active site in chymotrypsin. Reaction fields of graded strengths were used to sense the response of the active site to protein surrounding effects. The catalytic triad (Asp‐His‐Ser) is reduced to a model dyad represented by ammonia and methyl alcohol. Methyl acetate represents a substrate. One water molecule is added to the model as a local solvation effect. (This molecule plays a central role in the rupture of the acylated enzyme, which was not studied here). The reaction pathways of MeAc interacting with the alcohol and alcoholate were studied to determine the intrinsic properties of this system in the present level of wave function representation. The presence of the dyad alters the interaction potential of the reacting system. The canonical form in vacuo is significantly more stable than the diionic one. The reaction field produces stabilizing effects favoring the catalytic diionic form. The effect of the tetrahedralization in the substrate has been studied. A planar substrate is strongly repelled at distances shorter than 3.0 Å, whereas a tetrahedral substrate can approach the catalytic dyad in the native configuration without apparent steric hindrance.
Molecular orbital calculations on tumor‐inhibitory nitrosoureas: QSARs
Authors: Lewis David F. V.
Published: January 2005

Molecular Orbital (MO) calculations by the MINDO/3 method on tumor‐inhinbitory nitrosoureas is reported. Electronic structures for 18 chlorethyl nitrosoureas and 30 cyclohexyl nitrosoureas (CCNUS) are related to biological activity in the form of toxicity, therapeutic activity, and increase in life span and chemical reactivity in the form of alkylating and carbamoylating activity. Hydrophobicity, as measured by the logarithm of the partition coefficient (octan‐1‐o1/water), shows a parallelism with calculated bulk molecular properties. Mechanisms of alkylation and other reactions related to biological action are proposed and discussed.
Adiabatic perturbation theory for the degenerate case. III. Adiabatic formalism by Gell‐Mann and low with an arbitrary switching function
Authors: Dmitriev Yuri Yu. , Solnyshkina Olga V.
Published: January 2005

An adiabatic formalism in the degenerate or quasidegenerate subspaces, which does not depend on the particular form of the switching function g(α, t), is outlined. A general factorization theorem for the dynamic operator Sα(t, t0 | g) is proved. This theorem enables one to formulate the perturbation expansion for the effective Hamiltonian and the wave operator which is free from the adiabatic divergencies.
The concept of the topological atom within the MO‐LCAO approach. II. On the nature of the nephelauxetic effect
Authors: Proinov E. , Neshey N. , Andreev A.
Published: January 2005

A new MO‐LCAO description of the nephelauxetic effect is proposed based on the concept of the topological atom and on the method of reduced density matrices. This approach allows one to overcome some conceptual difficulties of ligand‐field theory and to derive effective parameters of d‐d electron repulsion of a bound transition‐metal in a proper way. The two ligand‐field mechanisms of the nephelauxetic effect—the central field covalency and the symmetry‐restricted covalency—are clarified and generalized. In addition, a new factor, important for the nephelauxetic effect is found: its size‐dependence on the region of the topological atom.
The sequential product of geminals and the ground states of some atoms
Authors: Jiang X. Q. , Jin B. Y. , Zeng Z. H. , Sun C. C. , Coleman A. J.
Published: January 2005

By means of the SPG function which is associated with an extreme point of the set of N‐representable second‐order reduced density matrices, an attempt is made to perform the calculations of the ground states of some atoms with four electrons such as Be. The results show that the SPG function is as suitable as the well‐known AGP function for approximating the ground states of atoms and molecules.
A sequential product of geminals and its applications
Authors: Jin B. Y. , Jiang X. Q. , Zeng Z. H. , Sun C. C. , Coleman A. J.
Published: January 2005

In this paper, an SPG function, which is associated with an extreme point of the set of N‐representable second‐order reduced density matrices, is used to perform the calculation of the ground state energy of LiH with the variation of internuclear separation. The result of our calculation essentially is in accordance with that of AGP function.
A Crystal Orbital approach for two‐ and three‐dimensional solids on the basis of CNDO/INDO Hamiltonians. Basis equations
Authors: Ramírez Rafael , Böhm Michael C.
Published: January 2005

