bluuebunny/crossref_metadata_2025_split huggingface dataset:
Quantum dynamics of wave packets on phase space cells in nonlinearly coupled oscillators
Authors: Brickmann Jürgen , Schmidt Peter C. 
Published: December 2004

AbstractThe time evolution of harmonic oscillator coherent states (minimum uncertainty wave packet) | Ψμ located on regular and random von Neumann lattice points in phase space is analyzed for nonlinearly coupled anharmonic vibrational systems. The Henon–Heiles system is studied as an example. A quasiprobability measure \documentclass{article}\pagestyle{empty}\begin{document}$ \bar P_{\mu \mu '} $\end{document} is introduced to investigate the relative probabilities for the transition between phase space cells within a narrow energy range. The probability \documentclass{article}\pagestyle{empty}\begin{document}$ \bar P_{\mu \mu '} $\end{document}, as well as the information entropy Sμ, is studied as a function of energy. A smooth transition from regular to chaotic motion is found indicated by a change of the fluctuations of these quantities as a function of energy.
Chemical potential for harmonically interacting particles in a harmonic potential
Authors: Phillips Philip , Davidson Ernest R. 
Published: December 2004

AbstractThe chemical potential μ, as it appears in density functional theory, is examined extensively for harmonically interacting spin‐½ fermions in three dimensions. For this system the energy and chemical potential are discontinuous functions of the particle number if the most straightforward equation is used to define the energy for a noninteger particle number.
Two‐Dimensional fully numerical solutions of molecular Schrödinger equations. II. Solution of the Poisson equation and results for singlet states of H2 and HeH+
Authors: Laaksonen Leif , Pyykkö Pekka , Sundholm Dage 
Published: December 2004

AbstractTwo‐dimensional fully numerical solutions of the Hartree–Fock problem are reported for the singlet ground states of H−, He, H2, and HeH+. The H2 energy at R = 1.4 a.u. is −1.13362957 a.u.
Structure of dislocation cores in the silicon crystal
Authors: Altmann S. L. , Lapiccirella A. , Lodge K. W. 
Published: December 2004

AbstractWe have recently produced a Lifson–Warshel force field for the silicon crystal. This field, that goes further than the harmonic approximation, is particularly adapted for the calculation of defect structures. It requires five free parameters, but one of them in the field already produced, the linear bending term, is significant for the perfect lattice structure only and should be eliminated in dealing with defect structures. Also, one of the fixed parameters can be adjusted to fit precisely the experimental value of the stacking fault energy. We show that an excellent fitting of the phonon dispersion curves, in the least squares sense, is obtained with the parameters thus changed. We illustrate the use of this field in discussing the problem of reconstruction of the 90° partial dislocation in silicon.
Nonlinear Schrödinger‐type field equation for the description of dissipative systems. II. Frictionally damped motion in a magnetic field
Authors: Schuch D. , Chung K.‐M. , Hartmann H. 
Published: December 2004

AbstractWith the aid of a method similar to the one we used in an earlier work (part I) a new Schrödinger‐type field equation with logarithmic nonlinearity can be derived from a Fokker–Planck equation for a distribution function. This nonlinear field equation describes the frictinally damped motion of a system under the influence of a magnetic field and can be interpreted in the same way as the nonlinear Schrödinger‐type equation (NLSE) derived in part I, where no magnetic fields were taken into account. The NLSE for the two‐dimensional motion of a charged material system in a homogeneous magnetic field is solved exactly. The solutions are compared with the quantum‐mechanical solutions of the corresponding undamped problem. The method is extended to include also anisotropic conditions; i.e., in the Fokker–Plank equation the diffusion constant has to be replaced by a diffusion matrix, as different diffusion constants may be possible for different space directions. We regard the three‐dimensional motion under the combined influence of magnetic and electric fields according to K = (q/c)(v × B) + qE − mγv with Ey = (m/q)ωy, Ez = −(m/q)ωz, B = (0, 0, B) as an example. This is an approximation of the conditions existing in an ion cyclotron resonance spectrometry cell, neglecting an additional drift motion in the x direction which could be taken into account by Galilean transformation and gauge transformation. The corresponding NLSE for the coupled three‐dimensional motion is specified and solved exactly.
Spherical tensor theory of long‐range interactions between two molecules
Authors: Piecuch Piotr 
Published: December 2004

