bluuebunny/crossref_metadata_2025 huggingface dataset:
N‐band Hubbard models for copper oxides and isoelectronic systems. New models for organic and organometallic magnetic conductors and superconductors
Authors: Yamaguchi Kizashi
Published: January 2005

The electronic structures of undoped and doped copper oxides and other related oxides are investigated on the basis of the N‐band Hubbard models. The Hubbard Hamiltonians for clusters of transition metal oxides are exactly diagonalized by the full valence‐bond (VB) configuration interaction (CI) method in order to elucidate populations of doped holes, electronic excitation energies, etc. Possible mechanisms of the high‐Tc superconductivity for oxide superconductors are discussed on the basis of the calculated results, together with available experiments. The analysis of correlation and spin correlation effects on doped copper oxides indicates theoretical possibilities of new models for organic and organometallic magnetic conductors and superconductors. Organic and organometallic analogs to copper oxides are therefore proposed on the basis of these results.
Partitioning of electronic properties in two‐center, one‐electron coulombic systems
Authors: Cioslowski J.
Published: January 2005

Separability of the Hamiltonian describing a two‐center, one‐electron Coulombic system in the prolate spherical coordinates allows for a detailed comparison between the partitioning of electronic properties based on Bader's quantum theory of atoms in molecules and the newly developed GAPT partitioning. The one‐electron systems can serve as the simplest models of the covalent and ionic bonds. The GAPT partitioning correctly describes the effects associated with the infinite range of Coulombic interactions.
The Hubbard connection
Authors: Matsen F. A.
Published: January 2005

Hubbard theory is an approximation to the Pariser‐Parr‐Pople theory which presents many of its important features in a relatively simple form. Our Hubbard Hamiltonian employs a single electron‐correlation parameter: 0 ⩽ x ≡ U/(t + U) ⩽ 1, where t is the one‐electron hopping integral (the negative of the Hueckel β), and U is the Hubbard one‐center, two‐electron repulsion parameter. This parameter provides the Hubbard connection between the following:

Molecular orbital and valence bond theory

The exchange approximation and full CI

Conductors and insulators

Fermi‐Dirac and Boltzmann statistics

Normal and superconductors

We present Hubbard theory in the freeon (spin‐free) formulation where each N‐electron state is pictorially represented by a Gel'fand diagram which specifies both the orbital configuration and the multiplicity. The simplicity of the freeon formulation makes the Hubbard connection quite transparent.
Calculation of band structure of doped polyacetylene
Authors: Yang Cao , You‐Liang Wang , Bo Chen
Published: January 2005

In the present paper, the band structures of valence‐band and conduction‐band for polyacetylene and Lidoped polyacetylene were calculated by LCAO‐SCF ab initio crystal orbital (CO) method. The influences of doping on the geometric structures, the band structures, and the changes of atomic charges were analyzed and discussed to explain the insulator‐conductor transition and electric conducting mechanism of doped polyacetylene.
Investigation of the influence of the substitutes on the intensity of the absorption band of some polymethine dyes
Authors: Balevičius L.‐M. , Bolotin A. , Shatkovskaya D.
Published: January 2005

The dependence of the long‐wave absorption‐band intensity on the structural peculiarities of a number of polymethine dyes has been investigated using the PPP method. It has been shown that the analyzed dependence is caused by the electronic properties of the substitutes.
The method of moments and chemical bonding: Interaction of two adatoms on simple cubic and B.C.C. transition metal (001) surfaces
Authors: Pick Štěpán , Tomášek Mojmír , Luchini Marco U.
Published: January 2005

The generalization of the well‐known Hückel rule of quantum chemistry is combined with the crossing theorem of the method of moments to interpret the calculated properties of two adatoms on the (001) surfaces of the simple cubic metal and the B.C.C. transition metal. The relation between the fourth‐order energy moment and the repulsive interaction between adatoms is emphasized. Some conclusions are drawn on the mechanism of the W (001) surface reconstruction.
Density matrix of crystalline systems. II. The influence of structural and computational parameters
Authors: Pisani C. , Aprà E. , Causà M. , Orlando R.
Published: January 2005

The one‐electron density matrix (DM) of a number of crystalline systems—lithium, graphite, boron nitride, silicon, and beryllium—are considered here, as resulting from Hartree–Fock–SCF‐LCAO calculations. The influence of structural and computational parameters is discussed. It is shown in particular why the structure of chemical bonds in semiconductors leads to an oscillating long‐range behavior of the DM, similar to that observed in metals, where these oscillations are related to the very existence of a Fermi surface. Concerning computational parameters, the influence of the density of sampling k points and of basis set on the calculated DM is considered; it is shown that the choice of the basis set is not a very critical one as far as the DM range is concerned. Some critical aspects of the interrelation between DM range and exchange part of the Fock Hamiltonian are analyzed.
Analysis of molecular shape changes along reaction paths
Authors: Arteca Gustavo A. , Mezey Paul G.
Published: January 2005

