bluuebunny/crossref_metadata_2025 huggingface dataset:
Evolution of polarizabilities and hyperpolarizabilities with molecular aggregation: A model study of acetylene clusters
Authors: Augspurger Joseph D. , Dykstra Clifford E.
Published: January 2005

Ab initio and model calculations on linear clusters of acetylene molecules have been carried out to identify the effect of weak intermolecular interaction on the intrinsic dipole polarizability (‐) and the second hyperpolarizability (γ) and, in particular, to determine the three‐body and higher‐order effects. Ab initio and model calculations on a linear dimer show clearly that the evolution of properties from the separated limit is largely a consequence of the mutual polarization as the monomers begin to interact. This reveals that intermolecular quantum features are not significant. Furthermore, higher‐order response properties play a negligible role in the evolution of lower‐order cluster properties. For instance, the hyperpolarizability γ of the monomer is relatively unimportant in the evolution of α of the dimer; the change in α due to dimer formation is dictated largely by the mutual polarization via the intrinsic α′s of the monomer. With this determination, an electrical interaction model can be used to explore α and γ of long acetylene chains, and this serves as a guide to the vibronic coupling effects on hyperpolarizabilities of longchain species. We find, in particular, that the hyperpolarizability of the subunits of long acetylene chains are dramatically enhanced by intermolecular electrical interaction.
The accurate calculation of dipole moments and dipole polarizabilities using Gaussian‐based density functional methods
Authors: Sim Fiona , Salahub Dennis R. , Chin Steven
Published: January 2005

Dipole moments and static dipole polarizabilities have been calculated for a number of small molecules using the linear combination of Gaussian‐type orbitals–local spin density method. The effect of augmenting standard orbital basis sets with polarization functions has been investigated. A set of optimum ζd, for use in calculating polarizabilities, has been derived for the first‐row atoms C, N, O, and F. The results of this optimized doubly polarized double‐zeta basis set compare well with results obtained using a double‐zeta basis set augmented by four even‐tempered ζd polarization functions. The results of the optimized basis set, and a basis set augmented with only a single ζd polarization function derived from it, compare very favorably with those obtained from Møller–Plesset perturbation theory and with experimental data. They show a marked improvement on results obtained using standard Hartree–Fock self‐consistent‐field molecular orbital methods where no treatment of electron‐correlation is included.
Electric‐field mapping of some substituted 3‐pyridinecarboxylic acid cardiotonics and the possible structure–activity relationships
Authors: Kumar Anil , Bhattacharjee A. K. , Mishra P. C.
Published: January 2005

Four esters of 5‐cyano‐1,6‐dihydro‐6‐oxo‐3‐pyridinecarboxylic acid involving substitutions of methyl, isopropyl, tert‐butyl, and phenyl groups at the 2‐position, which exhibit varying degrees of cardiotonic activities, have been studied using the electric‐field and electrostatic potential mapping techniques. The net charge distributions in the molecules were obtained using the MNDO method. Electric‐field mapping has been performed in three‐dimension in order to obtain information about the possible structure–activity relationships of these compounds. The results show a prominent electric‐field region in the methyl‐substituted compound extending from near the oxygen atom O6 to near the methyl group. This fact and orientation of the electric field in this region, in view of the Erhardt model, may be related to the greater cardiotonic activity of the methyl‐substituted molecule in comparison to those of the other molecules of this class. © 1992 John Wiley & Sons, Inc.
Variational principle and path integrals for atoms in molecules
Authors: Zou P. F. , Bader R. F. W.
Published: January 2005

Two things were done in this paper: (i) A generalization of Schwinger's variational principle to a subsystem was developed within the framework of quantum field theory and applied to the theory of atoms in molecules. This work generalizes the previous derivation given in the Schrödinger formulation. (ii) It is demonstrated that Feynman's path integral, when expressed in terms of the coherent‐state representation, can be constructed for a subsystem of a many‐electron system if a divergence term, which serves as a variational constraint in the definition of an atom in a molecule, is added to the Lagrangian. This formulation is equivalent to the atomic statement of the variational principle if the divergence term is suitably constructed. It is shown that the path integral can be expressed as a product of the individual atomic contributions to the steps along the paths with the action being determined by a corresponding sum of the atomic contributions to the action integral. © 1992 John Wiley & Sons, Inc.
Internal orbitally resolved charge sensitivity analysis
Authors: Nalewajski Roman F.
Published: January 2005

The intramolecular (internal) charge sensitivity analysis (ICSA) is presented in the molecular orbital (MO) resolution, with diagonal idempotency constraints being imposed on the MO occupations, n, which can then be considered as independent electron population variables of the system for the assumed fixed shapes of MOS. The standard closed‐shell (C.S.) SCF MO framework is adopted with the energy function E(n) approximated by the average energy of a configuration expression to cover fractional MO occupations. The components of the gradient of the auxiliary energy function, including the constraint terms, with respect to n, identified as negative MO internal electron potentials, vanish identically for the ground‐state c.s. configuration, whereas their responses to hypothetical intramolecular charge displacements assure the system stability. An application of the ICSA to the iterative SCF procedure is suggested. Illustrative results for the water molecule are reported and general properties of molecular normal orbitals (eigenvectors of the hardness matrix) are discussed. © 1992 John Wiley & Sons, Inc.
An analysis of molecular electrostatic potentials obtained by a local density functional approach
Authors: Murray Jane S. , Seminario Jorge M. , Concha Monica C. , Politzer Peter
Published: January 2005