AbstractThe Rayleigh–Schrödinger perturbation treatment can be applied in the quantum mechanical study of long‐range interactions between molecules, when we can assume that the molecular charge distributions do not overlap. In these cases the multipole expansion is a good approximation of real interaction potential and can be treated as a perturbation. In this paper we obtain closed expressions for the anisotropic long‐range interaction energy between two molecules in all orders of the perturbation, using spherical tensor formalism. Then we show how spherical multipoles and polarizabilities of the isolated molecules can be inserted into general formulas for interaction energy.
Unitary group approach to the many‐electron problem. II. Adjoint tensor operators for U(n)
Authors: Gould M. D. , Chandler G. S. 
Published: December 2004

AbstractIn this paper we present a derivation of the U(n) adjoint coupling coefficients for the representations appropriate to many‐electron systems. Since the states of a many‐fermion system are to comprise the totally antisymmetric Nth rank tensor representation of U(2n), the work of this paper enables the matrix elements of the U(2n) generators to be evaluated directly in the U(n) × U(2) (i.e., spin orbit) basis using their transformation properties as adjoint tensor operators. A connection between the adjoint coupling coefficients, as derived in this paper, and the matrix elements of certain (spin independent) two‐body operators is also presented. This indicates that in CI calculations, one may obtain the matrix elements of spin‐dependent operators from the known matrix elements of certain spin‐independent two‐body operators. In particular this implies a segment‐level formula for the matrix elements of the U(2n) generators in the spin‐orbit basis.
Localized molecular orbitals for multiple bonds in the ZDO approximation: The σ‐π vs. banana bonds dilemma
Authors: Paniagua Juan Carlos , Moyano Albert , Tel Luis María 
Published: December 2004

AbstractThe multiple bond description supplied by localized molecular orbitals obtained within the ZDO approximation is analyzed. In particular, conditions for the appearance of σ‐π separation and of continuous degeneracy of the localization sum against σ‐π mixing are given for two current ZDO energy‐ and density‐localization methods. Likewise, a convenient modification of the latter is presented together with some illustrative examples.
Motion of a particle in a ring‐shaped potential: An approach via a nonbijective canonical transformation
Authors: Kibler Maurice , Negadi Tidjani 
Published: December 2004

AbstractThe problem of a particle in the three‐dimensional ring‐shaped potential ησ2(2a0/r − ηa/r2 sin2 θ)ε0 introduced by Hartmann is transformed into the problem of a coupled pair two‐dimensional harmonic oscillators with inverse quadratic potentials by using a nonbijective canonical transformation, viz., the Kustaanheimo–Stiefel transformation. The energy E of the levels for the ring‐shaped potential is obtained in a straightforward way from the one for the two‐dimensional potential — (4Eρ2 + η2σ2a ε0/ρ2).
Multibody analysis of potential energy surfaces for first‐ and second‐row tetramers. I. The tetrahedral structures of P4 and N4
Authors: Novaro O. , Castillo S. 
Published: December 2004

AbstractSCF calculations using a split‐valence basis set were carried out for N3, P3, N4, and P4 showing that there are substantial structural differences between the clusters of these elements, nitrogen and phosphorus. An analysis of the nonadditive three‐ and four‐body contributions to the binding energies of these systems is carried out and shown to be quite close to the values predicted from qualitative considerations by Murrell [Chem. Phys. Lett. 55, 1 (1978)].
Interaction between photons, “trapped electron” and vibronic excitation
Authors: Mishra R. K. , Dubey S. K. , Tyagi R. S. 
Published: December 2004

AbstractThe role of “trapped electron,” photon, and vibronic state coupling has been worked out in relation to an aspect of cancer, namely, to the activity of an anticancer drug. The main emphasis for such study comes from the fact that in cancerous systems the participation of usual electronic states of the molecule may not be sufficient. Because of disorder in the cancer tumour, additional states, viz. trapped electron states, could be formed in the manner of localised states in solids. The drug activity of mitomycin C obtained in this way agrees with the experimental values. An additional feature of the study is that it shows that it will be effective mainly in the initial phases of cancer.
A theoretical investigation of electron correlation and relaxation in organometallic polymers
Authors: Böuhm Michael C. 
Published: December 2004

