bluuebunny/crossref_metadata_2025 huggingface dataset:
On the complex relations between equations describing the dynamics of wave and particle aspects
Authors: Schuch D.
Published: January 2005

Equations of motion on the levels of classical mechanics, hydrodynamics, and wave mechanics are analyzed and existing connections are shown. The manifestation of particle and wave aspects on the different levels are investigated. Dissipative frictional forces are included and a nonlinear wave mechanical equation for these systems can be found. It follows the discussion of an alternative to the time‐dependent Schrödinger equation (SE) in order to obtain the dynamical information on particle and wave aspects in a different form. This can be achieved by means of a Newtonian equation for a complex variable in connection with a conservation law for a nonclassical angular momentum‐type quantity. With the help of this complex variable it is also possible to develop a Hamiltonian formalism for the wave aspect contained in the SE, the fluctuation, or uncertainty of position and momentum. In this case the Hamiltonian function is equivalent to the difference between the mean value of the Hamiltonian operator and the classical Hamiltonian function. Possible extensions and applications are mentioned.
A fragment multipole approach to long‐range Coulomb interactions in Hartree–Fock calculations on large systems
Authors: Panas Itai , Almlöf Jan
Published: January 2005

An efficient ab initio method for electronic structure calculations on extended molecular systems is presented, along with some illustrative applications. A division of the system into subunits allows the interactions to be separated into short‐ and long‐range contributions, leading to a reduction of the computational effort from the original fourth‐power size‐dependence to one that is approximately quadratic. The short‐range contributions to the Fock matrix are obtained in an essentially conventional fashion, while the long‐range interactions are evaluated using a two‐center multipole expansion formalism. The number of short‐range contributions grows only linearly with the number of subunits, while the long‐range contributions grow as N2. Systematic studies of the computational efforts for systems of up to 99 water molecules organized as one‐stranded chains, three‐stranded chains, and three‐dimensional clusters, as well as alkane chains with up to 69 carbon atoms, have been performed. In these model systems, the overall computational effort grows as NK where 1 < K < 2.
Conformational structure of the tetrapeptide Boc–Aib–Leu–Leu–Aib–OMe–the central fragment of the nonapeptide antibiotic leucinostatin A
Authors: Nandel Fateh S. , Singh Balvinder , Saran Anil
Published: January 2005

The conformational structure of the tetrapeptide Boc–Aib–Leu–Leu–Aib–OMe has been investigated by the PCILO method. The computational results show the formation of two closed β‐turns, both of which are of type III, and the peptide backbone folds into a right‐handed 310‐helical conformation stabilized by two intramolecular 4 → 1 hydrogen bonds. The helix thus formed generates a pore of ∼3 Å along helix axis with hydrophobic amino acid side chains located on the outside of the helix, and this tendency of leucine side chains may enable leucinostatin A to fit into the membrane bilayer. The pore thus formed is cation‐selective, and through this pore, the cation can pass only in a single file.
Molecular quantum similarity measures and N‐dimensional representation of quantum objects. I. Theoretical foundations
Authors: Carbó R. , Calabuig B.
Published: January 2005

A conceptual general definition of quantum similarity and similarity indices are given. The interpretation of molecular similarity from a quantum theoretical point of view is analyzed. Various approximations are also discussed.
Quasispin symmetry for the derivation of coupled cluster equations for the Hubbard model of benzene
Authors: Vinette F.
Published: January 2005

The concept of quasispin is applied to a special case of the Pariser–Parr–Pople (PPP) model of the benzene molecule, namely, the Hubbard Hamiltonian. Added to the spin, space, and alternancy symmetries already taken into account in the PPP Hamiltonian, this new symmetry, called quasispin symmetry, has the effect of reducing the size of the CI matrix. Coupled cluster (CC) equations are then obtained after applying the CC approach with doubles as well as its extension that accounts for triexcited clusters (CCSDT‐1). The derivation of these equations following the use of quasispin to the Hubbard model of benzene constitutes the most simple nontrivial example of CC results. In addition, the CC equations can be written in explicit algebraic form using the symbolic computation language MAPLE.
On the calculation of the hyperpolarizabilities of organic molecules by the sum over virtual excited states method
Authors: Morley J. O. , Pavlides P. , Pugh D.
Published: January 2005

The version of time‐dependent perturbation theory commonly used in the calculation of the hyperpolarizabilities of organic molecules through an expansion over electronic excited states is briefly rederived by a direct method, simplified for application to the nonresonant case. The application of the method within the framework of semiempirical quantum theory and singly and doubly excited configuration interaction is described. A particular parametrization of the CNDO/S method (CNDO/VS) that has been successful in estimating molecular β values for polar aromatic molecules is reviewed. Applications of the method to the interpretation of the molecular and crystal second‐order properties of 2‐(α‐methylbenzylamino)‐5‐nitropyridine (MBANP) and to the calculation of the γ tensor for various types of conjugated compounds are given.
Relations among functional groups within a stoichiometry: A nuclear configuration space approach
Authors: Dubois Jacques‐Emile , Mezey Paul G.
Published: January 2005