Local density functional theory (DFT–LDA) has been explored as a tool for obtaining the molecular electrostatic potential V(r), using the code DMol. We have presented and discussed DFT–LDA electrostatic potentials for a representative series of molecules: ethylene, benzene, formamide, cytosine, and 2,3,7,8–tetrachlorodibenzo–p–dioxin. V(r) results obtained with a double numerical plus polarization (DNP) basis set show the key features that are characteristic of the ab initio potentials of these compounds and suggest that this is a useful approach, especially for large molecules that are difficult to study by ab initio methods.
Modeling solvent effects in molecular dynamics simulations of proteins
Authors: Solmajer T. , Mehler E. L.
Published: January 2005

A series of computer simulations has been carried out on bovine pancreatic trypsin inhibitor using various models to mimic the effects of explicit bulk solvent on the structure of the protein. The solvent properties included are the polarization of the solute by the polar bulk solvent and the restraining effect on the motional freedom of the solute due to frictional drag at the solvent–protein surface interface. The former has been included by using a distance–dependent dielectric permittivity to screen the electrostatic interactions, whereas the latter is simulated by adding a limited number of solvent molecules near the protein surface. To achieve the proper mobility of the water molecules, their motion was restrained by adding a harmonic restraining force. It was found that a very small force constant was sufficient to model the static and dynamical behavior of the fully solvated solute, but that it was necessary to include enough explicit waters to occupy the first solvation shell. © 1992 John Wiley & Sons, Inc.
MNDO Calculations as a valuable tool for structure evaluation of contact ion pairs
Authors: Havlas Z. , Nick S. , Bock H.
Published: January 2005

Contact ion pairs, essential intermediates of both chemical and biochemical reactions in solution, can be satisfactorily approximated by MNDO calculations as exemplified by the lithium and potassium salts of 2,5‐trimethylsilyl‐p‐benzosemiquinone radical anion and by sodium tetraphenylallyl anion diethyl ether. Topics discussed are the structural changes of p‐benzoquinone derivatives on single‐electron reduction, the dynamics of the countercations in semiquinone radical contact ion pairs measured by temperature‐dependent ESR spectra, as well as structural details of the sodium tetraphenyl‐allylanion complex isolated such as its intramolecular Na dibenzene sandwich or its diethylether solvation. © 1992 John Wiley & Sons, Inc.
Ab initio study of the internal rotation barrier of formamide and the formamide–H2O complex
Authors: Wang Xiao‐Chuan , Facelli Julio C. , Simons Jack
Published: January 2005

The barriers to internal rotation about the NC bond of formamide and the formamide–H2O complex have been examined by ab initio quantum chemistry methods. Both self‐consistent field and correlated approaches have been utilized to determine the geometries, energies, and local harmonic vibrational frequencies of the minimum‐energy and transition‐state structures of these two systems. We find that formamide's rotation barrier of 14–15 kcal/mol is increased to 16–18 kcal/mol when a single H2O molecule is attached. This result contrasts with the effect of a single H2O solvent molecule on the barrier to tautomerization of formamide (to form formamidic acid HNCHOH) for which a barrier lowering of ca. 20 kcal/mol has been observed. The rotation barriers obtained for formamide and for its H2O complex are compared with barriers obtained experimentally in various solvents. © 1993 John Wiley & Sons, Inc.
The MRSDCI studies of four low‐lying electronic states of the BF2 radical
Authors: Cai Z.‐L.
Published: January 2005

The equilibrium geometries, excitation energies, force constants, and vibrational frequencies for four low‐lying electronic states X 2A1, 2B1, 2B2, and 2A2 of the BF2 radical have been calculated at the MRSDCI level with a double zeta plus polarization basis set. Our calculated excitation energy for X2A1 → 2B1 is in agreement with available experimental data. The electronic transition dipole moments, oscillator strengths for the 2B1 → X2A1 and 2B2 → X2A1 transitions, radiative lifetimes for the 2B1 and 2B2 states, and the spin properties for the X2A1 state are calculated based on the MRSDCI wave functions, predicting results in reasonable agreement with available experimental data. © 1993 John Wiley & Sons, Inc.
Møller–Plesset expansion of the dispersion energy in the ring approximation
Authors: Moszynski Robert , Jeziorski Bogumił , Szalewicz Krzysztof
Published: January 2005

Coupled‐cluster equations for the calculation of the nonexpanded (fully damped) dispersion energy are derived. These equations are solved in the ring approximation using the Møller–Plesset expansion in terms of the fluctuation potentials WA and WB for the individual molecules. Numerical results of high‐order perturbative calculations for the He, H2, LiH, H2O, and HF dimers are presented and compared with the converged results computed using the same basis sets. It is found that the convergence of the Møller‐Plesset expansion of the dispersion energy in the ring approximation is very fast. The padé approximants still accelerate this already good convergence. For all complexes studied in this paper, the sum of the corrections through the second‐order in WA + WB reproduces over 99% of the converged value. The sum of third‐ and higher‐order corrections in the ring approximation is found to be one or two orders of magnitude smaller than the sum of second‐order terms not included in the ring approximation and, therefore, may be safely neglected. Thus, it appears that a second‐order calculation, which does not require iterating coupled‐cluster equations or solving random phase approximation equations, offers the best compromise between accuracy and computational requirements. © 1993 John Wiley & Sons, Inc.
General algebraic expressions of totally symmetric potential functions for AXn (n = 3,4) molecules
Authors: Ischtwan Josef , Peyerimhoff Sigrid D.
Published: January 2005

