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  • 1
    Electronic Resource
    Electronic Resource
    Chemical bonding in the hydrogen molecule (1996)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 60 (1996), S. 421-431 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The chemical bond in the hydrogen molecule is examined using the electron density and the generalized overlap amplitudes. Logarithmic derivatives of the electron density provide a clear picture of its behavior in the bonding region as well as in the outer region. The GOA expansion of the density is used to examine the dependence of the rate of decay of the density on the GOA ionization potentials. The increase in the electron density at the nuclei and in the bonding region coincides with the higher ionization potential of H2 over the H atom. The density in the bonding region along the internuclear axis does not decay exponentially, but its shape is very nearly an inverted Gaussian. © 1996 John Wiley & Sons, Inc.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 2
    Electronic Resource
    Electronic Resource
    The extended Koopmans' theorem Fock operatorThis work is in part based on a thesis submitted by J. Mauricio O. Matos to the Department of Physics of the University of Ceará as a requisite to obtaining a master's degree. (1987)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 31 (1987), S. 871-892 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: By expanding the wave function of a system of N particles in terms of products of functions of one and (N-1) particles, the one-particle, nonlocal operator F̂EKT (extended Koopmans' theorem) is determined. It is shown that although this operator is nonhermitian, its eigenvalues and eigenfunctions represent the ionization energies and occupied orbitals, respectively. The eigenfunctions of F̂EKT are the one-particle functions that enter into the expansion of the wave function of the system as partners of the (N-1)-particle wave functions. The eingenvalues are also one-particle energies that, multipled by the orbital occupancy probalities, enter the expression for the total N-particle energy of the system.
    Additional Material: 7 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560310604
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  • 3
    Electronic Resource
    Electronic Resource
    A local one-electron operator for the generalized-overlap amplitudes (1995)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 56 (1995), S. 547-562 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An approach to the N-electron behavior is presented which emphasizes the dynamics of an individual electron. The generalized overlap amplitudes (GOAS), although formally defined by an integration over the coordinates of N - 1 electrons, are, instead, resolved as a column vector, eigenfunction to a local one-electron differential operator. These amplitudes have no restrictions of linear independence between them, but each satisfies the one-electron boundary conditions at the nuclei and at large distances. The one-electron (or charge) density is the sum of the squares of the elements of the column. The energy density, a constant times the one-electron density, maintains this one-to-one relationship throughout modifications in total number of electrons or external potential, although the constant of proportionality, the total energy of the system, may change in the process. Indistinguishability of electrons and antisymmetry is always observed by the dynamics of each electron. A numerical example, the ground state of helium, is presented. © 1995 John Wiley & Sons, Inc.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560560512
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  • 4
    Electronic Resource
    Electronic Resource
    Analysis of density functionals and their density tails in H2 (1998)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 69 (1998), S. 541-550 
    Details
    ISSN: 0020-7608
    Keywords: density functional theory ; long-range behavior ; electron density ; Kohn-Sham ; orbital energy ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The total energy, internuclear distance, vertical ionization potential, and electron density function were determined for the hydrogen molecule (H2) with a configuration interaction calculation, a Hartree-Fock calculation, all 22 density functional theory (DFT) methods built into Gaussian 92/DFT, and the Davidson and Jones natural orbital expansion of the Kolos and Roothaan wave function. These data were used to explore the performance of DFT methods in modeling the chemical bond. We noted that although the vertical ionization potentials suggested by the highest occupied molecular orbital energies of DFT methods are generally quite poor, the medium-range bahavior of the electron density from DFT methods is close to that of more accurately determined electron densities. Accordingly, we propose a method of finding an approximate vertical ionization potential for a density functional calculation from the medium-range behavior of the electron density. We explain why the density functionals' electron densities decay in a manner different from that which their orbital energies lead us to expect and explore the relationship between the errors in the exchange-correlation potentials, electron densities, and the orbital energies.   © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 541-550, 1998
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Generalized overlap amplitudes for the lithium atom (1996)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 57 (1996), S. 355-360 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Generalized overlap amplitudes (GOAS) are calculated between the lithium atom and several states of Li+. An examination of the long-range behavior of the GOAS indicates that they are coupled, appearing to have the same exponential decay at large r. At intermediate distances from the nucleus, the GOAS decay with their unique exponential rate and the decay rates only merge at large r. Although many of the GOAS appear to be similar, their distinctness indicates that they may, in fact, be linearly independent. © 1996 John Wiley & Sons, Inc.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 6
    Electronic Resource
    Electronic Resource
    The extended Koopmans' theorem Fock operator and the generalized overlap amplitude one-electron operator (1996)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 57 (1996), S. 391-399 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The wave function of a system may be expanded in terms of eigenfunctions of the N -1 electron Hamiltonian times one-particle functions known as generalized overlap amplitudes (GOAS). The one-electron operator whose eigenfunctions are the GOAS is presented, without using an energy-dependent term as in the one-particle Green function or propagator approach. It is shown that this operator and the extended Koopmans' theorem (EKT) one-electron operator are of similar form, but perform complementary roles. The GOA operator begins with one-electron densities and total energies of N -1 electron states to generate the two-matrix and total energy of an N-electron state. The EKT operator begins with the two-matrix of an N-electron state to generate one-electron densities and ionization potentials (or approximations thereto) for N -1 electron states. However, whereas the EKT orbitals must be linearly independent, no such restriction applies to the GOAS. © 1996 John Wiley & Sons, Inc.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Analysis of chemical bonding in C2 using Dyson orbitals (1996)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 60 (1996), S. 1623-1631 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Multireference configuration interaction wave functions with single and double excitations were calculated for the 1Σ+g ground state of the C2 molecule and the excited states of C+2 with symmetries 2Σ+g, 2Σ-u, 2Πu, and 2Πg. The corresponding σg, σu, πu, and πg valence Dyson orbitals were calculated. Most of the density due to the valence electrons is accounted for by three σg, one σu, and one degenerate pair of πu Dyson orbitals. Electron correlation plays an important role in the bond strength of C2 by increasing the occupation of the σg valence orbitals and decreasing the occupation of the σu and πu valence orbitals. © 1996 John Wiley & Sons, Inc.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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