In this work, a detailed discussion and illustrative example are given for a new conceptual approach to the notion of similarity between nuclear configurations. We analyze the changes in molecular shape, as described by a topological characterization of molecular envelope surfaces, along reaction paths. This approach provides an independent definition of formal species along the path, defined in terms of molecular shape, rather than based on the curvature properties of the potential energy function. The two approaches are compared in this work, using the [1,3] hydrogen‐shift in formic acid as an illustrative example. The reaction is studied at SCF and MP2 ab initio levels. Although the actual reaction paths are different, the molecular shape changes encountered along them are similar, indicating that the essential shape changes provide chemical information on a more fundamental level than do detailed reaction paths.
Exploring the potential energy hypersurface of histamine monocation: Tautomerism in gas phase
Authors: Tapia O. , Cárdenas R. , Smeyers Y. G. , Hernández‐Laguna A. , Rández J. J. , Rández F. J.
Published: January 2005

The potential energy hypersurface of the histamine monocation is determined by ab initio methods at the STO‐4G level using analytical gradient techniques. Three transition states and two minima have been found for the NτH tautomer. One of the transition states connects the trans conformational region with a minimum gauche structure, where the proton of the ammonium group is approximately halfway between the Nπ of the imidazole group and the N of the ammonium group, but nearer to the Nπ. This minimum connects the potential energy surface of the NτH tautomer with the imidazolium one. In the latter region, three transition states and two minima have been found. Critical points are discussed in relation with experimental data and histamine H2 receptor models.
An intermediate neglect of differential overlap model for second‐row transition metal species
Authors: Anderson Wayne P. , Cundari Thomas R. , Zerner Michael C.
Published: January 2005

An intermediate neglect of differential overlap (INDO) model for elements of the second transition series is described. Values of exponents for the radial portion of the Slater basis atomic orbitals, the orbital ionization energies, and the beta (or bonding) parameters for these elements are reported. Use of the model to investigate equilibrium geometries, relative energy ordering of geometric isomers, spectroscopic transition energies, energy ordering of state wave functions of different symmetry, trends in dipole moments, and equilibrium stretching frequencies is reported. The results indicate that the INDO method is capable of yielding quality results for species containing atoms of the second transition series.
Calculations using a set of evenly spaced S‐type gaussian functions
Authors: Jensen James O. , Leonard Joseph M.
Published: January 2005

A basis set of evenly spaced S‐type Gaussian functions with common exponents is examined. Formulas for common one‐ and two‐electron integrals are derived. Because of thesymmetry of this basis set, a very compact two‐electron integral list is produced. The number of two‐electron integrals that must be stored is approximately eight times the number of basis functions. Use of this basis set in an SCF calculation is examined. Numerical results show that this approach works well for molecules containing only small atoms such as hydrogen, helium, or lithium, but that the method has problems with the core orbitals of heavier atoms. Procedures for augementing this basis set in calculations involving heavier atoms are examined.
A study on the electronic spectra of vinylpyridines and 1,2‐(dipyridyl)ethylenes. Molecular orbital calculations
Authors: Abu‐Eittah R. , Hamed Maher M. , Mohamed A. A.
Published: January 2005

The electronic absorption spectra of 2‐, 3‐, and 4‐vinylpyridines and 1,2‐(2,3‐dipyridyl), 1,2‐(2,4‐dipyridyl), 1,2‐(3,4‐dipyridyl), and 1,2‐(4,4‐dipyridyl) ethylenes have been investigated in polar and nonpolar solvents. A correlation has been made between the geometry of the molecule and the observed spectrum. Molecular orbital calculations have been carried out using the INDO/SCI procedure and a limited geometry optimization. The solvent effect at the MO level has been calculated. MO calculations predicted the existence of nπ* transitions that were not observed experimentally. The wave functions of the different CI states were calculated. The experimental transition energy as well as oscillator strength corresponded satisfactorily with the calculated ones. The observed transitions were assigned according to the results of MO calculations.
The discovery of the chemical evolution of singlet oxygen. Some current chemical, photochemical, and biological applications
Authors: Khan Ahsan Ullah
Published: January 2005

From the speculations of G. N. Lewis in 1916, [J. Am. Chem. Soc.38, 762 (1916)], the spectral predictions of R.S. Mulliken [Nature122, 505 (1928)], and the quantum mechanical treatment by E. Hückel [Z. Phys.60, 423 (1930)], the three lowest states of molecular oxygen (3Σg−,1Δg, and1Σ) remained spectroscopic elusives until Gerhard and Lisa Herzberg [G. Herzberg, Nature133, 759 (1934); L. Herzberg and G. Herzberg, Astrophys. J.105, 353 (1947); G. Herzberg and L. Herzberg, Astrophys. J.108, 167 (1948)], precisely defined them by observed infared transitions. The excited singlets remained of interest mainly to atmospheric spectroscopists and astrophysicists, and research on these species was scarce. The discovery in 1963 by A.U. Khan and M. Kasha [J. Chem. Phys.39, 2105 (1963)] of the simple chemical production of singlet molecular oxygens by the aqueous reaction of hydrogen peroxide and hypochlorite released an explosion of research on the neglected species. Fifteen research symposia and research treatises confirm the broad range of chemical activities of singlet oxygen. The extension to biological systems is now proceeding, with surprising evidence of involvement of natural processes, including the action of singlet oxygen in white blood cell phagocytosis.
Dipole moments, transition moments, oscillator strengths, radiative lifetimes, and overtone intensities for CH and CH+ as computed by quasi‐degenerate many‐body perturbation theory
Authors: Kanzler Alfred W. , Sun Hosung , Freed Karl F.
Published: January 2005