The integrity bases for representations of the nuclear permutation groups Sn (n = 3,4) in the space of internal coordinates describing AXn molecules are determined. This allows optimal expressions of the molecular potential energy functions in terms of internal coordinates that are totally symmetric with respect to permutations of indistinguishable nuclei. © 1993 John Wiley & Sons, Inc.
Some applications of nonlinear convergence accelerators
Authors: Homeier Herbert H. H.
Published: January 2005

A number of established nonlinear convergence acceleration methods are presented. It is discussed how these methods, and also some new algorithms, can be applied successfully to Fourier series. Some of the new accelerators are tailored for these‐series. Others are also useful for other types of series and sequences, and not only for convergence acceleration, but also for extrapolation or summation problems. Applications to the numerical inversion of the Laplace transform and to a Fourier series arising in the Matsubara formalism are presented. © 1993 John Wiley & Sons, Inc.
On the solid state of hydrogen fluoride: A self‐consistent crystal field study
Authors: Panas Itai
Published: January 2005

A recently developed self‐consistent crystal field (SCCF) method is applied to two suggested crystal structures of solid hydrogen fluoride, polar and nonpolar, respectively. Constrained geometry optimizations are performed and the results are compared with experiment and previous theoretical studies. Comparisons are also made with a previous SCCF study on hydrogen cyanide. The Pauli repulsion, dispersion, and “classical” crystal field contributions to the lattice energy are calculated. © 1993 John Wiley & Sons, Inc.
Electronic states and nature of bonding in the molecule YN by all‐electron ab initio CASSCF calculations
Authors: Shim Irene , Gingerich Karl A.
Published: January 2005

In the present work, we present results of all‐electron ab initio CASSCF calculations of nine electronic states of the molecule YN. Also reported are the spectroscopic constants derived on the basis of the calculated potential energies. The predicted electronic ground state is 1∑+, and this state is found to be separated from the excited states 3∑+, 3Π, and 1Π by 5177, 9290, and 9915 cm−1, respectively. The chemical bond in the YN molecule is polar with charge transfer from Y to N, giving rise to a dipole moment of 8.19 Debye at 3.3 au in the 1∑+ ground state is basically a double bond composed of two π bonds. The dissociation energy of the YN molecule has been derived as 4.59 eV. © 1993 John Wiley & Sons, Inc.
The complex coordinate scattering theroy and its application to the study of the surface asymmetry effect in helium diffraction from copper
Authors: Peskin Uri , Moiseyev Nimrod
Published: January 2005

The Complex Coordinate Scattering Theory is reformulated for the general case of a time‐independent Hamiltonian. It is applied to scattering of He atoms from a Cu(115) crystal surface by constracting the Green operator for the T‐matrix from the eigenvectors of both the complex scaled Hamiltonian and its transposed (“right” and “left” eigenvectors), which are different in this case. The weakly asymmetric corrugation function describing the (115) face of Cu is shown to cause a strong dependence of the calculated diffraction intensities upon the direction of the incident atomic beam. The calculated transition probabilities are in excellent agreement with the experimentally measured ones, previously obtained by Perreau and Lapujoulade. We show that additional information about the gas atom/surface physisorption interaction potential can be obtained if the incident angle of the atomic beam (the angles between the beam and the surface normal) is changed from γ to −γ. © 1993 John Wiley & Sons, Inc.
A configuration‐interaction‐oriented implementation of the complex coordinate method
Authors: Saenz Alejandro , Weyrich Wolf , Froelich Piotr
Published: January 2005

An implementation of the complex coordinate method is demonstrated that exploits a new technique for obtaining the matrix representation of the complex dilated Hamiltonian. The purpose is to make the complex coordinate method applicable together with standard numerical ab initio codes designed for large‐scale calculations on many‐electron atoms and/or molecules. No complex intergrals have to be calculated, and no changes of the standard codes are required even in the common case where the kinetic and potential energy components are not stored separately. Instead, two standard (real) CI calculations are used to generate the dilated (complex) CI matrix representation. The performance of the procedure is demonstrated in the context of the GAMESS program and applied to obtain the resonant structure of the Bethe surface pertinent to the absorption spectrum of the helium atom. © 1993 John Wiley & Sons, Inc.
A multiple‐transition‐point WKB investigation of complex energy resonances
Authors: Andersson Nils
Published: January 2005