AbstractThe importance of many‐body interactions beyond the mean‐field approximation of the Hartree–Fock (HF) self‐consistent‐field crystal orbital formalism is analyzed in one‐dimensional (lD) transition‐metal (3d) polymers with extended organic π ligands. The correlation energies are expressed in a quasiparticle picture. They are divided into long‐range contributions that are coordinated with the basis of spatially uncorrelated Bloch orbitals and into short‐range correlations derived for local rearrangement processes that are described in terms of a one‐electron basis which breaks the translational symmetry of the lD system. Both contributions (long‐range and short‐range correlations) are fragmented into elements of physical significance (hole and electron self‐energies for the former interactions; relaxation, pair‐relaxation and pairremoval terms for the local virtual excitations). The magnitude of these elements is analyzed as a function of the characters of the one‐electron states in the HF bands, the occupation patterns at the 3d centers, the available particle and hole channels in the elementary fluctuations and the energies and shapes of the various bands. The broad spectrum of possible amplifications and compensations leading to the quasiparticle shifts in metallomacrocycles is discussed. The different mechanisms to change the dispersions and to modify the width of the ϵ(k) curves are studied. It is shown that electron correlation and relaxation in transition‐metal polymers can lead even to a broadening of the energy bands. This behavior is in contrast to the influence of many‐body effects in simpler homogeneous materials where electron correlation is in any case accompanied by a narrowing of the dispersions (i.e., detraction of the group velocities of particles and holes). Possible modifications in the shapes of the one‐particle curves and the quasiparticle bands are also considered in the text [transition from a “normal ϵ(k) dispersion” to an energy band with a negative slope as a result of electron correlation]. Simplified formulas are derived that allow for a rough assessment of the various correction terms even in structurally complicated transition‐metal stacks with extended organic ligands. The approximate relations are used to correct the HF band structures of complex onedimensional metallomacrocycles as well as simpler crystalline materials by means of the quasiparticle approximation.
Structure of the electronic energy bands of molecular crystal NMP‐TCNQ
Authors: Qi‐Yuan (Q. Y. Zhang) Zhang , Ji‐Min (J. M. Yan) Yan 
Published: December 2004

AbstractThe electronic energy band of the molecular crystal NMP‐TCNQ is calculated by means of the EHMO/LCAO‐MO‐CO method. In the calculation, both NMP and TCNQ are treated as quasi‐one‐dimensional columns, respectively. The results demonstrate that (i) the positions of the electronic energy bands of a molecular crystal are determined by that of the corresponding molecular orbitals of the respective isolated molecules; (ii) the widths of energy bands are determined by the interaction between the molecular orbitals of adjacent molecules in the crystal. These facts support the conclusion which we have given in the previous articles. The relationship between the structure of energy bands of the crystal NMP‐TCNQ and its electrical conductivity at room temperature is discussed and compared with the crystal TTF‐TCNQ. The differences of electrical conductivities of both crystals can be explained by the formula given by Fröhlich and Sewell.
Potential‐Derived point‐charge model study of electrostatic interaction energies in some hydrogen‐bonded systems
Authors: Ray Naba K. , Shibata Masayuki , Bolis Giorgio , Rein Robert 
Published: December 2004

AbstractMulliken's atomic charges (MC) and potential derived (PD) point charges obtained from STO‐3G wave functions are used to study the electrostatic interaction energies for a series of representative hydrogenbonded complexes. The results of the above‐mentioned models are compared with the more accurate results of segmental multipole moment (SMM) expansion, and it is shown that the PD model is superior to the Mc model. The results of PD model are shown to be well correlated with the results of SMM expansion technique. Results of our calculations using 6‐31G and 6‐31G** PD charges are also reported here. Electrostatic interaction energies obtained using 6‐31G** PD charges are compared with the 6‐31G** SCF interaction energies available for the nine hydrogen‐bonded dimers of ammonia, water, and hydrogen fluoride and a good con‐elation between the two is shown. The interrelationship between the results of different basis sets are also examined for the PD point‐charge model. The electrostatic interaction energies obtained using STO‐3G PD model are shown to be well correlated to the results of 6‐31G and 6‐31G** PD models.
Angular aspects of exchange correlation and the fermi hole
Authors: Ugalde J. M. , Boyd Russell J. 
Published: December 2004