A general scheme is proposed for the study of the interrelations and transformations of flexible functional groups within the configuration space M of all possible chemical species of a fixed overall stoichiometry S. The methods presented provide a concise but sufficiently detailed description of the occurrence of various functional groups in different families of nuclear arrangements, as well as their transformations into one another during chemical reactions and conformational changes. The approach uses experimental information on the importance of various functional groups, topological criteria for the flexibility of these functional groups, and the fundamental pattern of distribution of configurational families within the nuclear configuration space. The resulting schemes have simple, easily programmable representations. © 1992 John Wiley & Sons, Inc.
Ab initio study on the mechanism of cycloaddition reaction of ketene with methylenimine: A new reaction scheme
Authors: Fang Decai , Fu Xiaoyuan
Published: January 2005

The cycloaddition reaction of ketene and methylenimine, leading to 2‐azetidinone, has been studied theoretically by RHF/3‐21G and IRC. This reaction is believed to be nonsynchronous and concerted, taking place through a twisted transition state. Four π orbitals are involved in this reaction, which is a “2 × [1 + 1]”‐type cycloaddition. In the course of the reaction, rotation of the methylene group instead of oxygen in ketene was ascertained. The activated barrier is calculated to be 33.9 kcal/mol. © 1992 John Wiley & Sons, Inc.
The rotation–vibration coupling equations for polyatomic molecules in internal coordinates
Authors: Chen Guang‐Ju , Tang Au‐Chin , Fu Xiao‐Yuan
Published: January 2005

An exact vibration–rotation kinetic energy operator for polyatomic molecules has been obtained on the basis of Sutcliffe's method, in terms of curvilinear internal coordinates and rotational angular moment operators. This operator is derived from the kinetic energy operator in Cartesian coordinates by the successive transformations using the chain rule. This kinetic energy operator can be used not only for the system of any triatomic and tetraatomic molecules and common polyatomic molecules in chemistry, but also for the investigation of the collision problems between two molecules after some modifications. Finally, using this Hamiltonian, the rotation–vibration coupling equations of polyatomic molecules have been derived and discussed. © 1992 John Wiley & Sons, Inc.
The variation of spectroscopic properties with numbers of electrons
Authors: Laurenzi Bernard J. , Gaylord Donald R.
Published: January 2005

A formalism that describes the variation of the spectroscopic properties, De, Re, and ke, of homonuclear, diatomic molecules, with the number of molecular electrons has been developed. The theory describes the interrelation of these properties and predicts “critical” behavior in sequences of “isonuclear” and neutral molecules. Detailed calculations are possible with the help of experimental data in lieu of a deeper, dynamical theory of molecular behavior with respect to electron number. The present work points the way toward a first‐principle's theory. © 1992 John Wiley & Sons, Inc.
Molecular conformation of bilirubin from semiempirical molecular orbital calculations
Authors: Shelver Weilin L. , Rosenberg Harry , Shelver William H.
Published: January 2005

Semiempirical methods were utilized in the computation of a fully optimized structure of bilirubin. Bond lengths and bond angles obtained using either AM1 or PM3 calculations showed excellent agreement with those obtained by X‐ray diffraction. This indicated that molecular orbital methods satisfactory reproduced the complex conjugation found in bilirubin. Dihedral angles of the crucial “hinge” and the dihedral angles of the propionic acid side chains agreed well with those found by X‐ray diffraction. Calculated hydrogen‐ bond parameters (distance and angles) showed substantial differences from experimental values, probably due to inherent weakness in the parameterization of the molecular orbital techniques. Conformational studies were carried out using AM1 by rotating the C9C10 bond in 5° increments showed that the most stable structure exhibited a minimum at about 125° and exhibited a structure similar to those postulated from X‐ray and NMR experiments. The hydrogen bonds showed remarkable tenacity during rotation of the C9C10 bond and resisted breaking until the molecule was under extreme strain. © 1992 John Wiley & Sons, Inc.
Quantum mechanical parametrization of a conformationally dependent hydrophobic index
Authors: Alkorta Ibon , Villar Hugo O.
Published: January 2005

An extension of our previous work on the development of a conformationally dependent hydrophobic index is presented. The parameter was computed in four alternative ways based on steric parameters, such as the total molecular surface area or the solvent accessible surface, and on quantum mechanically computed electronic properties, such as the molecular dipole moment, Mulliken charge densities, and a lone–pair index. The method was parametrized based on 110 rigid analogs and all properties required were calculated using the semiempirical methods PM3, AM1, and MNDO. Examples of the application of this method in calculating hydrophobic indices are presented.
Structural and electronic requirements for binding at the Mu–opioid receptor
Authors: Cometta–Morini Chiara , Loew Gilda H.
Published: January 2005

A pharmacophore for μ‐opioid receptor recognition based on a study of the fentanyl class of opioids has recently been characterized in our laboratories. To validate this pharmacophore, we have extended our theoretical studies to include four opiate analogs from structurally different classes and with high affinity but varying selectivity for the μ‐opiate receptor. An extensive conformational search of the flexible regions of these compounds has been carried out at two levels of approximations, using the CHARMm force field and the semiempirical molecular orbital method AM1. In a subsequent step, we have determined a series of structural, environmental, and electronic properties for each low‐energy conformer of the analogs studied. All four analogs studied can assume a low‐energy conformation in which at least three of the four stereoelectronic properties identified as modulators of recognition in the fentanyls are present in the same spatial arrangement. These results provide additional evidence for the plausibility of the proposed pharmacophore for μ–opioid receptor recognition. © 1992 John Wiley & Sons, Inc.
Semiempirical calculations of TiO2 (rutile) clusters
Authors: Hagfeldt Anders , Siegbahn Hans , Lindquist Sten‐Eric , Lunell Sten
Published: January 2005