Approximate conditions determining the complex energy resonances of a one‐dimensional model potential, originally discussed by Moiseyev et al., are derived within a multiple‐transition‐point WKB treatment. It is shown that an erroneous energy spectrum is generated if too few transition points are considered. The numerical results of a correct semiclassical treatment of the problem, where several transition points are included, agree well with the, presumably exact, results of Rittby, Elander, and Brändas. © 1993 John Wiley & Sons, Inc.
First‐order corrections to sums of zeroth and first power of absolute values of negative eigenvalues of Schrödinger operators with potentials with Coulomb singularity in the semiclassical limit
Authors: Siedentop Heinz
Published: January 2005

First‐order corrections jointly obtained with B. Helffer, A. Knauf, and R. Weikard to the sum and the number of negative eigenvalues of Schrödinger operators with potentials that have a negative Coulomb singularity in the quasi‐classical limit are reviewed. The relevance of the result to the ground‐state energy of large atoms is pointed out. © 1993 John Wiley & Sons, Inc.
Protonic delocalization and quantum correlations in the H‐bond dynamics of G–C and κ–π DNA base pairs
Authors: Chatzidimitriou‐Dreismann C. A.
Published: January 2005

A new base pair (called κ–π) of Watson–Crick type, with a H‐bond pattern different from that in A–T and G–C base pairs, has been recently synthesized and shown to be stable and incorporable into duplex DNA and RNA by polymerases. This new basepair, which contains three H‐bonds, is compared with G–C, in the framework of modern dynamical theory of quantum nonlocality and quantum correlations. Connection with the traditional treatment of proton transfer in DNA base pairs, which uses the adiabatic approximation, is explicitly made. As a result, the dynamics of the H‐bond pattern of G–C is shown to exhibit a specific quantum mechanical phase stability, which is clearly missing in the case of κ–π. This finding is discussed and illustrated, also in connection with recent quantum chemical calculations of proton transfers in DNA base pairs. Additionally, certain speculations concerning the “evolutionary advantage” of G–C with respect to κ–π are briefly considered. © 1993 John Wiley & Sons, Inc.
On some properties of general linear operators
Authors: Löwdin Per‐olov
Published: January 2005

Some elementary properties of a general linear operator, which is defined on a Hilbert space but is not necessarily self‐adjoint, are briefly reviewed: the classical canonical form, the bi‐orthogonality theorem, the bivariational principle, the spectral resolution of the resolvent, and the properties of exponential forms. © 1993 John Wiley & Sons, Inc.
The non‐N‐representability of the Colle–Salvetti second‐order reduced density matrix
Authors: Morrison Robert C.
Published: January 2005

The Colle–Salvetti second‐order reduced density matrix (2‐matrix) is an approximation to the 2‐matrix obtained from a wave function that is a product of a reference wave function containing little or no correlation times a product of correlation factors that are functions of the coordinates of pairs of electrons. A formal proof is given for the non‐N‐representability for the Colle–Salvetti 2‐matrix using the nonnegativity condition of the 2‐matrix. The nonnegativity condition of the particle‐hole overlap matrix (G matrix) is also not satisfied. The proof is valid for Colle–Salvetti 2‐matrices obtained from both the Hartree–Fock and small multiconfigurational‐self‐consistent‐field wave functions. Even though the Colle–Salvetti 2‐matrix is not N‐representable, it does satisfy the Pauli principle component of the G‐matrix condition because it reduces to an N‐representable first‐order reduced density matrix. © 1993 John Wiley & Sons, Inc.
Spin‐unrestricted calculations in quantum chemistry
Authors: Cassam‐Chenaï P. , Chandler G. S.
Published: January 2005

The unrestricted complete active space self‐consistent field (UCASSCF) function is defined, and a proof that a UCASSCF eigenfunction of the spin operator S2 is a CASSCF function is given. The spin‐contamination for an unrestricted Hartree–Fock (UHF) function is evaluated by using Araki angle operators, and the UHF function is then projected on the restricted open‐shell Hartree–Fock (ROHF) space. The present analysis has deep consequences since it implies that the only non‐spin‐contaminated UHF functions are the ROHF functions. This is illustrated in a calculation of the spin density of He. © 1993 John Wiley & Sons, Inc.
A study of the weak interaction in SCO/He and SCO/N2 systems
Authors: Sadlej Joanna , Edwards W. Daniel
Published: January 2005

The structure and energetics of the complexes formed between SCO/He and SCO/N2 were investigated using ab initio wave functions at both the SCF and correlated levels of theory with a medium‐sized polarized basis set. The energy of the T‐structure for SCO ⃛He was found to be lower than the energy of the corresponding linear complexes with He bonded to the oxygen or sulfur atoms. Two linear structures for SCO ⃛ He were found to be nearly isoenergetic. There is only a small difference in energy between the T‐structure for SCO ⃛N2 and the OCS ⃛NN colinear structure, with the T‐structure being the lowest. The electron correlation contributions to the interaction energy were calculated using Möller–Plesset perturbation theory at the MP2, MP3 and SDTQ–MP4 levels. Analysis shows the importance of the triple excitations in these complexes. © 1993 John Wiley & Sons, Inc.
Theoretical study of ionization potentials in monosubstituted benzenes
Authors: Melo André , Gomes J. A. N. F.
Published: January 2005