The correlated, size‐consistent, ab initio effective valence‐shell dipole operator (μv) method is used to calculate dipole moments and transition dipole moments of the CH molecule and transition dipole moments of the CH+ ion as a function of internuclear distance. The dipole and transition dipole moments computed here compare well with those of other accurate ab initio methods. The transition dipole moments are then used to calculate oscillator strengths and radiative lifetimes for the A → X and B → A transitions of the CH+ ion and the A → X transition of the CH molecule. Comparisons are made with the best available theoretical and experimental lifetimes. Finally, the CH ground‐state dipole moment function is used to evaluate overtone intensities and to examine simple models of the CH overtone intensities in polyatomic molecules.
A generalization of the method of stimulated emission pumping
Authors: Tersigni Samuel H. , Rice Stuart A.
Published: January 2005

Drawing on the results of an analysis of the nature of the pulse that generates complete transfer of population from one to another level in a system with a discrete spectrum, a generalization of the method of stimulated emission pumping is proposed. It is shown that a small subset of the Fourier components of the optimal pulse will, if their relative amplitudes are the same as in the optimal pulse, generate almost as efficient a population transfer, thereby generating the opportunity to prepare a system in a selected state with a selected population.
Interaction between theory and experiment in molecular core electron spectroscopies
Authors: ÅGren Hans
Published: January 2005

The interaction between theory and experiment in the field of molecular core electron spectroscopies is reviewed. Those aspects that distinguish the theoretical descriptions of core and valence electron spectra are analyzed in particular. Differences in the theoretical approaches to atomic and molecular spectra in terms of scattering and many‐body theories are commented on. The molecular core electron spectroscopies are analyzed from a common point of view with respect to molecular orbital theory, many‐body theory, and the role of localization and local selection rules. A brief analysis is presented for the particularities that enter the calculations of core hole spectra. Solutions are described to computational problems posed by the quasi‐bound, highly excited nature of core hole states and by the large electronic relaxation following their creation. Two areas where the interaction between theory and experiment is particularly fruitful are briefly reviewed, namely, the theory of vibronic excitations in core electron spectra and the theory of the core photoelectron chemical shift.
Quantum rigid dipole in a permanent electric field. II. Model of librational motion in liquid water and ice Ih: Preliminary results
Authors: Kryachko Eugene S. , Yanovitskii Oleg E.
Published: January 2005

A theoretical one‐body model of librational motion in liquid water and ice Ih is proposed within the quantum mechanical treatment of a rigid and pointlike dipole in a permanent electric field and the concept of the internal electric field justified for V‐structure of liquid water.
A BSSE‐free SCF algorithm for intermolecular interactions
Authors: Mayer I. , Vibók Á.
Published: January 2005

A very simple modification of the usual (∼N4) SCF procedure is proposed, permitting the exclusion of basis set superposition errors (BSSE) in problems of intermolecular interactions. No a posteriori corrections are required. The results of this “CHA/F method” are numerically close to those of the Boys–Bernardi correction scheme but are free from the “overcompensation” characteristic of the latter at smaller distances.
Normal (decoupled) representation of electronegativity equalization equations in a molecule
Authors: Nalewajski Roman F.
Published: January 2005

The decoupled (normal) representation of the electronegativity (chemical potential) equalization equations, in which the hardness tensor {ηij}={∂μi/∂Nj} becomes diagonal, is examined in the atoms‐in‐a‐molecule (AIM) approximation; μi=∂E/∂Ni is the chemical potential of the i‐th AIM, Ni is its electron population, and E is the system energy. All relevant chemical potential, hardness, softness, and Fukui function quantities corresponding to the normal electron redistribution channels, Qy, are discussed and expressed in terms of the canonical AIM parameters. The normal chemical potentials, μγ=∂E/∂Qγ, provide a natural classification of the normal modes into three groups: (a) acceptor normal modes (μa < 0, positive mode Fukui function, hardness, and softness), (b) donor normal modes (μd > 0, negative mode Fukui function, hardness, and softness), and (c) polarization normal modes (μp=0, zero mode Fukui function, hardness, and softness). The implications of the normal mode analysis for the theory of chemical reactivity are briefly summarized.
Ab initio methods for large systems
Authors: Panas Itai , Almlöf Jan , Feyereisen Martin W.
Published: January 2005

Methods for calculations on extended systems are proposed, in which long‐range Coulombic interactions are treated classically. The basic mode of description for the system is still in a quantum mechanical language, involving wave functions, Hamiltonians, etc. The electron density in a large molecular system is divided into suitable fragments, and the electrostatic potential generated by such a fragment at some distance away from it is then expressed by a generalized multipole expansion relative to a single point in space, conveniently taken as the center of charge distribution for that fragment. The computational effort required for evaluating the interactions involving those multipoles is modest and scales favorably (quadratically) with the size of the system. The remaining interactions, which need to be treated with conventional methods, i.e., with explicit one‐ and two‐electron integrals, scale only linearly with size in extended systems. An important characteristic of the approach is that, while the approximations and shortcuts introduced have a clear physical origin, they can be justified on strict numerical grounds, such that calculated energies and other properties are identical to those obtained with conventional methods.
A new expansion for r−212
Authors: Lüchow A. , Kleindienst H.
Published: January 2005