The densities of states for small (TiO2)x‐clusters, x = 1, 3, 6, 9, and 14, have been calculated by means of the INDO method. The shape of the valence bands' density of states (DOS) are discussed in terms of the distribution of coordination numbers. A one‐slab cluster with uniform distribution of the coordination numbers was used to compare our calculations with experimental spectra. The photoelectric DOS and DOS for a cluster with an oxygen vacancy are in very good agreement with experimental findings for the TiO2 (001) surface. O1s core level shifts between a surfacelike and a bulklike oxygen atom have been estimated. It is concluded that the observed surface–bulk shift for the TiO2 (001) surface contains a substantial relaxation contribution. © 1992 John Wiley & Sons, Inc.
Semiempirical calculations of hyperpolarizabilities for extended π systems: Polyenes, polyynes, and polyphenyls
Authors: Matsuzawa Nobuyuki , Dixon David A.
Published: January 2005

The dipole moments (μ), polarizabilities (α), hyperpolarizabilities (β), and second‐order hyperpolarizabilities (γ) of polyenes, polyynes, and polyphenyls have been calculated by a finitefield method with the PM‐3 parameterization of the semiempirical MNDO Hamiltonian at the optimum geometries. These results were compared to experimental values obtained from EFISH and THG measurements. The calculations reproduce the magnitudes of β and γ, as well as the effect of the substituents and the effect of bond alternation on β and γ. The coefficients of the power law, which describes the dependence of β and γ on the number of π centers, were calculated. For β, exponents of 1.5–2.2 and 0.03–0.04 were obtained for polyenes and polyynes, respectively, and for γ, exponents of 3.9–4.9, 2.9–3.3, and 2.5–2.7 were obtained for polyenes, polyynes, and polyphenyls, respectively. These results confirm the efficiency of enhancing γ by insertion of C = C double bonds into a chain. © 1992 John Wiley & Sons, Inc.
The electronic structure of Keggin anion (PW12O40)3− and catalytic properties
Authors: Chen T. L. , Ji J. , Xiao S. X. , Cai T. X. , Yan G. S.
Published: January 2005

The electronic structure of the Keggin anion (PW12O40)3− has been calculated by the DV–Xα method. The nature of the chemical bonds of the Keggin anion and the relationship between electronic structure and catalytic behavior are discussed. At the same time, the difference in electronic structure and the relationship in catalytic behavior between (PW12O40)3− and (PMo12O40)3− are compared. © 1992 John Wiley & Sons, Inc.
Average virtual orbitals in configuration interaction studies with application to the low‐lying singlet states of the carbon monoxide and acetone molecules
Authors: Mogensen Benny J. , Rettrup Sten
Published: January 2005

A method is described for obtaining a modified virtual orbital space that improves the rate of convergence in configuration interaction studies of electron correlation for both ground‐state and excited‐state properties. The validity of the method has been compared with other procedures by performing a series of test calculations of the electric dipole properties of the CO molecule in the X1Σ+ ground state and the first excited singlet states A1∏, I1Σ−, and D1Δ using different optimization schemes. The low‐lying Rydberg and valence excited states of the acetone molecule have been investigated using different N – 1‐electron potentials in the construction of virtual orbitals. The examples indicate that the presented average virtual orbitals (AVOs) constitute a compromise set of orbitals suited for simultaneously improving the description of several electronic states. © 1992 John Wiley & Sons, Inc.
Half‐projected Hartree–Fock natural orbitals for defining CAS–SCF active spaces
Authors: Bone Richard G. A. , Pulay Péter
Published: January 2005

We have extended the range of systems to which the half‐projected Hartree–Fock (HPHF) method has been applied, including the triplet state of the wave function. In our implementation, DIIS overcomes the convergence difficulties reported in earlier studies. HPHF allows generation of a symmetry‐broken wave function in regions of the potential energy surface where the RHF wave function is triplet‐stable. The fractionally occupied natural orbitals (FONOS) of the HPHF wave function are good starting vectors for CAS–SCF calculations. A CAS–SCF in the space defined by the HPHF FONOS should be used instead of the unrestricted natural orbital CAS–SCF method in regions of triplet stability and for small active space problems. We draw extensive comparisons between the results of both the UNO–CAS and HPNO–CAS methods and those of full CAS–SCF calculations. © 1993 John Wiley & Sons, Inc.
Accurate second‐order correlation energies for Mg and Ar
Authors: Flores Jesús R. , Redondo Pilar
Published: January 2005

A p‐version finite element method has been used to calculate second‐order pair and total correlation energies for closed‐shell Mg and Ar. Comparison with the best results found in the literature suggests that the present values are the most accurate and that the method should perform comparatively better for heavier elements. © 1993 John Wiley & Sons, Inc.
Variation–iteration method in momentum space: Determination of Hartree–Fock atomic orbitals
Authors: De Windt Laurent , Defranceschi Mireille , Dehalle Joseph
Published: January 2005