Monosubstituted benzenes, in which the substituents participate in the π‐electron system, are studied following a classification in two classes according to the π‐electronic structure of the substituent. For this type of molecule, a relation is established between the nature of the substituent and, on the one hand, the energies of the two highest occupied molecular orbitals and, on the other hand, their respective differences. The two orbitals referred to above have π‐character and belong to the a2 and b1 species if a C2v point group is assumed. Simple symmetry arguments lead to the conclusion that the a2 orbitals have, essentially, an intraring character, whereas the π‐orbitals of the substituents do give an important contribution to the b1 orbitals. Therefore, an a2 electron must have a larger interaction with the benzene ring and a smaller kinetic energy, whereas a b1 electron must have a larger interaction with the substituent and a larger kinetic energy. It is also expected that the changes in the π‐electronic structure of the substituent must much more influence the variations on the b1 energies and on the components of orbital energies associated with the substituent than the variations on the a2 energies and on the intraring components of the orbital energies. A modified version of the MOPAC program was prepared to perform the decomposition of the orbital energies in their kinetic and potential energy components and these in their monocentric and bicentric terms. MNDO calculations on nine monosubstituted benzenes, using the modified MOPAC program, give good confirmation of the symmetry predictions and prove the consistency of the classification of the substituents that is introduced. © 1993 John Wiley & Sons, Inc.
A study of excited states in trans‐polyacetylene in the Hartree–Fock, Tamm–Dancoff, and random‐phase approximation
Authors: Vracko M. G. , Zaider M.
Published: January 2005

We report calculations of the excitonic spectra for trans‐polyacetylene obtained in the Hartree–Fock, Tamm–Dancoff, and random‐phase approximations. In the first case, in terms of two‐particle propagator theory, the interaction between the excited electron and the hole is neglected. In the latter two cases, this interaction is considered in the first order. In this framework, the interaction between excitations of different bands and k‐vectors has been included. We discuss the bandwidths and density of states for π–π*, σ–π*, π–σ*, and σ–σ* excitons. © 1993 John Wiley & Sons, Inc.
A mutually consistent procedure for excitation energies and transition densities based on the extended Brillouin's theorem
Authors: Dmitriev Yuri Yu. , Mitrushenkov Alexander O. , Fülscher Markus P. , Roos Björn O.
Published: January 2005

A mutually consistent method to calculate excitation energies and corresponding transition densities is proposed. The method is based on the extended Brillouin's theorem that is derived from the nonstationary variation principle. Within the proposed procedure, the Brillouin's conditions, which appear in this extension, are used as a set of nonlinear equations for molecular orbitals and configuration interaction coefficients of the trial ground‐ and excited‐state functions. The excitation energy is an eigenvalue of the set. To some extent, this procedure is related to the variational treatment of the conventional random‐phase approximation within the equation‐of‐motion method. The basic features of the proposed procedure are discussed and it is illustrated by numerical examples. © 1993 John Wiley & Sons, Inc.
Examination of the Hund rule in closed‐shell systems: Investigation of spin correlation effects
Authors: Parrondo Ramón Martín , Karafiloglou Padeleimon , Marcos Enrique Śnchez
Published: January 2005

The validity of the Hund rule in atomic orbitals (AOs) of the carbon atoms inside closed‐shell molecules, such as acetylene, ethylene, and ethane, is examined. Electron‐pair populations and contributions of the two‐electron covalent structures with parallel (⇈) and antiparallel (↑↓) spins are calculated by multielectron population analysis of MO + CI wave functions. Such an analysis, which allows the visualization of various cooperative electronic effects in some target AOs, is extended on the basis of (strictly orthogonal) hybrid orbitals. Although the HF level shows, incorrectly, that the Hund rule is not satisfied, the CI clearly shows a preference for (⇈) spins to those of (↑↓): This holds for both the electron‐pair populations [those of (↑↓) spins diminish with the CI more drastically than those of (⇈) spins], as well as for contributions of the two‐electron covalent structures [those of (⇈) spins increase with the CI more drastically than do those of (⇈) spins]. The calculation of the correlation functions (or dependent functions) in AO space allows the comparison of repulsive or “attractive” behaviour of (⇈) and (↑↓) spins in various AO couples. Mutual dependence of the two electrons inside the sigma system increases in the series ethane < ethylene < acetylene. Also found is that parallel spins in (pure) AOs of sigma systems are preferred to the antiparallel spins when going from ethane to acetylene. The preference parallel–antiparallel spins in AOs belonging to two different atoms, including hydrogens, is also examined. © 1993 John Wiley & Sons, Inc.
Selective dynamic energy transfers in proton collisions with hydrogen fluoride
Authors: Gianturco F. A. , Buonomo E. , Serna S.
Published: January 2005

Earlier experimental data by Friedrich et al. found out, from time‐of‐flight experiments of collisions between H+ and HF molecules, that most of the available relative energy becomes transferred into internal rotations of the target and that vibrational excitation only begins to be noticeable around and above 30 eV of relative collision energy. The present theoretical and computational model starts from the potential energy function presented in the preceding paper and carries out quantum calculations that explicitly include the coupling of vibrational target states. The results indeed show very few vibrational excitations and rather large rotational energy transfers as the collision energy is increased up to 50 eV. Microscopic features of both the interaction and the dynamics are found to be responsible for such behavior, which brings the present calculations in agreement with experimental findings. © 1993 John Wiley & Sons, Inc.
Topological analysis of the charge density of solids:bccsodium and lithium
Authors: Mei Changjiang , Edgecombe Kenneth E. , Smith Vedene H. , Heilingbrunner A.
Published: January 2005