A new expansion for r−212 expressed in terms of Legendre polynomials is given. The explicit expression is

. For the coefficients C′l,k and Cl,k numerically stable formulas are derived.
Algebraic approximation to the Franck–Condon factors for the Morse oscillator
Authors: Palma A. , Rivas‐Silva J. F. , Durand J. S. , Sandoval L.
Published: January 2005

An algebraic approach is proposed to calculate the Franck–Condon factors for the Morse potential of diatomic molecules. The Morse oscillator is approximated by means of a fourth‐order anharmonic oscillator. In the second‐quantized formalism, this anharmonic Hamiltonian is diagonalized by way of the Bogoliubov–Tyablikov transformation. The Franck–Condon factors are estimated using the harmonic frequency equivalent and the recurrence relations for the Franck–Condon factors of the harmonic oscillator. Overlap integrals are shown for three band systems and compared with values calculated with an RKR potential. Excellent agreement is achieved.
Quantum fluid density functional theory of helium atom in an intense laser field
Authors: Chattaraj P. K.
Published: January 2005

Dynamic response of a helium atom in an intense laser field has been studied within a quantum fluid density functional framework. Several time‐dependent quantities have been calculated by solving a recently derived generalized nonlinear Schrödinger equation.
On the quantum properties of adsorbed particles within the model of a hydrogen atom near a hard wall
Authors: Kovalenko A. F. , Sovyak E. N. , Holovko M. F.
Published: January 2005

A hydrogen molecule near a hard wall was considered within the Heiteler–London method using the atomic orbits in the presence of the wall. Rapidly converging expansions of the atomic wave functions were proposed. The asymptotics were obtained and studied. The atomic dipole moment induced by the surface gave rise to a long‐range interatomic interaction. The covalent bond length increased near the wall. Depending on the orientation relative to the wall, the potential well can vanish. It is interpreted as an interaction between the atomic dipole moments. An approximation of the interatomic potential was proposed.
On Boolean algebra and its importance for the computer sciences
Authors: Löwdin Per‐Olov
Published: January 2005

A brief survey is given of the abstract contentless Boolean algebra and its realizations to logic, class theory, and electric circuits as well as its applications to the software and hardware of the modern electronic computers. It is shown that three relations, 1 + 1 = 1, 1 + 1 = 0, and 1 + 1 = 10, correspond to three different realizations of the algebra, and that they, hence, represent an elementary example of a Gödelian branching point in the abstract Boolean algebra.
A project for an intelligent system: Vision and learning
Authors: Poggio Tomaso , Stringa Luigi
Published: January 2005

One of the most critical aspects of a truly intelligent system is the ability to learn, that is, to improve its own functionality by interacting with the environment and exploring it. In this paper, we argue that learning from exploring the environment should be the main goal in developing artificial intelligence. We also argue in favor of an integrated system—combining several state‐of‐the‐art aspects of artificial intelligence, such as speech, vision, natural language, expert systems—as the experimental platform with which to approach this problem. We then describe the main features of a project of this type, MAIA, which is under development at I.R.S.T. The vision components of the system will be discussed in some detail, especially the navigation architecture of the indoor robot available to MAIA. We will conclude outlining some initial learning problems that will be approached within the MAIA project, such as learning to recognize faces and learning to update the map of the Institute used for indoor navigation.
A theoretical study of electronic spectra of radical cations of some dihydroxynaphthalenes
Authors: Khan Zahid H.
Published: January 2005

Electronic transition energies of radical cations of 1.2‐, 1.3‐, 1.6‐, and 1.7−dihydroxynaphthalenes are calculated using an open‐shell SCF method with configuration interaction. The results are critically analyzed and a correlation diagram is given that shows the energy‐shift and intensity variation in the electronic transitions when moving from one system to another, thus revealing the characteristic behavior of the transitions depending on the positions of the hydroxyl substituents. An interesting relation connecting the electronic spectroscopy with the UV photoelectron spectroscopy is suggested on the basis of which the first ionization potentials (IPS) of the substituted aromatic systems can be inferred from the calculated energy of the A‐type (HOMO → LUMO) transitions for their radical cations. Furthermore, the predictability of the IPs is found to be considerably increased with the incorporation of “molecular size” in the regression.
Thomas–Fermi–Dirac models of atoms constrained by nuclear cusp and long‐range conditions
Authors: Zhou Zhongxiang , Parr Robert G.
Published: January 2005

The traditional Thomas–Fermi–Dirac model of the electronic structure for a neutral atom is deficient in that it predicts an infinite electron density at the nucleus and a sharp cutoff of the electron density at a finite radius. This study was carried out to remedy these faults in the model. Extending an idea used earlier in Thomas–Fermi (TF) theory [Proc. Natl. Acad. Sci. U.S.A. 83, 3577 (1985)], the Thomas–Fermi–Dirac (TFD) energy functional is minimized under constraints ∫ρ(r) dr = N, ∫e−2kr▽2ρ(r)dr < ∞ and ∫(1 − e−k′r)ρ4/3(r)dr < ∞, with k and k′ determined by the nuclear cusp condition and the correct asymptotic behavior. Optimum coordinate scaling also is considered. It is found that the TFD model is substantially improved by constraining the minimization search domain of the energy functional in this way. Energies are given for five noble gas atoms, and Compton profiles for these atoms are calculated. The behavior of electrons in momentum space is improved in both this modified TFD model and in the corresponding modified TF model.
Local Hammond postulate and a local model for monitoring reaction paths
Authors: Majumdar D. , Bhattacharyya S. P. , Maity D. K.
Published: January 2005