A Hartree–Fock (HF) self‐consistent field (SCF) crystal orbital (CO) formalism for two‐ and three‐dimensional (2D/3D) solids on the basis of semiempirical CNDO/INDO (complete neglect of differential overlap; intermediate neglect of differential overlap) Hamiltonians is presented. The employed SCF variants allow for the treatment of atomic species up to bromine under the inclusion of the first (i.e., 3d) transition metal series. Band structure investigations of 2D and 3D materials containing more than 30 atoms per unit cell are feasible by the present SCF HF CO formalism. The theoretical background of the computational scheme is given in this contribution. Special emphasis is placed on physically reliable truncation criteria for the lattice sums, the adaptation of the crystal symmetry in k space, as well as the suitable choice of domains in Brillouin zone (BZ) integrations required in the determination of charge‐density matrices. The capability and limitations of the semiempirical SCF HF CO approach is demonstrated for some simpler solids by comparing the present computational results with those of ab initio CO schemes as well as conventional numerical methods in soid‐state theory. The employed model solids are graphite and BN (2D and 3D networks for both solids) as well as diamond, silicon, germanium, and TiS2.
The two‐dimensional band structure of (polyphthalocyaninato)Ni(II)
Authors: Ramírez Rafael , Böhm Michael C.
Published: January 2005

The two‐dimensional (2D) band structure of (polyphthalocyaninato)Ni(II), Ni(ppc), has been analyzed by a self‐consistent field (SCF) Hartree–Fock (HF) crystal orbital (CO) formalism based on an INDO (intermediate neglect of differential overlap) type Hamiltonian. The calculated HF band gap of Ni(ppc) amounts to 0.24 eV. The highest filled band is a ringlike a1u combination (D4h symmetry label) localized at the carbon sites of the organic fragment. Remarkable hybridization in the valence band leads to the considerable band width Δϵv of 2.92 eV. This value is close to the Δϵv numbers which are conventionally encountered in one‐dimensional metallomacrocycles. The effective width of the states in Ni(ppc) is 13.8 eV. In graphite a net π interval of 13.0 eV is predicted by the present CO formalism; i.e., the energetic distribution of the π electrons is roughly comparable in both 2D solids. The Ni 3d states in Ni(ppc) are far below the Fermi level which is calculated at −4.9 eV; they are predicted between −12.2 and −16.4 eV in the mean‐field approximation. Quasi‐particle corrections lead to a significant shift of these strongly metal‐centered states. Important electronic structure properties of Ni(ppc) are compared with those of 1D metallomacrocycles with similar molecular stoichiometry. The total density of states distribution of Ni(ppc) has been fragmented into projected (ligand π and σ, Ni 3d) contributions in order to allow for a transparent interpretation of the 2D band structure.
Simplified expansion of Slater orbitals about displaced centers
Authors: Rico J. Fernández , Lóapez R. , Ramíarez G.
Published: January 2005

A new and very simple one‐range expansion of the 0s function is derived and employed as the starting point of three recurrence relations which allow the expansion of arbitrary Slater functions over displaced centers. Convergence of the expansions, both pointwise and in norm, are analyzed, and three‐center nuclear attraction integrals are chosen for a further test of the formal developments and the numerical behavior of these expansions.
Control over theoretical descriptions of atoms and molecules. An information theoretic approach to the automatic classification and systematic improvement of approximate wave functions
Authors: Maroulis George
Published: January 2005

A rigorous approach to the study of the quality of theoretical descriptions of atoms and molecules is proposed. Theoretical descriptions, i.e., collections of atomic or molecular properties obtained via quantum chemical methods, are associated with information quantities defined with respect to reference theoretical or experimental data. In this way the comparison of two theoretical descriptions is reduced to the comparison of the respective information quantities. An increase in information is interpreted as improvement of the theoretical description. The aforementioned approach should be useful in problems related to classifications and systematic improvements of approximate wave functions and consequently for comparing the performance of quantum chemical methods in calculations of atomic and molecular properties. This approach should also constitute a powerful tool for the construction of suitable basis sets for use in calculations of atomic and molecular properties.
Structure and properties of nonclassical polymers. VII. Polymers with heteroatoms
Authors: Tyutyulkov N. N. , Ivanov C. I. , Schopov I. , Polansky O. E. , Olbrich G.
Published: January 2005

It is shown that the Coulson–Rushbrooke theorem for odd alternant hydrocarbons [15] can be generalized for some classes of nonclassical systems containing heteroatoms. The energy spectrum of such conjugated polymers containing heteroatomic groups, in particular a nitroxide group >NO, is analogous to that studied [1–4] in homonuclear alternant nonclassical polymers, whose ground state is characterized by maximum spin multiplicity. Their band structure is characterized by a wide energy gap, in the middle of which there is a band of degenerate or nearly degenerate quantum states.