Studies of electronic structure of solids have concentrated mainly on Hilbert space properties such as energy‐band structures and density of states, as well as some properties that can be reduced from them. Here, we report application of the topological charge density analysis to crystals. It is found that the pseudoatoms (or nonnuclear attractors, which are charge accumulations in nonnuclear regions), first found in Li2, exist in solid lithium and sodium as well. In the former, the pseudoatoms form aconnectednetwork; in the latter, they are separated from one another. Although such networks obey the space group symmetry of the corresponding crystal, their existence is an intrinsic property of a specific crystal. © 1993 John Wiley & Sons, Inc.
Fluorination effect on the structural properties in benzocyclobutenes and benzocyclobutadienes
Authors: Koch Wolfram , Eckert‐Maksić Mirjana , Maksić Zvonimir B.
Published: January 2005

Structural features of benzocyclobutenes, benzocyclobutadienes, and some of their fluoroderivatives are studied at the HF/SCF niveau employing a 6–31G* basis set. A Mills–Nixon‐type of distortion (lengthening of the annelated bonds with concomitant shortening of the adjacent bonds in the benzene moiety) is found in all molecules, with the exception of polyannelated benzocyclobutenes with perflouro‐substituted methylene groups. The latter compounds exhibit a weak anti‐Mills–Nixon effect. Peripheral double bonds in benzocyclobutadienes enhance the double‐bond localization in the benzene ring, but the main effect originates from angular deformations of the σ‐skeleton. Salient structural features are rationalized by rehybridization at the carbon junction atoms and variation of Coulson's π‐bond orders. Finally, several scales for quantifying the Mills–Nixon effect are briefly discussed. © 1993 John Wiley & Sons, Inc.
Electronic structure and hyperpolarizability of some conjugated molecules in excited states
Authors: Kanev Ivo
Published: January 2005

For the examples of aromatic and antiaromatic five‐membered heterocycles, the static electronic polarizabilities and hyperpolarizabilities are determined in the ground and first singlet‐ and triplet‐excited electronic states. The theoretical calculations are carried out in the SOS formalism and the correlation effects are taken into account using all mono‐ and biexcited configuration in the PPP approximation. It is shown that the singlet excitation of the molecules for the antiaromatic case is connected to an significant decrease of both polarizabilities and hyperpolarizabilities. Their values are discussed in terms of the index of average bond‐order alternation for the ground and excited states and the localization of the electronic transitions in the molecules. © 1993 John Wiley & Sons, Inc.
Ab initio studies on the IRC and rate constant of the reaction between acetylene and the hydrogen atom
Authors: Fang De‐Cai , Fu Xiao‐Yuan
Published: January 2005

The geometries of the reactant, product, and transition state of the reaction between acetylene and the hydrogen atom have been optimized at the level of HF/6‐31G using the energy gradient method. The barrier height for this reaction was calculated to be 105.9 kJ/mol with a zero‐point energy correction and elimination of spin contamination. The intrinsic reaction coordinate (IRC) for this reaction was traced and the coupling between the IRC and normal modes was analyzed along the IRC. The variational transition‐state theory with the correction of the tunnel effect has been used to evaluate the reaction rate constant. It is in good agreement with an experimental estimate. © 1994 John Wiley & Sons, Inc.
On the relation between the Kratzer molecular potential and a set of displaced morse oscillator potentials
Authors: Cooper Ian L.
Published: January 2005

The radial Schrödinger equation for the Kratzer molecular potential is equivalent to that of a radial Coulomb problem with an effective (nonintegral) value of rotational angular momentum. The radial Coulomb and the Morse oscillator problems provide different realizations of the algebra so(2,1), whereby the Casimir operators of the Coulomb and Morse oscillator problems are related to the angular momentum quantum number and to the energy, respectively. These relationships permit mappings between the Kratzer molecular potential and the Morse oscillator potential such that the vibrational energy levels of a Kratzer potential with a fixed rotational angular momentum quantum number may be mapped onto degenerate vibrational levels of a set of displaced Morse oscillators. The ground vibrational level of the Kratzer potential is mapped onto the ground vibrational level of a specific Morse oscillator and the remaining (infinite) set of higher vibrational levels are mapped onto degenerate states of displaced Morse oscillators, corresponding to systematic unit increase in the number of bound vibrational levels and successive decrease in equilibrium separation. This behavior is contrasted with that of the finite set of displaced Morse potentials arising as supersymmetric partner potentials to a given parent Morse potential, where there is a systematic unit decrease in the number of bound vibrational levels and a successive increase in equilibrium separation. © 1994 John Wiley & Sons, Inc.
Chemistry and electronegativity
Authors: Allen Leland C.
Published: January 2005

This article addresses the chemical aspects of electronegativity: (1) What is its present status in the chemical community? (2) What are the necessary chemical criteria for a quantitative definition? (3) To what extent do contemporary proposals satisfy these criteria? (4) What connection can be made between the traditional free‐atom scales and an in situ electronegativity appropriate for a particular atom in a specific molecule or solid? A longstanding special feature of electronegativity has been the seeming inability to measure it in the laboratory and this aspect proves to be a key to its definition. © 1994 John Wiley & Sons, Inc.
Why define atoms in real space?
Authors: Bader Richard F. W.
Published: January 2005