A method using the Svartholm iterative procedure to solve atomic Hartree–Fock equations in momentum space is defined and applied to the ground states of Be and B+. The calculated atomic orbital properties follow a monotonic and stable convergence, but with rates of convergence depending on each property. The evolution of the orbitals during the iterations is explained by the combined actions of the variational principle, the Svartholm iterative procedure, and the momentum space representation. © 1993 John Wiley & Sons, Inc.
Third‐order methods for molecular geometry optimizations
Authors: Vogel S. , Fischer T. H. , Hutter J. , Lüthi H. P.
Published: January 2005

Third‐order optimization methods that require the evaluation of the gradient and initial estimates for the second and third derivatives are described. Update algorithms for the Hessian and the third‐derivative tensor are outlined. The direct inversion in the iterative subspace scheme is extended to third order and is combined with the third‐order update procedures. For geometry optimization, an approximate third‐derivative tensor is constructed from simple empirical formulas. Examples of application to Hartree–Fock geometry optimization problems are given. © 1993 John Wiley & Sons, Inc.
Ab initio study of the influence of aggregation on the infrared spectrum of acetonitrile
Authors: Mathieu Didier , Defranceschi Mireille , Delhalle Joseph
Published: January 2005

With the aim of investigating the influence of direct intermolecular interactions between nitrile groups on the infrared features of nitrile polymers, vibrational frequencies and infrared intensities of acetonitrile and of its antiparallel dimer are compared. It is found that whereas frequencies are unchanged upon association infrared intensities are dramatically affected. In particular, the striking difference between the intensities of the CN stretching band measured in gas phase, on the one hand, and in the liquid, on the other, is already accounted for at the dimer level. Despite the poor reliability of absolute values of calculated intensities, it is interesting to note that consistent trends are obtained at various levels of theory. These results suggest that ab initio calculations of infrared intensities can be useful to interpret infrared measurements, thus contributing to the elucidation of molecular structure of materials. © 1993 John Wiley & Sons, Inc.
Redshifts and blueshifts of OH vibrations
Authors: Hermansson Kersti
Published: January 2005

Ab initio calculations of potential energy, dipole moment, equilibrium OH distance, force constants, and anharmonic frequencies, and correlation between these quantities, are presented for a water molecule and an OH− ion in a uniform electric field of varying field strength. It is explained why a bound H2O molecule in nature always experiences a frequency downshift with respect to the free molecule, and a bound OH−1 ion, either a downshift or an upshift. The frequency‐field variation is well accounted for by the expression ΔνOH α −E‖ · (d μ/drOH + 1/2 · ∂μ/∂rOH). A frequency maximum occurs at the field strength where ∂μ‖tot/∂rOH ∼ 0. Two cases can be discerned: (1) the frequency maximum falls at a positive field strength when dμ/drOH is positive (this is the situation for OH−), and (2) the maximum frequency falls at a negative field when dμ/drOH is negative (this occurs for water). In general, for an OH bond in a bonding situation where the intermolecular interactions are dominated by electrostatic forces, the nonlinearity of the frequency shift with respect to an applied field is governed by how close to the frequency maximum one is, i.e., by both dμ/drOH and ∂μ/∂rOH. Correlation curves between the external linear force constant, kext, and rOH,e are closely linear over the whole field range studied here, whereas the frequency vs. rOH,e and force constants vs. rOH,e correlation curves form two approximately linear, parallel branches, corresponding to “before” and “after” the maximum in the frequency vs. field curves. Each branch of the ν vs. rOH,e curves has a slope of ∼ − 16,000 cm−1/Å. © 1993 John Wiley & Sons, Inc.
Nonlinear optical properties of organic molecules. XII. Calculations of the hyperpolarizabilities of donor–acceptor polyynes
Authors: Morley John O.
Published: January 2005

The hyperpolarizabilities of polyynes containing a donor and acceptor group situated at either end of the molecular have been calculated at the sum‐over‐states CNDOVSB level using geometries derived from crystallographic data and ab initio studies. The calculated values increase with increasing chain length, though the maximum value obtained are considerably less than those for the related polyynes. Although the hyperpolarizability of the polyynes is dominated by one excited π‐electron state, there are a significant number of additional low‐lying excited states in the polyynes that contribute to the overall value by opposing the usual direction of charge transfer along the chain from donor to acceptor. © 1993 John Wiley & Sons, Inc.
Data parallel large‐scale molecular dynamics for liquids
Authors: Hedman Fredrik , Laaksonen Aatto
Published: January 2005

An efficient data parallel computational scheme is presented for large‐scale molecular dynamics (MD) simulations of liquids with short‐range interactions. The method is based on decomposition of the simulation cell into equally sized subcells, with the shortest side length equal to the cutoff radius. Inter‐ and intracell interactions are calculated in a coarse‐grained manner. A geometric sorting procedure, based on particle distances to subcell boundaries, is used to minimize the overall computations and the nonproductive communications. Using only nearest‐neighbor communications, an efficient scheme is developed for periodic updates of the contents of subcells due to the migration of particles. Special “null‐particles” are introduced, which act as buffers during the periodic updates and allow for a globally uniform algorithm during the calculations. Communication cost is about 7% of the total CPU time. The method is found to be linearly scalable with the number of particles, performing better as the ratio of virtual to physical processors increases. The MDcode is written in Fortran 90 and implemented on a CM‐200. The overall speed is approximately 5.9 μs. per MD step and per particle for 1 million particles and 5.5 μs for 5 million particles. The method should be easily transferred to other massively parallel computers of SIMD and MIMD type. © 1993 John Wiley & Sons, Inc.
SCF Wave functions for (CuO2)n lamella in crystal field of T′–Nd2CuO4
Authors: Acrivos J. V. , Stradella O.
Published: January 2005