The presence of a narrow band of degenerate quantum states, the Hund rule, and the alternant character of the polymers of this group determine the maximum multiplicity of their ground state and may give rise to the creation of magnetic order in such compounds, if interchain correlations occur. This is in line with the investigations in Refs. 1–11.
A measure of the error in wave functions
Authors: Fraga Serafin
Published: January 2005

The quantity ϵ = (Φ||(H − E)Φ|) gives a measure of the error in the approximate solution, Φ (with corresponding energy expectation value E), to an eigenfunction of the Hamiltonian operator H of the system under consideration; this quantity vanishes for the exact function ψ. In a percentage scale (with 0% error for the exact function and 100% for a reference, approximate function), the error of Φ may be expressed as 100(ϵ/ϵr), where ϵr corresponds to the reference function (e.g., obtained with a minimal basis set). This approach eliminates the need of knowing beforehand the exact solution in order to have an estimate of the error of an approximate solution.
Thomas–Fermi theory from a perturbative treatment of the hydrogenic limit energy density functional: A possible link to local density functional theory
Authors: Bartolotti Libero J. , Parr Robert G. , Tal Yoram
Published: January 2005

A perturbation expansion which connects the hydrogenic limit energy density functional to the Thomas–Fermi functional is discussed. This perturbation series, where the Coulomb energy density functional is treated as the perturbation to the hydrogenic limit functional, is, in fact, the q = (N/Z) expansion of Thomas–Fermi theory. A truncated form of the first‐order correction to the functional provides further insight into the model which treats the ground state energy as a local functional of the electron density.
An interaction potential between an alanine zwitterion and a water molecule based on ab initio calculations
Authors: Ni Xiangshan , Shi Xiufan , Ling Lunjiang
Published: January 2005

Interaction energies between an alanine zwitterion and a water molecule at 150 different positions and orientations have been calculated using the ab initio method with the minimal basis set and employing the counterpoise method to eliminate the basis set superposition error. Dispersion energies are estimated using the Slater–Kirkwood formula. Out of a total of 150 computed interaction energies, 140 whose SCF interaction energies are below 5 kcal/mol have been fitted with a summation of atom‐atom pair potentials in the form of the Lennard–Jones potential plus an electrostatic term. The standard deviation for this fitting is 0.49 kcal/mol.

A sampling scheme regarding geometrical configurations is presented. Twenty rays are uniformly drawn from the origin of coordinates, a floatable division with equal ratios is made along each ray, and one of 60 orientations is randomly taken as the orientation of a water molecule. A nonlinear fitting method is used with a restriction on the sign change of fitting coefficients.
The use of symmetry in reciprocal space integrations. Asymmetric units and weighting factors for numerical integration procedures in any crystal symmetry
Authors: Ramirez Rafael , Böhm Michael C.
Published: January 2005

A systematic collection of spatial domains for reciprocal space integrations is derived for all possible crystal symmetries. This set can be used as a simpler alternative to the conventional Brillouin zones. The analysis is restricted to integrations where the function in the integrand satisfies inversion symmetry in k space. In this case only 24 different spatial domains have to be defined in order to allow for k space integrations in the 230 different crystal symmetries. A graphic representation of the asymmetric unit for each of the 24 integration domains is given. Special positions and the associated weighting factors required for numerical integrations in theoretical solid‐state approaches are tabulated.
Hydrophobic effect in biological associates: A Monte Carlo simulation of caffeine molecules stacking
Authors: Danilov Victor I. , Shestopalova Anna V.
Published: January 2005

Results of a Monte Carlo simulation of the hydration of caffeine (1,3,7‐trimethyl‐2,6‐dioxipurine) and three different configurations of its stacked dimer are presented. Simulations were performed in a cluster approximation; the system contained 200 water molecules. The nature of the stabilization of caffeine stacking associates in water was considered. A hydrophobic behavior of methyl groups during association of caffeine molecules in water is shown. Results of the simulation of caffeine hydration are compared with experimental data from the study of the system of caffeine–water.
Conformational analysis of oligosaccharides in solution
Authors: Tvaroška Igor
Published: January 2005

A complete understanding of the role of carbohydrates in biological systems is to a large extent dependent on the information available about the equilibrium mixture and about the preferred conformation of the carbohydrate molecules in solution. The conformational analysis offers a tool which can determine all possible conformations which influence the solution behavior of carbohydrates.