The physics of a system is determined by a variation of the action integral, i.e., by a variation of the space–time volume integral of the Lagrange function. If one demands that the properties of an atom in a molecule be derived from physics, the atom must generate its own space–time volume, requiring that its boundaries be defined in real space. The variations in the action are related to the actions of generators of infinitesimal unitary transformations. In the general case, the action integral is altered by generators acting in both the spacelike and timelike surface bounding the space–time volume, whereas for a total isolated system, the physics is totally determined by their action in just the spacelike surfaces at the two time endpoints. It is shown and illustrated for a one‐dimensional system that the definition of an atom corresponds to the possibility of choosing a subsystem in such a way that the contributions to the change in action resulting from the evolution in time of its spatial boundaries vanishes identically. The properties of these subsystems and of the total system of which they are a part are, therefore, determined by one and the same action principle. This choice of subsystem corresponds to the possibility of augmenting the Lagrange function by the divergence of the gradient of the electron density a step that, while leaving the equations of motion unchanged, modifies the generating operators in the required manner. © 1994 John Wiley & Sons, Inc.
Theory of relaxed density matrices: Application to second‐order response properties
Authors: Cybulski Slawomir M. , Bishop David M.
Published: January 2005

The evaluation of second derivatives of the electronic energy for nonvariational wave functions using an energy functional is discussed. It is shown that, in certain cases, the formation of the first‐order relaxed density matrix leads to an efficient algorithm for the calculation of second‐order response properties. Detailed formulas are given for second‐order Møller–Plesset perturbation theory. © 1994 John Wiley & Sons, Inc.
Electronic structure of the benzene–tetracyanoethylene complex: A synthesis of molecular orbital and density functional descriptions
Authors: Cioslowski Jerzy
Published: January 2005

The electronic structure of the benzene–tetracyanoethylene electron donor–acceptor complex is investigated at theHF/6‐311G**level of theory. The computed electronic wave function is analyzed with rigorous interpretive tools that involve both molecular orbital and density functional approaches. Thein situelectronegativity difference is calculated at 3.32 eV, resulting in a charge transfer of 0.016. This extent of charge transfer is found to account for only ca. 17% of the interaction energy of ca. 33% of the dipole moment. The remaining part of the dipole moment originates from buckling of the tetracyanoethylene moiety. The dependence of the electronegativity difference on the magnitude of charge transfer is found to be highly nonlinear. © 1994 John Wiley & Sons, Inc.
Ab initio study of the low‐lying electronic states of the CH2NO2 radical
Authors: Cai Z.‐L.
Published: January 2005

Ab initio electronic structures calculations are reported for the four low‐lying electronic states X 2B1, 2B2, 2A2, and 2A1 of the CH2NO2 radical. The geometric parameters for the ground‐state X 2B1 are predicted by MRSDCI calculations with a double zeta plus polarization basis set. The vertical excitations energies for these electronic states are determined using MRSDCI/DZ+P calculations at the ground‐state equilibrium geometry and in agreement with the recent experimental data obtained via PES of the CH2NO anion. The oscillator strenghts and the radiative lifetimes for these electronic states and the spin properties for the ground state are calculated based on the MRSDCI wave functions, predicting results in good agreement with available experimental data. © 1994 John Wiley & Sons, Inc.
Optimized triple‐zeta Gaussian basis sets for use with relativistic effective potentials
Authors: Pacios L. Fernández , Gómez P. C.
Published: January 2005

Contracted split valence 311 Gaussian basis sets optimized for the averaged relativistic effective potentials (AREP) of Christiansen et al. are developed for the main‐group elements BNe, AlAr, and GaKr. These triple‐zeta basis sets are intended for use in valence‐only molecular calculations with inclusion of correlation. The performance of the optimized basis functions is first analyzed in HF atomic calculations and compared with HF‐limit results. Molecular calculations at the HF, MP2, and CISD levels of theory are performed for some selected diatomics, using these potentials and the optimized sets supplemented by one standard d‐type polarization function. Results are reported for bond lenghts, harmonic vibrational frequencies, dipole moments, atomization energies, and ionization energies and compared with all‐electron reference calculations and experimental data. © 1994 John Wiley & Sons, Inc.
Molecular cyclicity and centricity of polycyclic graphs. I. Cyclicity based on resistance distances or reciprocal distances
Authors: Bonchev Danail , Balaban Alexandru T. , Liu Xiaoyu , Klein Douglas J.
Published: January 2005

Rules for molecular cyclicity based on the global indices resulting from reciprocal distances (Harary number, H) or from resistance distances (Kirchhoff number, Kf) were tested in comparison with those elaborated earlier by means of the Wiener index, W. The Harary number and the Wiener number were found to match molecular cyclicity in an almost identical manner. The Kirchhoff number also generally follows cyclicity trends described previously. H is slightly less degenerate than is W, but Kf has practically no degeneracy in the graphs investigated here. Being much more discriminating than the Wiener number (i.e., practically nondegenerate), Kf allowed the formulation of new rules for systems formed from linearly condensed ribbons of even‐membered rings with different sizes as well as for branched ribbons. The topological cyclicity patterns are thus reformulated in an extended basis, proceeding from three different graph metrics. © 1994 John Wiley & Sons, Inc.
Correlated polarization propagator calculations of static polarizabilities
Authors: Sauer Stephan P. A. , Oddershede Jens
Published: January 2005