A local model for the following reaction path is suggested. Exploratory calculations on simple isomerization reactions are undertaken. A local version of Hammond's postulate is proposed and tested on some model systems.
A search for properties which produce discrimination between cannabinoid psychoactivity and analgesic activity
Authors: Reggio Patricia H.
Published: January 2005

One long‐range goal of our work has been the design of cannabinoid analgesics with reduced psychopharmacological liability. We review here the progress we have made toward this goal. When we began our work on the cannabinoids, no cannabinoid analgesic had been reported that did not also possess significant psychoactivity. We approached the cannabinoid problem by calculating molecular reactivity characteristics (MRCS) of template molecules for each activity: (−)‐trans‐delta‐9‐tetrahydrocannabinol (Δ9‐THC) for psychoactivity, and (−)‐9‐nor‐9‐betahydroxyhexahydrocannabinol (9‐nor‐9β‐OHHHC) for analgesic activity. We then compared the MRCs of each template with the MRCS of a carefully chosen set of other cannabinoids (both active and inactive). Our focus in the calculation of MRCS was on accessible conformations of each subject molecule and on the molecular electrostatic potential generated in key planes by each accessible conformer. Our working hypothesis concerning the molecular basis of psychopharmacological activity in the cannabinoids was that activity is conferred by the set of molecular properties generated (1) by the orientation of the lone pairs of electrons of the phenyl group hydroxyl oxygen and (2) by the orientation of the carbocyclic ring and its C–9 substituent relative to this oxygen. Our working hypothesis concerning the molecular basis of cannabinoid analgesic activity was that activity is conferred by the set of molecular properties generated by the presence and relative location of two negative potential regions in the top half of the cannabinoid analgesic molecule. Our work thus far has revealed important steric and electronic features of the cannabinoids that may be used to enhance discrimination. We have shown that a simple structural feature, a C–9 substituent protruding into the α face of the molecule, can abolish or significantly diminish psychoactivity. We have also demonstrated that a free phenol group is not an absolute requirement for activity. Instead, we have found that compounds that do not possess free phenolic hydrogens, but that do maintain the orientation of the lone pairs of electrons of the “phenolic” oxygen toward the carbocyclic ring, exhibit selectivity toward analgesia.
The semiempirical approach to chemistry
Authors: Dewar Michael J. S.
Published: January 2005

Two kinds of quantum mechanical treatment are needed in chemistry: First, a treatment accurate enough to provide definitive solutions of chemical problems, in particular, the prediction of reactions and reaction mechanisms, without reference to experiment. As yet, treatments of this degree of accuracy are restricted to a few small atoms and molecules. Second, a treatment that chemists can use as a practical aid to their own research, on the same basis as mass spectrometry or NMR. Here, the need has been largely met by the series of progressively better semiempirical methods, in particular, those developed by our group. Since only the best and most expensive ab initio procedures are superior to ours and since the computing time they need is far greater, their use as a practical aid in chemistry is restricted. Our procedures, therefore, serve as a useful supplement to ab initio ones in areas where the latter cannot be applied effectively, as the leading ab initioists now fully recognize. Since the semiempirical approach is capable of almost unlimited further development, this situation is likely to continue in the foreseeable future. © 1992 John Wiley & Sons, Inc.
Group electronegativity and Fukui function studies of the substituent effects in aromatic and inorganic systems
Authors: Korchowiec J. , Nalewajski R. F.
Published: January 2005

The group electronegativities (GE) of molecular fragments, including the environmental contributions due to both the electrostatic interactions and electron distribution relaxation, and the Fukui function (FF) indices of the charge sensitivity analysis (CSA) are correlated with the known substituent effects in molecular systems. The semiempirical CSA in the atoms‐in‐molecules (AIM) resolution has been applied to substituted benzenes and square platinum complexes treated as illustrative examples. The calculated FF indices and GE are both shown to constitute adequate reactivity criteria that qualitatively reproduce the known substituent effects. The FF index (second‐order property) is found to be a more sensitive detector of the substituent influence than is the corresponding GE parameter (first‐order property). © 1992 John Wiley & Sons, Inc.
Eigenvalue distributions and asymptotic lines of the energy in alternant hydrocarbons
Authors: Hall G. G. , Arimoto S.
Published: January 2005

The bands of orbital energies for several polymeric species of alternant hydrocarbon are calculated. From these, the densities of states are graphed. By integration over the bands, the slope of the asymptotic line for the energy is calculated and compared with the energies of members of the same series calculated directly. For some series, the second, constant, term in the asymptotic line can also be calculated theoretically and compared with that derived from the molecular energies. The results for some related series indicate that for long molecules the number of Kekulé structures does not influence the major term in the energy. The extension of the argument to twodimensional arrays of hexagons is indicated and some results reported. © 1993 John Wiley & Sons, Inc.
Nonlocal approximation to the exchange and kinetic energy functionals: Application to metallic clusters
Authors: Glossman M. D. , Rubio A. , Balbáas L. C. , Alonso J. A. , Serra L I.
Published: January 2005