This paper attempts to survey the progress in the theoretical conformational analysis of saccharides in solution. The conformational analysis will be discussed in detail both with respect to the strategy for the investigation of conformational properties but also with regard to the quality of the method used for calculations of the energy of the isolated molecule and free energy of solvation.

Finally, examples will be given to illustrate how the methods of conformational analysis can be used to estimate the solution behavior of cyclic model compounds of carbohydrates 2‐methoxytetrahydropyran, monosaccharide D‐glucopyranose, and two disaccharides; β‐maltose and β‐cellobiose.
Interaction model for the antiinflammatory action of benzoic and salicylic acids and phenols
Authors: Mehler E. L. , Gerhards J.
Published: January 2005

Ab initio, quantum chemical methods have been used to develop an interaction model for the binding of benzoic and salicylic acids and phenols to cyclooxygenase, leading to their antiinflammatory action. The model is based on a regression analysis of the energy of the highest occupied molecular orbital with the potency of the active substances to inhibit prostaglandin production in mouse macrophages and on an analysis of the frontier orbital charge distributions and electrostatic potentials of active and inactive compounds. The model suggests that binding is controlled by an electrostatic orientational factor and a charge transfer or polarization contribution. The observed relative potencies of the phenols and acids can be rationalized with the help of the proposed interaction model.
Generalized statistical approach to the study of interatomic interactions
Authors: Santamaría R. , Berrondo M. , Novaro O. , Kryachko E. S.
Published: January 2005

We present a simple model for calculating the interatomic interaction energies in the electron gas approximation. We use a generalization of the supermolecular electronic density which includes a density overlap term. We present numerical calculations for the He‐He interaction as an illustration of the method.
The compton spectrometer
Authors: Carlsson Gudrun Alm , Berggren Karl‐Fredrik , Carlsson Carl A. , Matscheko Georg , Ribberfors Roland
Published: January 2005

This is the story about how knowledge of the Compton profile led to the technical development of a useful apparatus. It is also the story of interdisciplinary collaboration between condensed matter theorists and medical physicists.
Nonlocal and nonlinear electromagnetic effects at surfaces
Authors: Lundqvist S.
Published: January 2005

The reflected and transmitted electric fields generated by s‐ and p‐polarized incident radiation are discussed using a microscopic approach that matches the solution of Maxwell's equation (obtained by integration over the surface region) to the incident and the reflected fields in the vacuum and to the transmitted fields in the bulk. At positions where the dielectric response is varying rapidly, the parallel components of the oscillating polarization are the sources of reflected as well as transmitted fields, and the corresponding perpendicular components (which exist only for p‐polarized incident radiation) lead to charge oscillations that are the source of both longitudinal and transverse fields. The presence of the surface makes possible the generation of transverse and longitudinal excitations with large normal components of the wave vector, whose propagation directions are given by the conservation of the parallel component of the wave vector. This formulation does not make use of additional surface boundary conditions (ABC) but requires an explicit model for the nonlocal dielectric function in the surface region. Besides discussing the fields, we discuss the choice of electromagnetic potentials. We also discuss nonlinear properties with applications to second harmonic generation.
Some remarks on the perturbation and variation–perturbation calculations of the free energy for quantum systems
Authors: Löwdin Per‐Olov , Nagel Bengt
Published: January 2005

A generalization of the Gibbs–Bogoliubov inequality F ⩽ F0 + 〈H − H0〉0 for the free energy F is studied which leads to a variation principle for this quantity that may be of importance in certain computational applications to quantum systems. This approach is coupled with a study of the perturbation expansion of the free energy for a canonical ensemble with H = H0 + λV in the general case when H0 and V do not commute. The second‐ and high‐order derivatives of the free energy with respect to the perturbation parameter λ are calculated. From the second‐order term is finally obtained a second‐order correction to the previous variational minimum for the free energy.
Explicit representation of Gel'fand–Tsetlin states in clifford algebra unitary group approach
Authors: Li Xiangzhu , Paldus Josef
Published: January 2005