An SCF analysis has been carried for ensembles that simulate the CuO2 conduction layer in the tetragonal layer crystal T′—Nd2CuO4 (Fig. 1). In this work, the CuO2 layer is described by a planar macromolecule, (CuO2)n, subject to the crystal field produced by the point charges in the ionic layers of D4h symmetry The computations were carried out using the KGNMOL, HONDO, and KGNGRAF codes in MOTECC ‐91. The computations were carried out with different oxygen and copper basis sets and energy convergence to less than 10−8 Hartrees. The purpose of the SCF computation was to estimate the cohesive energy of the ensembles, the electron density for the individual molecular orbitals, and the excess correlation energy, to ascertain the nature of the CuO bond in the conduction layer. The results indicate the following: (1) The cohesive energy of the ensembles (measured by the SCF energy plus the correlation energy, above the atomic values): ΔUc ≡ ΔESCF + ΔEC = −4.35 to −4.17 Hartrees per CuO bond as n increases from 4 to 9. Further insight was obtained by considering the electrostatic energy contributions to ΔUc; Eelectrostatic (ensemble) → EModeling (infinite lattice) were evaluated by replacing the oxygen and copper atoms by point charges determined by a Mullion population analysis. The larger oxygen basis set (13, 8/5,3) gave consistent results for the different ensembles of ΔEcovalent ≡ ΔUc − Eelectrostatic = −1.1 Hartrees per CuO bond. (ii) The electron density indicates that covalent bonds are formed and that the oxygen atoms play an important role in the structure stability. The covalent bonds formed indicate that nominal ionic valences do not apply. Mulliken population analyses gave valences of the order of one at the copper and oxygen atoms. The CuO bond orders are 0.47 between neighboring atoms and 0.048 for those separated by two atoms. (iv) The covalent nature of the CuO bonds in (CuO2)n was compared to that for the H2 molecule using as a measure the electron density and the excess correlation energy. The excess correlation energy per CuO bond above the atomic values is one order of magnitude lower that that for the H2 molecule and that for the CC bond in alternant hydrocarbons. © 1993 John Wiley & Sons, Inc.
Ewald summation of multipolar interactions at an arbitrary order on a two‐dimensional lattice
Authors: Lambin Ph. , Senet P.
Published: January 2005

There exist problems in condensed‐matter theory that require evaluating infinite Bloch sums of multipolar potential r−l−1Yl,m(θ,φ) on a periodic lattice. For an arbitrary multipolar order l, tractable formulas are given for summing such interactions on a two‐dimensional Bravais lattice and evaluating their Bloch sums at a point outside as well as inside the plane of the lattice. The approach used is the Ewald method, which consists of separating the original series in rapidly converging sums in reciprocal and real spaces. Computational aspects of the present formulation are briefly reviewed. © 1993 John Wiley & Sons, Inc.
Complex scaling and self‐adjoint dilations
Authors: Kurasov P. B. , Elander N.
Published: January 2005

Complex scaling of the Schrödinger equation on the halfaxis with a nontrivial boundary condition at the origin is investigated. A self‐adjoint dilation of the corresponding dissipative operator is constructed. The relations between the scattering problems for the operator and it's dilation are clarified. © 1993 John Wiley & Sons, Inc.
Accurate algebraic densities and intracules for heliumlike ions
Authors: Koga Toshikatus , Kasai Yoshiaki , Thakkar Ajit J.
Published: January 2005

Accurate electron number densities and interelectronic distance (intracule) densities are given in simple algebraic form for the ground states of H−, He, Li+, Be2+, B3+, and Ne8+. The densities are obtained from systematic sequences of increasingly accurate Hylleraas‐type wave functions. The most accurate densities are obtained from 204‐term wave functions that lead to variational energies no more than 16 nano‐Hartrees above the exact the exact ones. The algebraic permit the evaluation of systematic sequences of many expectation values. Some moments of the densities are evaluated in this manner. © 1993 John Wiley & Sons, Inc.
Redshifts and blueshifts of OH vibrations
Authors: Hermansson Kersti
Published: January 2005

Ab initio calculations of potential energy, dipole moment, equilibrium OH distance, force constants, and anharmonic frequencies, and correlations between these quantities, are presented for a water molecule and an OH− ion in a uniform electric field of varying field strength. It is explained why a bound H2O molecule in nature always experiences a frequency downshift with respect to the free molecule, and a bound OH− ion either a downshift or an upshift. The frequency‐field variation is well accounted for by the expression ΔνOH ∝ −E∥·(dμ/drOH + 1/2 · ∂μ/∂rOH). A frequency maximum occurs at the field strength where ∂μ/∂rOH ∼ 0. Two cases can be discerned: (1) the frequency maximum falls at a positive field strength when dμ/drOH is negative (this is the situation for OH−), and (2) the maximum frequency falls at a negative field when dμ/drOH is positive (this occurs for water). In general, for an OH bond in a bonding situation where the intermolecular interactions are dominated by electrostatic forces, the nonlinearity of the frequency shift with respect to an applied field is governed by how close to the frequency maximum one is, i.e., by both dμ/drOH and ∂μ/∂rOH. Correlation curves between the external linear force constant, kext, and rOH,e are closely linear over the whole field range studied here, whereas the frequency vs. rOH,e and force constants vs. rOH,e correlation curves form two approximately linear, parallel branches, corresponding to “before” and “after” the maximum in the frequency vs. field curves. Each branch of the v vs. rOH,e curves has a slope of ∼ −16,000 cm−1/Å. © 1993 John Wiley & Sons, Inc.
Helical region of the potential energy surface of α‐aminoisobutyric acid: A theoretical study
Authors: Alemán Carlos , Perez Juan J.
Published: January 2005