The nonlocal weighted density approximation (WDA) to the exchange and kinetic energy functionals of many‐electron systems proposed several years ago by Alonso and Girifalco in the context of density functional theory is used to compute, within the framework of the spherical jellium model, the ground‐state electronic density, chemical potential, and total energy of neutral and negatively and positively charged sodium clusters containing up to N = 800 atoms. From these calculations, we study the behavior of the total energies per atom, chemical potentials, ionization potentials, I(N), and electron affinities, A(N). These results are compared with analogous calculations using the well‐known Thomas–Fermi–Weizsäcker–Dirac (TFWD) approximation for the kinetic (TFW) and exchange (D) energy functionals. Calculations including the local density approximation (LDA) to the correlation energy in both WDA and TFWD functionals are also presented. © 1993 John Wiley & Sons, Inc.
On the use of corresponding orbitals for the construction of mutually orthogonal orbital sets
Authors: Broer R.
Published: January 2005

Consider two orbital sets χk, k = 1…m and η1, 1 = 1…n, which are mutually nonorthogonal. Provided that n > m, at least n − m orbitals of the set {η} can be orthogonalized to the set {χ} by a transformation within the set {η}. The orthogonalization of the remaining orbitals of {η} to the set {χ} requires a transformation in which the χk appear explicitly. The orthogonalization of one orbital set to another is relevant for SCF optimizations in a truncated basis set, in the presence of frozen occupied orbitals. Examples are frozen core calculations, ECP calculations, and embedded cluster calculations, where the cluster is embedded in a frozen environment. A simple orthogonalization scheme, which makes use of a corresponding orbital transformation, is presented. It is suggested that with a small, well‐defined extension of the set {η} the complete orthogonalization can be done with a transformation in which the {χ} do not appear explicitly. © 1993 John Wiley & Sons, Inc.
Multiconfigurational second‐order perturbation theory: A test of geometries and binding energies
Authors: Andersson Kerstin , Roos Björn O.
Published: January 2005

Multiconfigurational second‐order perturbation theory is tested for the calculation of molecular structure and binding energies. The scheme is based on the Complete Active Space (CAS) SCF method, which gives a proper description of the major features in the electronic structure, independent of its complexity, accounts for all near degeneracy effects, and includes full orbital relaxation. Remaining dynamic electron correlation effects are in a subsequent step added using second‐order perturbation theory with the CASSCF wave function as the reference state (CASPT2). The approach is applied to the calculation of equilibrium geometry and atomization energies for 27 benchmark molecules containing first‐row atoms (the “G1” test). Large atomic natural orbital (ANO)‐type basis sets are applied (5s4p3d2f for LiF and 3s2p1d for H). It is shown that the CASSCF/CASPT2 approach is able to predict the equilibrium geometry with an accuracy better than 0.01 Å for bond distances and 0°–2° for bond angles. Calculated atomization energies are underestimated with between 3 and 6 kcal/mol times the number of extra electron pairs formed. The error in the heat of reaction for a number of isogyric reaction (no difference in number of pairs) varies between −2.5 and +1.0 kcal/mol. The same type of accuracy is obtained in calculations for excited states. The molecules B2, C2, FO, FOO, and FOOF have also been studied. Results for the first three molecules are in accordance with those of the benchmark molecules. The FO bond distance in FOO is predicted to be 0.02 Å longer than experiment. The heat of formation for FOO is computed to be 2.9 kcal/mol with an uncertainty of ±3 kcal/mol. Preliminary results for FOOF (obtained with a smaller basis set) indicate that the approach yields a somewhat too long FO bond distance (1.64 Å compared to 1.58 Å experimentally). © 1993 John Wiley & Sons, Inc.
Resolution of Schrödinger's equation for a scattering problem by a finite‐element method
Authors: Laloyaux Th. , Vigneron J.‐P. , Lambin Ph. , Derycke I. , Lucas A. A.
Published: January 2005

We present a new numerical method for solving the Schrödinger equation in the case of scattering or tunneling states. As an example, we study a model of the scanning tunneling microscope. The method uses a finite‐element approximation of the wave function in the region of the scattering potential. From the wave function that we obtain, we derive the tunnel current density. © 1993 John Wiley & Sons, Inc.
The effects of atomic multipole moments obtained by the potential‐derived method on hydrogen bonding
Authors: Kong Jing , Yan Ji‐Min
Published: January 2005

A potential‐derived atomic multipole method called the cumulative potential‐derived atomic multipole method is developed, with which electrostatic atomic multipole moments are derived by fitting the molecular electric potential in a cumulative way. It is applied to the hydrides of N, O, F, S, Cl, and methanol and the hydrogen‐bonded dimers formed between them. The relationship between atomic multipole moments and molecular charge distributions is found. The structures calculated with Buckingham's electrostatic model are in good agreement with experiments. The phenomena of nonlinear structures of most H‐bonded complexes—the deviations of symmetry axes of electron donors from H bonds—and correct distinguishing between two alternative structures are attributed to atomic dipole and quadrupole moments. Compared with other methods, this method has a quantitative and qualitative advantage and simple algorithm. The main conclusion is that the atomic multipole moments play a substantial role, although a potential‐derived charge model was deemed sufficient previously. © 1993 John Wiley & Sons, Inc.
Dissipative and coherent dynamics induced by a nonadiabatic electron–phonon coupling: Aspects of superconductivity
Authors: Baňacký Pavol , Svrček Michal
Published: January 2005