A explicit expression for the unitary group Clebsch–Gordan coefficients, which couple two fully antisymmetric single‐column states into the two‐column Gel'fand–Tsetlin states, is given in terms of isoscalar factors for the canonical subgroup chain U(n) ⊃ U(n – 1) ⊃ …︁ ⊃ U(1). The isoscalar factors are expressed through the step numbers labeling canonical basis states and enable a straightforward construction of Gel'fand–Tsetlin states in the Clifford algebra unitary group approach, without the use of the tables for the symmetric group outer‐product reduction coefficients.
Electric field variant ket for the calculation of dynamic polarizabilities. Application to H2O and N2
Authors: Rérat M.
Published: January 2005

The use of a new time‐dependent ket, variationally determined as a linear combination of Slater determinants associated with an electric field variant factor, provides an efficient technique for the calculation of dynamic polarizability tensors. Including electron correlation, the method is applied to the evaluation of the frequency‐dependent polarizability of H2O and N2 and can be used even when the photon energy is near the excitation energy. With relatively small basis sets, calculated polarizabilities and resonance frequencies are in good agreement with experimental values for H2O but have to be improved for N2.
Charge density by the use of the hiller–sucher–feinberg identity. Perturbative corrections and configuration interaction effects
Authors: Ishida Kazuhiro
Published: January 2005

Configuration interaction (CI) calculations are carried out for He atom and H2, LiH, and BH molecules in order to obtain the value of the charge density at the nucleus by the use of the Hiller–Sucher–Feinberg (HSF) identity. The HSF density also can be calculated with the double perturbation theory based on the Møller–Plesset‐type theory and also on the Epstein–Nesbet type. It is found that each value of the HSF density for these perturbative corrections is very similar to the corresponding value by the CI with single‐ and double‐electron excitations. Especially for the He atom, the HSF density value by the full‐CI wave function coincides with the exact value of the charge density in three significant figures. The electron correlation effects are found to be small but cannot be ignored in the HSF density. It can be shown that the superiority of the HSF density over the usual delta‐function‐type density is excellently confirmed.
An empirical potential for interactions of large molecules: Application to binding of dipeptides to DNA
Authors: Hobza P. , Havlas Z.
Published: January 2005

An empirical potential is introduced that is suitable for calculation of the interaction enegies of biomolecules with thousands of atoms. The potential consists of electrostatic, repulsion, and dispersion energy terms. The approach used for parametrization of the potential is entirely different from that used with other existing potentials. Namely, all the terms were parametrized independently to retain their physical significance. The sum of the electrostatic and repulsion terms mimic the SCF interaction energy calculated using Huzinaga's minimal basis set MINI‐1. The dispersion energy is very important and is usually predominant for the interactions of large (polar) molecules in the gas phase as well as in the liquid phase.
Theoretical study of carbonic anhydrase‐catalyzed hydration of co2: A brief review
Authors: Liang Jiin‐Yun , Lipscomb William N.
Published: January 2005

Quantum mechanical calculations have been used to study the reaction mechanism of human carbonic anhydrase‐catalyzed hydration of CO2. This reaction is responsible for fast metabolism of CO2 in the human body. For each of the reaction steps, possible catalytic effects of active site residues are examined. The pertinent results are as follows. (1) For CO2 binding, the experimentally observed 2.5 cm−1 frequency shift of the asymmetic stretching frequency between measurements taken in the aqueous solution and in the enzyme is reproduced in our theoretical calculations. Our results suggest that CO2 binds to the zinc ion within the hydrophobic pocket. (2) No energy barrier is found for the nucleophilic attack from Zn2+−bound OH− to C of CO2 to form Zn2+−bound HCO3−. (3) For the internal proton transfer within zinc‐bound HCO3−, the barrier of 35.6 kcal/mol for the direct internal proton transfer is reduced to 3.5 and 1.4 kcal/mol, respectively, when one or two water molecules are included for proton relay. (4) Displacement of Zn2+−bound HCO3− by H2O is facilitated by the presence of the negatively charged Glu 106‐Thr 199 chain and by the association and the subsequent ionization of a fifth water ligand. (5) For the intramolecular proton transfer between Zn2+‐bound H2O and His 64, the Zn2+ ion lowers the pKa of Zn2+−bound water and repels the proton. His 64, or a similar proton receptor with a larger proton affinity than H2O, functions as proton receiver; and the active site water molecules visualized by x‐ray crystallography are important for the proton relay function. In summary, it is demonstrated that in order to achieve effective catalysis, a sequence of precisely coordinated catalytic events among all participating catalytic elements in the enzyme's active site is essential.
Proton transfer and solitonic excitations in model one‐dimensional hydrogen‐bonded systems
Authors: Misiak P. , Chojnacki H.
Published: January 2005