AbstractThe complete (nonreduced) αα probability density functions evaluated from the Hartree–Fock and simple Hartree product wavefunctions have been used to elucidate the angular features of spin correlation and the Fermi hole in the 23S state of helium and the ground state of beryllium. This approach shows that the local Fermi holes in these two cases are very similar and that the Fermi hole is essentially spherically symmetric when the reference electron is close to the nucleus. As the reference electron is removed to larger radial distances, appreciable polarization of the Fermi hole is observed. The polarization is greater in the direction of the nucleus than away from the nucleus, contrary to the situation in the Coulomb hole of the helium ground state where the polarization is greater away from the nucleus than toward the nucleus. Several other differences between the He 23S Fermi hole and the He 11S Coulomb hole are noted.
Electronic structures of the π‐π type charge‐transfer complexes of pyridine with boron trihalides
Authors: Ji‐Min(J. M. Yan) Yan , Jian‐Guo (J. G. Zhao) Zhao 
Published: December 2004

AbstractThe electronic structures of the π‐π type complexes of pyridine with boron trihalides have been studied by means of IEHMO calculation. The results indicate that BX3(X = F, Cl, Br, I) tends to react with C5H5N in a planar configurations against the plane of C5H5N. The most stable configurations of complexes are at 60° of orientation angle φ for X = Cl, Br, I, but at 0° for X = F. A linear relationship between In Eb, the logarithm of rotation potential barriers, and the radii of halogen atoms r0 has been observed, and has been deduced from Morse potential function. In the complex, the donating properties of BX3 have an increase from X = F to I, and BF3 functions as an acceptor, but the others as donors. It has been shown that every energy level of the complex is corresponding to that of the donor or the acceptor, which we have discussed by the perturbation theory. The bonds between D and A appear essentially as π‐π type but not pure.
Approximate calculation of lifetimes of resonance states in the continuum from real stabilization graphs
Authors: Löwdin Per‐Olov 
Published: December 2004

AbstractSimons has previously derived a simple formula for the linewidth Γ of a resonance state in the continuum from real stabilization graphs under the assumption that the energy curves vary almost linearly near the points of avoided crossing. This formula is now rederived without this restricting assumption under the condition that Γ is still small.
Many‐Electron, multicenter integrals in superposition of correlated configurations method. I. one‐ and two‐electron integrals
Authors: Preiskorn Aleksandra , Żurawski Bronislaw 
Published: December 2004

AbstractThe calculations by means of the superposition of correlated configurations method (Hylleraas‐CI), that is, the combination of configuration interaction with the Hylleraas‐type correlation factors, needs the effective evaluation of some nontrivial integrals. This series of papers gives the formulas for all types of integrals needed for molecular calculations when Gaussian lobe functions are used as a basis set. The formulas for two‐electron integrals are given in the present paper. The preliminary results for two‐electron systems are presented.
The antisymmetrized geminal power approximation to the excitation propagator
Authors: Weiner Brian , Kurtz Henry A. 
Published: December 2004

AbstractA consistent propagator approximation, denoted as the excitation propagator, is introduced. This propagator describes excitations between N‐particle states and its approximation has properties required of consistent random phase approximation schemes. Several properties of this propagator are explored when based on a generalized antisymmetrized geminal power wavefunction. How singularities in the metric occur and how to remove them is discussed in detail. The excitation propagator is also contrasted with the principal (polarization) propagator.
Can nondegenerate many‐body perturbation theory Be applied to quasidegenerate electronic states?
Authors: Kaldor Uzi 
Published: December 2004

AbstractWilson, Jankowski, and Paldus have recently applied nondegenerate many‐body perturbation theory (MBPT) to simple models, in which the degree of quasidegeneracy could be varied continuously, and concluded that the nondegenerate theory was applicable even near degeneracy. The error in their results changes, however, considerably with geometry, leading to an incorrect potential surface. An extension of their calculations shows convergence even at exact degeneracy (square planar H4). It is shown here that the apparently good convergence is due to the suppression of the large (infinite at exact degeneracy) component of the perturbation energy in low order by the way the Hamiltonian is partitioned. This component will, however, resurface at higher orders, leading to slow convergence or even divergence. The low‐order sum of the perturbation series is not very meaningful, depends strongly on details of the zero‐order Hamiltonian, and yields, in general, incorrect potential surfaces. Multireference MBPT eliminates these problems.
A proposed definition of resonant states
Authors: Cisneros Arturo , McIntosh Harold V. 
Published: December 2004