The helical region of the potential energy surface of blocked α‐aminoisobutyric acid (Aib) dipeptide has been studied by using ab initio and semiempirical quantum mechanical methods, as well as force‐field‐derived methods. Depending on the method, an α‐helix or a 310‐helix is found to be the energy minimum. The conformations obtained from computations performed at the ab initio quantum mechanical level, as well as by using the AMBER force field, are in excellent agreement with X‐ray data. Semiempirical results display some important differences with regard to experimental data. On the other hand, the CVFF force field predicts no energy minimum in the helical region of the Aib potential energy surface. © 1993 John Wiley & Sons, Inc.
Geometrical, spectroscopic, and magnetic properties of an oxygen atom adsorbed on the Ni(100) surface
Authors: Goursot Annick , Mele Franca , Russo Nino , Salahub Dennis R. , Toscano Marirosa
Published: January 2005

Spin‐polarized linear combinations of Gaussian‐type orbital–model core potential–local spin density (LCGTO–MCP–LSD) computations have been performed for oxygen chemisorption on a Ni(100) surface simulated by four different clusters. Results show that the oxygen atom chemisorbs preferentially on the fourfold hollow site with an equilibrium distance of 1.931 Å and a vertical vibrational frequency of 401 cm−1. The corresponding experimental values are 1.960 Å and 423 or 430 cm−1. A satisfactory agreement with experiment is also found for the adsorption energy (6.7 vs. 5.6 eV). The bridge position lies at only 0.4 eV above the fourfold hollow one. It is found that oxygen adsorption leaves the bare cluster total spin magnetic moment unchanged, but induces appreciable reductions of the local atomic moment on the surface nickel atoms. © 1993 John Wiley & Sons, Inc.
Second‐order Jahn–Teller instability and the activation energy for Al+(1S) + H2 → AlH+(2∑+) + H
Authors: Rusho Jon , Nichols Jeff , Simons Jack
Published: January 2005

The interaction of Al+ (1S) ions with H2 on the lowest electronic energy surface is studied using ab initio electronic structure methods. A Cs symmetry transition state is located and found to have the geometry of a product AlH+ ion loosely bound to a H atom, consistent with the Hammond postulate for this endothermic reaction. Locating this transition state, beginning at geometries that characterize vibrationally cold H2 and translationally hot Al+, posed special challenges to the commonly used “hill‐climbing” algorithm because of regions of geometrical instability along the path thus generated. This instability was found to be a result of second‐order Jahn–Teller coupling with a low‐lying 1B2 electronic state. In addition to these primary findings, a weakly bound T‐shaped Al+ ——— H2 C2v van der Waals complex is found that lies only 242 cm−1 below the Al+ and H2 asymptote, with HH internuclear separation only slightly distorted from the equilibrium bond distance of H2 and AlH distance (3.5 Å) much longer than the covalent bond length in AlH+ (1.6 Å). The locally stable but thermodynamically unstable linear HAlH+ (1∑) species and, of course, the H + AlH+(2∑+) reaction products have also been identified as critical points on the ground‐state surface. Where known, the geometries and energies that we calculte agree well with experimental data. © 1993 John Wiley & Sons, Inc.
On the applicability of the screened‐Coulomb exchange model in Kohn–Sham density functional studies
Authors: Proynov E. I. , Salahub D. R.
Published: January 2005

The screened‐Coulomb exchange model used first in the Xα method and later on in Kohn–Sham density functional theory is reexamined. Based on the well‐elaborated framework of the local spin‐density approximation, we show that this model is not well suited when systems with a finite number of electrons are concerned, because it does not respect the pair‐density sum rule. A proper modification of the model is proposed by reformulating it in terms of a screened‐exchange hole and ensuring the sum rule for this hole. As a result, it is shown how the static screened exchange in finite systems is accompanied by a conjugate antiscreened one. The possible consequences of this effect on the application of the screened‐Coulomb exchange model are discussed. © 1994 John Wiley & Sons, Inc.
Applications of the molecular orbital graph theory: A topological method to calculate aN–K based on aN
Authors: Zhao Honggang , Li Jiping , Hu Shixian , Zhang Jicai
Published: January 2005

A formula of the coefficient aN–K of the eigenpolynomials connected with the zero‐order term's coefficient of the eigenpolynomials corresponding the k‐order‐induced subgraph's molecular fragments has been induced. From this formula, aN–K can be calculated and the contributions of the induced subgraph's molecular fragments to the stability and reactivity of the molecules are revealed. © 1994 John Wiley & Sons, Inc.
Building blocks for electron density in free molecules and in condensed matter phases
Authors: March N. H.
Published: January 2005

