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  • 11
    Electronic Resource
    Electronic Resource
    The non-N-representability of the Colle-Salvetti second-order reduced density matrix (1993)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 46 (1993), S. 583-587 
    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 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560460406
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  • 12
    Electronic Resource
    Electronic Resource
    Partitioning schemes for the 2-matrix and the pair densityWork supported in part by the Air Force Office of Scientific Research, Office of Aerospace Research, U.S. Air Force, under Grants 68-1544 and 69-1655. (1973)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 7 (1973), S. 837-852 
    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: Several schemes are discussed for partitioning the second-order reduced density matrix Γ into two parts, Γ0 and Γ′.The Γ0s are based on the independent particle model and the Γ′s are corrections due to electron correlation. The difficulties of choosing a Γ0 that will serve as a suitable reference point for studying electron correlation are discussed.In order to compare alternative partitioning schemes, an atomic wave function for the 1S ground state of the Be atom in the configuration-interaction approximation was selected. A fifty-two configuration wave function was computed and contour graphs were made of the total pair density Γ(1 2) and of the “correlation pair density” Γ′(1 2) for several choices of the reference Γ0.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560070502
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  • 13
    Electronic Resource
    Electronic Resource
    Density and density matrix from optimized linearly independent product basis functions for Be (1988)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 34 (1988), S. 43-49 
    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 density matrix was computed from the density using basis orbitals which form linearly independent products (LIP). Calculations were performed on the Be atom using LIP bases containing several of the natural spin orbitals from an accurate nonrelativistic 650-term configuration interaction (CI) wavefunction. Calculations were also performed using a basis set of 6 s-type orbitals optimized so that the lowest eigenvalue, d1, of the overlap matrix of products is maximized and the energy of a small CI wavefunction is minimized. The value of d1 in the optimized basis is 1 × 10-7. The density and the potential energy obtained from the 650-term CI wavefunction were accurately reproduced by the density matrix expressed in the optimized LIP basis, but the kinetic energy was somewhat less accurate.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560340809
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  • 14
    Electronic Resource
    Electronic Resource
    Examination of the limits of accuracy of the extended Koopmans' theorem ionization potentials into excited states of ions of liH, He2, and Li2 (1994)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 52 (1994), S. 309-314 
    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: A comparison is made between the ionization potentials (IPS) calculated by the extended Koopmans' theorem (EKT) and by taking energy differences (ΔCI) from configuration interaction calculations in the same basis. Several ionization potentials were calculated for LiH, He2, and Li2. The best ΔIP, the difference between the EKT IP and the corresponding ΔCI value, was 0.05 meV for the 2σ orbital for LiH and 83.5 meV for the 3σ orbital. The ΔIPS for He2 were 0.7 meV for the 1σu orbital, 6 eV for the 2σu orbital, 5 meV for the 2σg orbital, and 3 eV for the 3σg orbital. The ΔIPS for Li2 are 0.1 meV for 2σg, 53 meV for 3σg, 0.6 meV for 2σu, and 1.73 eV for 3σu. © 1994 John Wiley & Sons, Inc.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560520832
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  • 15
    Electronic Resource
    Electronic Resource
    Extended Koopmans' theorem ionization potentials for beryllium atom shake-up transitions (1994)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 49 (1994), S. 649-656 
    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 ionization potentials were calculated for Be using the extended Koopmans' theorem (EKT) using several full configuration interaction (CI) and multiconfigurational-self-consistent-field (MCSCF) wave functions as reference wave functions. The wave functions used account for 89.7-96.7% of the correlation energy. Comparisons are made with experimental values and with δCI values calculated as the difference in energy obtained from CI wave functions for Be and Be+. The best EKT IP differed from the δCI value by 0.0003 eV for the lowest IP and by 0.0006 eV for ionization into the lowest 2P state of Be+. A calculation of ionization into the second 2P state of Be+ requires diffuse orbitals that are unimportant in the wave function for the ground state of Be. This results in small natural orbital occupation numbers for natural orbitals needed in the EKT calculation. © 1994 John Wiley & Sons, Inc.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560490510
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  • 16
    Electronic Resource
    Electronic Resource
    Extended Koopmans' theorem: Approximate ionization energies from MCSCF wave functions (1992)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 13 (1992), S. 1004-1010 
    Details
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The extended Koopmans' theorem has been implemented using multiconfigurational self-consistent field wave functions calculated with the GAMESS, HONDO, and SIRIUS programs. The results of illustrative calculations are presented for the molecules HF, H2O, NH3, CH4, N2, CO, HNC, HCN, C2H2, H2CO, and B2H6. The lowest extended Koopmans' theorem ionization potentials agree well within the experimental values and the ionization potentials representing excited states of the ions show some improvements over the Koopmans' theorem values in most cases. The extended Koopmans' theorem is easily implemented and the time required to calculate the ionization energies is insignificant compared to the time required to calculate the wave function of the un-ionized molecule. © 1992 by John Wiley & Sons, Inc.
    Additional Material: 11 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540130811
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  • 17
    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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  • 18
    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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  • 19
    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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