Band structure with a quasicontinuum of electronic states near the Fermi surface (FS) of a solid‐state matter indicates overlapping regions of the electronic and phonon spectra: (εP – εQ) ≈ ℏωv. This simple fact has an important impact on the theoretical aspects of the description and a study of an electronic structure and physical properties of a matter since velocities of the nuclei and electrons are on the same scale. The motion of the electrons is not adiabatic and the description of the electronic structure of a system cannot be based on the assumption of the validity of Born‐Oppenheimer approximation. For nonadiabatic systems in contrast to the descripton of adiabatic systems [(εp – εQ) > ℏωv], an effect of the finite mass of the electrons, i.e.˙ nonadiabatic corrections, cannot be calculated by a perturbation theory due to the divergency of a perturbation expansion. Quasiparticle transformation technique has disclosed the unexpected effects of nonadiabaticity on the electronic structure and physical properties of matter. The aspects of superconductivity are discussed. © 1993 John Wiley & Sons, Inc.
The optimized‐basis‐set multiconfiguration spin‐coupled method for the ab initio calculation of atomic and molecular electronic wave functions
Authors: Penotti Fabio E.
Published: January 2005

An ab initio method for the calculation of atomic and molecular electronic wave functions is presented. The “Optimized‐Basis‐Set Multiconfiguration Spin‐Coupled” (OBS–MCSC) method may be viewed either as a multiconfiguration generalization of the spin‐coupled approach or as a nonorthogonal variant of the MCSCF method. In addition, the OBS–MCSC method optimizes the basis‐set exponential parameters simultaneously with all other variational parameters, through a second‐derivative minimization procedure. Explicit analytic expressions for the required first and second derivatives of the energy with respect to all variational parameters are obtained. Test calculations prove the capability of the method to yield compact yet accurate electronic wave functions.© 1993 John Wiley & Sons, Inc.
Electron structure of a high‐spin hydrocarbon polyallyl: Hubbard approximation with a strong electron repulsion
Authors: Cheranovskii V. O.
Published: January 2005

The Hubbard model of the polyallyl chain with a strong repulsive potential and one hole in the half‐filled band is reduced to the effective spin Hamiltonian. In the case of infinite repulsion, the exact spectrum of the model with cyclic boundary conditions is obtained.© 1993 John Wiley & Sons, Inc.
Reaction path as a gradient line on a potential energy surface
Authors: Minyaev Ruslan M.
Published: January 2005

The reaction path is shown to be always a gradient line on a potential energy surface (PES) of a molecule. The properties of gradient lines on the PES are elucidated. Correct symmetry conservation rules along the gradient line are derived. The behavior of the gradient line on a PES with different topologies are considered. © 1994 John Wiley & Sons, Inc.
Maximum hardness in P6 isomers
Authors: Warren D. Scott , Gimarc Benjamin M.
Published: January 2005

Parr and Chattaraj proposed a principle of maximum hardness for stable molecular structures. Pearson and Palke used ab initio SCF MO calculations for ammonia and ethane to demonstrate the operation of the principle. In this paper, we present ab initio SCF MO results for five isomeric forms of the homoatomic P6 cluster as further support for the principle of maximum hardness. © 1994 John Wiley & Sons, Inc.
Study on improving the accuracy of the total energy calculated by the DV–Xα method
Authors: Li Le‐Min , Hong Gong‐Yi
Published: January 2005

The effect of the truncation errors resulting from the numerical integration on the accuracy of the calculation results in the DV–Xα method is analyzed and it is shown that evaluating the overlap integrals analytically or adopting orthogonalized basis sets can reduce the errors on the density matrices to the second order. An approach to improve the calculation accuracy of the total energy is proposed based on the error analysis. The calculation results for several molecules are presented to demonstrate the conclusion. © 1994 John Wiley & Sons, Inc.
Applications of molecular dynamics simulations coupled with Harris functional approximation to argon
Authors: Lee Chengteh , Long Xiping , Carpenter Ilene , Smithline Shep , Fitzgerald George
Published: January 2005

We have demonstrated molecular dynamics simulations using a combination of the classical molecular dynamics with density functional theory for argon clusters. Three different molecular dynamics schemes, which differ in their treatment of the potential energy and forces, have been carried out. The first uses a Lennard‐Jones potential. In the second, the potential is computed using the Harris functional, and in the third, a combination of Lennard‐Jones and Harris functional potentials is used. In addition to direct examination of the trajectories, the velocity autocorrelation function and its power spectrum have been computed to demonstrate the agreement between these three methods. The present studies show that a scheme that used a combination of model potentials and density functional theory provides a very useful tool for the dynamics simulation of systems that contain some fragments in which the analytical model potentials are not available. © 1994 John Wiley & Sons, Inc.
A correlation‐energy functional from a correlation‐factor model
Authors: Fuentealba P.
Published: January 2005