With the density functional theory as the underlying framework, the modeling of the ground‐state densityp(r), using fragments or bonds as appropriate, is considered in both free molecules and in some condensed phases. Emphasis is placed on bringing the models into contact with both first‐principles quantum mechanics and available diffraction experiments. Clusters of alkali metals are specifically referred to, since cluster science affords a bridge between the quantum chemistry of small molecules and condensed phases. Finally, amorphous silicon and both solid and liquid alkali metals are considered. © 1994 John Wiley & Sons, Inc.
Spin virial theorem in the density functional theory
Authors: Nagy Á.
Published: January 2005

The spin virial theorem is derived in the density functional theory. The theorem establishes a relation between the differences of spin‐up and ‐down kinetic and potential energies. The theorem is useful for checking the accuracy of spin orbitals. As an illustration, the example of the Xα method is studied. © 1994 John Wiley & Sons, Inc.
Potential energy surfaces of carbon dioxide
Authors: Xantheas Sotiris S. , Ruedenberg Klaus
Published: January 2005

Several bent valence states of CO2 are characterized by means of full‐valence‐space MCSCF calculations. The ground state potential energy surface exhibits a double well corresponding to a ring minimum, with C2vsymmetry (1A1) and a 73.1° OCO angle, in addition to the linear (1σ) global minimum. The transition state for the ring opening process, which has a barrier of 12.1 kcal/mole with respect to the ring minimum, is however found to have Cs symmetry. Double minima are also shown to exist for the 1A2, 1B1 and 1B2 excited states. However, in these cases all minima are bent. Cross sections through the ground state potential energy surface corresponding to the two collinear exchange reactions O(1D) + CO(1σ+) → OC(1σ+) + O(1D) C(3P) + O2(3σ) → CO(1σ+) + O(1D) are also calculated and their energy contour maps are reported. The latter reveals the existence of a stable linear intermediate with the structure COO. © 1994 John Wiley & Sons, Inc.
Chemical effects and surface properties: The nature of an adsorbed complex
Authors: Re Giuseppe Del , Peluso Andrea
Published: January 2005

The general Born–Oppenheimer Hamiltonian of an adsorbate is expressed with reference to an AO basis by means of the second quantization technique, and the part representing the in situ adcomplex (admolecule possibly involving adsorption site atoms) is decomposed so as to show how contributions of different effects can be separated. A basic reference Hamiltonian of the adcomplex is defined, and the suggestion is made that it essentially represents a molecular system susceptible of treatment in terms of ordinary localized bonds. This suggestion is shown to be valid for one thing in the highly unsaturated surface complex FeCO (compared with Fe5CO), provided maximum‐localization hybrids are used as elements of the AO basis. The example treated has also been used to show how two kinds of effects can be introduced and discussed: inductive effects, which appear to result from hybridization and from feedback compensations to charge shifts, and charge transfer between the adcomplex and the surface. The proposed local (chemical) description of an adcomplex appears to be an extremely useful tool for describing such complex adsorbates as those associated with Fischer‐Tropsch catalysts. © 1994 John Wiley & Sons, Inc.
Quadrupole and octupole Cauchy moments of the atoms through argon
Authors: Bartolotti Libero J. , Ortiz Luisa , Xie Qingshan
Published: January 2005

Quadrupole and octupole Cauchy moments of the atoms through argon are calculated using the hydrodynamic formulation of time‐dependent Kohn–Sham theory. The exchange‐correlation energy density functional is approximated by a gradient expansion for atoms that has an explicit dependence upon the number of electrons. The first‐order corrections to the Kohn–Sham amplitudes and phases are found by seeking variational solutions of the derived sequential set of functionals. The trial functions employed contain both linear and nonlinear variational parameters and are thus flexible enough to provide rapid convergence to the multipole polarizabilities. The resulting Cauchy moments provide information that allows the calculation of various properties that result from the linear interaction of atoms with a time‐varying electric field. © 1994 John Wiley & Sons, Inc.
On the use of explicitly correlated functions in variational computations for small molecules
Authors: Rychlewski Jacek
Published: January 2005

The explicitly correlated wave functions used in variational molecular calculations are reviewed. Different types of such functions are considered. The state of art and future perspectives are briefly discussed. © 1994 John Wiley & Sons, Inc.
Structure of the ammonia dimer studied by density functional theory
Authors: Zhu Tianhai , Yang Weitao
Published: January 2005

Self‐consistent Kohn–Sham density functional calculations have been carried out to study the structure of the ammonia dimer. The local‐density approximation yields unusually large binding energy and short internitrogen distance compared with the experimental and more accurate theoretical data. The results from the Becke–Perdew gradient‐corrected functionals are generally in good agreement with those at the SCF MP2 level when the geometry is fully optimized with various large basis sets. With our best estimation, the staggered quasi‐linear structure (Cs) is 0.6 kcal/mol lower in energy than the symmetric cyclic one (C2h). The hydrogen‐bonded N—H bond in the staggered quasi‐linear structure is found to be 0.008 Å longer than the N—H bond in ammonia. In our calculations, we could not find the minima on the energy surface corresponding to the two asymmetric cyclic structures suggested by microwave spectra and coupled pair functional calculations. © 1994 John Wiley & Sons, Inc.
Feynman path integral representation for many‐fermion interacting systems
Authors: Calamante F. , Bochicchio R. C. , Grinberg H.
Published: January 2005