The solitonic models of proton transfer in a molecular hydrogen‐bonded chain have been examined with respect to the shape of protonic interaction potential. The kink‐like excitations with quadratic, quartic, Morse, and Toda interactions are reported and analyzed.
Localization measure and maximum delocalization in molecular systems
Authors: Pipek János
Published: January 2005

A mathematically well‐defined measure of localization is presented based on Mulliken's orbital populations. It is shown that this quantity equals 1 for core‐ and lone‐pair orbitals, 2 for two‐atomic bonds, 6 for benzene rings, etc., and it is applicable for delocalized canonical HF orbitals as well. The definition of this quantity is general in the sense that ab initio MOS with overlapping AO expansion, and semiempirical wave functions using the ZDO approximation as well, can be treated. The localization quantity is essentially “intrinsic,” i.e., no subdivision of the molecule is required. For N‐electron wave functions, mean delocalization can be defined. This measure is not invariant to unitary transformations of the one‐electron orbitals, characterizing in this way the localized or extended representation of the N‐electron wave function. It can be proven, however, that for unitary transformed wave functions a maximum delocalization exists which depends only on the physical (N‐electron) properties of the molecule. It is shown that inhomogeneous charge distribution can cause strong electron localization in molecular systems. The delocalization of the canonical Hartree–Fock orbitals, the Parr–Chen circulant orbitals, and the optimum delocalized orbitals is studied by numerical calculations in extended systems.
Surface states in deformed and perturbed diatomic crystals
Authors: Andrade L. , Sánchez M.
Published: January 2005

The electronic properties of a one‐dimensional diatomic crystal have been analyzed by using the MO‐LCAO method in the tight binding approximation, with mathematical techniques involved in setting up and solving difference equations. The approach gives the exact sets of analytic solutions for both localized and nonlocalized states. The theory of surface states is developed as a characteristic value problem. To illustrate the method the surface states for a semiinfinite crystal which contains a local imperfection at the surface were examined. It appears that this method has advantages over previous methods developed to solve surface problems in crystalline lattices.
Ab initio SCF study of the interaction between L‐serine phosphate and ammonia
Authors: Nakamura Y. , Lunell S.
Published: January 2005

The possible conformational changes of L‐serine phosphate due to the interaction with ammonia are investigated by means of ab initio MO‐LCAO‐SCF calculations, using a supermolecule approach and an STO‐3G basis set. The most favorable conformation of a four‐hydrated L‐serine phosphate anion is found to be changed by the binding of an ammonium ion. Cointeraction of ammonia and NH suggests another conformational change through the displacement of the bridging water molecule of the polyhydrated L‐serine phosphate anion.
Quantal approach to study the structure of triatomic I2 ⃛ X (X = He, Ne) VDW clusters
Authors: García‐Vela A. , Villarreal P. , Delgado‐Barrio G.
Published: January 2005

Energy levels of I2 ⃛ X van der Waals (VDW) molecules, where X is a rare gas atom (X = He, Ne) are obtained in an approximate way by using cofocal elliptic coordinates and taking the I2 internuclear axis as a quantization axis. This is the starting point to study vibrational predissociation (VP) of larger I2 ⃛ Xn (n ⩾ 2) clusters, where a good energetic description may provide accurate initial conditions from which trajectory calculations can be carried out.
Generalized graphs and the Sinanoğlu graphical rules
Authors: Shen Mingzuo
Published: January 2005

A comparison of Sinanoğlu's VIF (Ref. 1) and generalized graph is presented. Generalized graphs have vertex and edge weights. An abridged history of generalized graphs in theoretical chemistry is given. VIF's are generalized graphs and therefore have adjacency matrices. The “graphical” rules of Sinanoǧlu can be represented by congruent transformations on the adjacency matrix. Thus the method of Sinanoǧlu is incorporated into the broad scheme of graph spectral theory. If the signature of a graph is defined as the collection of the number of positive, zero, and negative eigenvalues of the graph's adjacency matrix, then it is identical to the all‐important {n+, n0, n−}, the {number of positive, zero, and negative loops of a reduced graph} or the {number of bonding, nonbonding, and antibonding MOs}. A special case of the Sinanoğlu rules is the “multiplication of a vertex” by (−1). In matrix language, this multiplication is an orthogonal transformation of the adjacency matrix. Thus, one can multiply any vertex of a generalized graph by −1 without changing its eigenvalues.