AbstractThe widely cited definition of quantization in terms of square‐integrable wave functions does not apply to continuum wave functions, to such phenomena as metastable states, or many‐body resonances. A better philosophical foundation for quantum mechanics separates the probabilistic aspects based on square integrable Hilbert space functions from the dynamical aspects based upon the solutions of Shroedinger's (or Dirac's) equation. A Hilbert space may have a non‐Hilbert space basis, which may be described by Stieltjes integrals and a spectrum measure. This viewpoint is expounded by reference to a very detailed analysis of a simple model, through which a precise definition of a Bohr–Feshbach resonance can be given. We propose a definition of a “metastable state,” showing that it is consistent with accepted usage, and that it overcomes a series of objections which have been catalogued by Simon. Its rate of decay is given by the Fourier–Stieltjes transform of the spectral density function; it is moreover the longest‐lived initially localized state which can be formed from a small span of energy eigenfunctions near its mean energy.
The relationship between electron densities and the pKa values in a series of methylpyrazines
Authors: Pilarski Bogusław , OśMiałowski Krzysztof 
Published: December 2004

AbstractBased on the literature values, the pK1 and pK2 for pyrazine and its six methyl derivatives, the correlation with electron density on the nitrogen atoms N1 and N4 was found. The effect of methyl group was proved to be additive. The total electron density, π‐electron density, and dipole moments for compounds under study were determined by the CNDO/2‐MO method.
The general analytic expression for S4‐symmetry‐invariant potential functions of tetra‐atomic homonuclear molecules
Authors: Schmelzer A. , Murrell J. N. 
Published: December 2004

AbstractThe potential energy of a homonuclear X4 molecule is an invariant of the atom permutation group S4 acting on the internal coordinates of X4. It is shown by means of invariant theory that six algebraically independent invariants and five additional invariants are required to express the general invariant function for this group. Explicit expressions for these 11 invariants are given.
Theoretical investigation of the Na+ + H2 system. I. Ab initio calculations including electron correlations of potential energy hypersurface
Authors: Jeziorek Danuta , Żurawski Bronisław 
Published: December 2004

AbstractAn ab initio investigation of the potential energy hypersurfaces of the Na+/H2 system is presented. The calculations have been performed on SCF level and with the inclusion of correlation effects by means of the CEPA‐PNO, IEPA‐PNO, and PNO‐CI methods. The basis set consists of gaussian lobes (12s, 8p, d) on Na and (8s, p) on H. The distance of the Na nucleus to the midpoint of H2 was varied between 0.0 and 10 bohrs, whereas the region of HH distances considered was 0.5 to 10 bohrs. The angular dependence of the hypersurface was investigated as well. The system Na+/H2 has an absolute energy minimum for C2v geometry at R equal approximately 5.0 bohrs and rHH = 1.40 bohrs.
Molecular integrals arising in the use of the Hiller–Sucher–Feinberg–Harriman identity for describing the Fermi‐contact interaction
Authors: Ishida Kazuhiro 
Published: December 2004

AbstractGeneral formulas have been derived for molecular integrals arising in the use of the identity derived by Harriman for describing the Fermi‐contact interaction in a molecule. Computational aspects are discussed and numerical examples are shown for several sets of the usual Cartesian Gaussian‐type orbitals.
Collisional transfer of rovibrational energy from quantum calculations. II. The case of LiH with He
Authors: Gianturco F. A. , Palma A. , Lamanna V. T. , Petrella G. 
Published: December 2004

AbstractThe collisional exchange of energy between He atoms and a strongly polar diatomic, the LiH target, has been studied theoretically over a range of relative energies that had been previously sampled by experiments with molecular beams. The relative importance of the rotational and/or vibrational channels is examined by studying in detail the effect of the interaction via a model potential coupling parameter. The different behavior exhibited by differential cross sections (total and partial inelastic) is also analyzed in terms of the strength and shape of the interaction anisotropy.