A many‐fermion interacting system is investigated within the scenario of the Feynman path integral representation of quantum mechanics. Short‐time propagator algorithms and a basis set, closely related to the coherent states, are used to obtain the many‐body analytic propagator. A second‐quantized Hamiltonian involving a restricted set of two‐body interactions and the whole set of Coulomb interactions are separately and shown to lead to an exact and an approximate propagator, respectively. In the latter case, use of a grand canonical ensemble allows the grand partition function and the density operator matrix to be readily obtained. No further approximations are required in the calculation of the trace of the evolution operator involved in the evaluation of statistical expectation values. © 1994 John Wiley & Sons, Inc.
Brueckner coupled cluster response functions
Authors: Koch Henrik , Kobayashi Rika , Jørgensen Poul
Published: January 2005

A derivation of the linear response function for the Brueckner coupled cluster method is presented that enables the calculation of second‐order molecular properties such as frequency‐dependent polarizabilities. By using the Brueckner orbital variant of coupled cluster theory, the spurious pole structure inherent in the standard coupled cluster approach with orbital relaxation is avoided. © 1994 John Wiley & Sons, Inc.
A new single‐center method to compute molecular integrals of quantum chemistry in slater‐type orbital basis of functions
Authors: Bouferguene A. , Rinaldi D.
Published: January 2005

The present work is dedicated to the introduction of a new single‐center expansion method derived from the Barnett and Coulson approach leading to reliable numerical algorithms. The basic concept lies in the use of the integral representations of the modified Bessel functions Iλ+1/2 and Kλ+1/2, rather than employing their closed analytical expressions that are known to involve large numbers that usually make the numerical calculation worthless. It is applied to two‐center overlap and Coulomb integrals as well as to three‐center nuclear attraction integrals useful in density functional theory. © 1994 John Wiley & Sons, Inc.
Quasi‐Spin and the pseudo‐orthogonal group in the hubbard model
Authors: Gould M. D. , Paldus J. , čížek J.
Published: January 2005

In this article, we demonstrate a complementarity between the quasi‐spin SU(2) algebra of the Hubbard model and the pseudo‐orthogonal group O(m,m), where n = 2m is the number of lattice sites. It is shown that all N‐electron states for the one‐dimensional Hubbard model, corresponding to given values of spin and quasi‐spin, give rise to an irreducible representation of O(m,m). Moreover, the cyclic group Cn symmetry of the Hamiltonian is investigated and the O(m,m) ↓ Cn branching rules are determined with the use of the U(n) q‐dimension formula. © 1994 John Wiley & Sons, Inc.
End (electron nuclear dynamics) with the hydrogen molecule used as a model problem
Authors: Pohl Anna , Taylor Hugh , Calais Jean‐Louis
Published: January 2005

The method of electron nuclear dynamics (END) developed by Öhrn and Deumens has been applied to the coupling of electronic structure and vibrational motion in the hydrogen molecule with the aim of elucidating and illustrating the characteristic features of this method. © 1994 John Wiley & Sons, Inc.
Ab initio CI calculations on benzene with an extended basis set
Authors: Yamamoto Yuichi , Noro Takeshi , Ohno Kimio
Published: January 2005

An extended basis set of triple zeta plus polarization quality is employed to carry out configuration interaction (CI) calculations of the three lowest singlet and triplet excited states of benzene. The CI calculation is carried out by taking into account single and double excitations of π and σ electrons. In the CI, composite natural orbitals (CNOs), which are constructed from the natural orbitals of the ground state of ethylene, are used as virtual orbitals. The aim of using CNOs is to reduce the number of virtual orbitals to be used in constructing configuration‐state functions, thus cutting down CI dimensions without losing reasonable accuracy. The excitation energies resulting from the CI are in fairly good agreement with experiment. The root mean square of the deviation is 0.22 eV for the six calculated energies and the largest disagreement is 0.37 eV for the third singlet excited state. To obtain better excitation energies by an ab initio calculation, it seems likely that we need to take into account more electron correlation than in the present calculation. © 1994 John Wiley & Sons, Inc.
The helium atom in its ground state embedded in strong magnetic fields
Authors: Rivas‐Silva J. F.
Published: January 2005

The helium atom in its ground state, subject to strong magnetic fields, is treated using a variational method. Trial functions consisting of Gaussians with nonlinear parameters variationally optimized are used. The form of these functions is a generalized s‐symmetry‐state properly modified to admit spatial deformation along the direction on which the magnetic field is applied. © 1994 John Wiley & Sons, Inc.
Path integral approach to correlation energy
Authors: Kawabe H. , Nishikawa K. , Aono S.
Published: January 2005

The Feynman path integral method is applied to the many‐electron problem of quantum chemistry. We begin with investigating the partition function of the system in question; then, “a classical path of electron” that corresponds to the Hartree–Fock approximation is obtained by minimizing the thermodynamic potential of the system with respect to the electron coordinate. The next‐order approximation is obtained by evaluating the deviation from this classical path, which is approximately written by an easily integrable Gaussian integral. The result is expected to be the random‐phase approximation. As numerical examples, the hydrogen molecule and butadiene are treated. © 1994 John Wiley & Sons, Inc.