In this work, a way to approximate the correlation energy functional starting from a model correlation factor is shown. The problem is addressed by using formally exact properties of the second‐order density matrix and actual values of correlation energies for atoms. An Ansatz for the correlation factor is proposed that allows one to derive some known and some new correlation energy density functionals. Results for atomic systems show the reliability of the approach. © 1994 John Wiley & Sons, Inc.
Large‐Z and ‐N dependence of atomic energies from renormalization of the large‐dimension limit
Authors: Kais Sabre , Sung Stella M. , Herschbach Dudley R.
Published: January 2005

By combining Hartree–Fock results for nonrelativistic ground‐state energies of N‐electron atoms with analytic expressions for the large‐dimension limit, we have obtained a simple renormalization procedure. For neutral atoms, this yields energies typically threefold more accurate than the Hartree–Fock approximation. Here, we examine the dependence on Z and N of the renormalized energies E(N, Z) for atoms and cations over the range Z, N = 2 → 290. We find that this gives for large Z = N an expansion of the same form as the Thomas–Fermi statistical model, E → Z7/2(C0 + C1Z−1/3 + C2Z−2/3 + C3Z−3/3 + ⃛), with similar values of the coefficients for the three leading terms. Use of the renormalized large‐D limit enables us to derive three further terms. This provides an analogous expansion for the correlation energy of the form δE δZ4/3(δC3 + δC5Z−2/3 + δC6Z−3/3 + ⃛); comparison with accurate values of δE available for the range Z ⩽ 36 indicates the mean error is only about 10%. Oscillatory terms in E and δE are also evaluated. © 1994 John Wiley & Sons, Inc.
Electronegativity dynamics in a chemical reaction
Authors: Chattaraj P. K. , Nath S.
Published: January 2005

A generalized nonlinear Schrödinger equation has been solved in order to understand how electronegativity and the covalent radius of an atom vary during a chemical reaction. The chemical reaction is modeled as an atom in an external field and also as an atom colliding with an ion. Temporal evolution of charge density, current density, and effective potential has also been studied for a better understanding of the process. © 1994 John Wiley & Sons, Inc.
Analytic properties of connected moments expansions
Authors: Mancini Jay D. , Zhou Yu , Meier Peter F.
Published: January 2005

The derivation of the connected moments expansion (CMX) is examined as well as the singularities that arise in the series expansion for the ground‐state energy. Explicit analytic results are presented that show a canceling of these singularities. Also, an alternate moments expansion (AMX) is derived that closely models the CMX but displays a varied computational range. © 1994 John Wiley & Sons, Inc.
Calculation of electric dipole transition moments using quasi‐degenerate variational perturbation theory and averaged coupled‐pair functional theory
Authors: Cave Robert J. , Johnson Jenifer L. , Anderson Mark A.
Published: January 2005

Results are reported from calculations of electric dipole transition moments for various electronic transitions in Be, CH2, and A1H using multireference singles and doubles configuration interaction, quasi‐degenerate variational perturbation theory, and multireference averaged coupled pair functional theory. A simple normalization scheme is used for the quasi‐degenerate variational perturbation theory and multireference averaged coupled pair functional theory wave functions. In all cases, comparison is made with full configuration interaction results in the valence space. For Be and CH2, all methods are of comparable quality in calculating the transition moments and excitation energies, with averaged coupled‐pair functional theory yielding slightly quicker convergence of the excitation energies and transition moments in most cases. For AlH, multireference singles and doubles configuration interaction is somewhat more accurate for the calculation of the transition moment. Factors that affect the accuracy of the methods are discussed. © 1994 John Wiley & Sons, Inc.
Aromaticity in metallacyclobutadienes from the perspective of the valence bond theory
Authors: Rincón Luis
Published: January 2005

The valence bond method has been implemented for the study of π‐electron systems using a semiempirical CNDO‐type Hamiltonian. The algorithm used is based on the Clifford algebra realization of the Rumer–Weyl basis presented by Paldus et al. Using this version of the CNDO–VB approach, the effect of the metal hybridization in the electronic delocalization of metallacyclobutadienes is discussed. © 1994 John Wiley & Sons, Inc.
On conjugated–circuit polynomials
Authors: Klein Douglas J. , Randić Milan , Babić Darko , Trinajstić Nenad
Published: January 2005

Recursive formulas are derived for generating the conjugated‐circuit polynomials for circuits up to size n = 6, 10, or 14 on regular chain polyhex graphs. These counting polynomials are of use for a simple valence‐bond resonance‐theoretic derived model: the conjugated‐circuit model. © 1994 John Wiley & Sons, Inc.
Accurate upper and lower bounds to the 2S states of the lithium atom
Authors: Lüchow A. , Kleindienst H.
Published: January 2005

The first nonrelativistic lower bound to the ground state of the lithium atom is give with E0 > −7.47816 au using the method of variance minimization and an extension of Temple's formula. With large Hylleraas–CI basis sets, high‐precision upper bounds and isotope shifts are calculated for the three lowest 2S states of the lithium atom, which are best to date. © 1994 John Wiley & Sons, Inc.