We present a systematic comparison of the correlation contribution at the level of the second‐order polarization propagator approximation (SOPPA) and MP2 to the static dipole polarizability of (1) Be, BeH−, BH, CH+, MgH−, AIH, SiH+, and GeH+; (2) BH3, CH4, NH3, H2O, HF, BF, and F2; and (3) N2, CO, CN−, HCN, C2H2, and HCHO. Fairly extended basis sets were used in the calculations. We find that the agreement with experimental values is improved in SOPPA and MP.2 over the results at the SCF level. The signs and magnitudes of the correlation contribution in SOPPA are similar to those obtained in analytical derivative MP2 calculations. However, it is not possible to say, in general, which method gives the largest correlation contribution or the best agreement with experiment, nor is it possible to make a priori prediction of the sign of the correlation contribution. For the first group of molecules, which have a quasi‐degenerate ground state, additional CCDPPA and CCSDPPA calculations were performed and compared with polarizabilities obtained as analytical/numerical derivatives of the CCD and CCSD energies. The CCSDPPA results were found to be in better agreement with other calculations than were the SOPPA results, demonstrating the necessity of using methods based on infinite‐order perturbation theory for these systems. © 1994 John Wiley & Sons, Inc.
Ground‐state correlation energy of Ne
Authors: Noro Takeshi , Ohtsuki Kazumasa , Sasaki Fukashi
Published: January 2005

A series of basis sets and configuration interaction (CI) wave functions, both of which were constructed so as to systematically approach to the complete set limit and the full CI limit, were used for the ground state of Ne. These calculations yielded an estimated correlation energy of −0.3891 au, which is 99.6% of a recent theoretical estimate of −0.3905 au. The CI value, −0.3821 au, was obtained by SDCI calculation with seven reference configurations by using Slater‐type orbitals (STOs) from s to h functions. © 1994 John Wiley & Sons, Inc.
A density functional elongation method for the theoretical synthesis of aperiodic polymers
Authors: Aoki Yuriko , Suhai Sándor , Imamura Akira
Published: January 2005

The elongation method, a theoretical tool to synthesize the electronic states of polymers, is applied within the framework of the density functional approach and using a linear combination of Gaussian‐type orbitals. In this treatment, the wave function of a cluster is localized and the interaction with an attacking monomer is self‐consistently calculated according to the Kohn–Sham equation. The reliability and the applicability of our treatment are examined by the application to a random hydrogen molecule cluster, comparing the results with those obtained by the usual diagonalization method for the whole system. The results show that this treatment efficiently provides the electronic states of the end part of aperiodic polymers. © 1994 John Wiley & Sons, Inc.
Recent developments in the theoretical design of low‐gap polymers and their nonlinear optical properties
Authors: Otto P.
Published: January 2005

Geometry optimizations on molecular clusters of the five‐membered heterocyclic molecules pyrrole, furane, thiophene, and selenophene were carefully carried out. It is shown that the value of the band gap cannot be related to the bond alternation in the aromatic compounds. However, a correlation of the gap value with the ionization potential of the heteroatom in the ring is found and can be explained by the different stabilizations of the LUMO energy of the heterocycle with respect to the butadiene backbone. The energy band structure including also corrections for the electron correlation effects is reported. The newly developed variational method for the calculation of static polarizabilities of polymers is reviewed and applications to cyclopropene and heteroaromatic derivatives are reported. Finally, a possible approach to treat dynamical polarizabilities of polymers based on perturbation theory is briefly outlined. © 1994 John Wiley & Sons, Inc.
Theory of hopping conductivity of proteins
Authors: Ye Yuan‐jie , Ladik János
Published: January 2005

Quantum chemical calculations for two different kinds of native proteins (pig insulin and hen egg white lysozyme) were done by the extended negative factor counting method in which the matrix elements have been calculated at the ab initio level with the help of a minimal basis and the simulation of the aqueous solution environment. The hopping conductivities were worked out by the formulas of the random walk theory of Lax and co‐workers. The electronic density of states of these native proteins confirmed the conclusions obtained previously from aperiodic model peptides chains. The results show that the ac conductivity vs. frequency curve of these native proteins lies in the range of some typical good inorganic amorphous conductors and thus confirm that proteins, if doped, are amorphous conductors. The behavior of the ac conductivities of the proteins in different ranges of frequencies are discussed. © 1994 John Wiley & Sons, Inc.
One‐electron properties of molecules calculated using second‐order multireference perturbation theory
Authors: Kozlowski P. M. , Davidson E. R.
Published: January 2005

A new form of second‐order multireference perturbation theory coupled with finite‐field perturbation theory is applied to evaluate some one‐electron molecular properties. Several possible definitions of the zeroth‐order Hamiltonian are considered and results tested against bench‐mark full CI calculations. © 1995 John Wiley & Sons, Inc.