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  • 1
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Journal of the American Chemical Society 92 (1970), S. 5761-5764 
    ISSN: 1520-5126
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1520-5126
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 103 (1995), S. 6556-6561 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Approximate generalized overlap amplitudes (GOAs), also called Feynman–Dyson amplitudes, have been calculated from a full configuration interaction (CI) wave function for the ground state of beryllium using the extended Koopmans' theorem (EKT). The GOAs were also calculated from the ground state CI wave function for Be and the ground state and excited state CI wave functions for Be+. The EKT GOAs are nearly identical to the corresponding CI GOAs for the lower 2S states of Be+ and for the Be+ 1s2s2 state which has a large GOA occupation number. There are many CI GOAs for which there is not a corresponding EKT GOA. This may be due in part to the limited size of the basis set and to the inability to include natural spin orbitals with small occupation numbers in the EKT calculations. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Journal of chemical information and modeling 24 (1984), S. 271-275 
    ISSN: 1520-5142
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 99 (1993), S. 6221-6221 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Recent systematic, numerical calculations by Sundholm and Olsen [J. Chem. Phys. 98, 3999 (1993)] support the proof that the lowest ionization potential can in principle be obtained exactly using the extended Koopmans' theorem. Because of the nature of their calculations it cannot be concluded that only the lowest ionization potential could be obtained exactly using the extended Koopmans' theorem.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 96 (1992), S. 3718-3722 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The extended Koopmans' theorem (EKT) is shown to give accurate and potentially exact values for the lowest ionization potential (IP). Accurate results are reported for LiH, H+5, He2, and Li2. Results obtained for the lowest IP's of LiH and He2 are nearly identical with those obtained by taking the difference of the total energies from separate, full configuration interaction calculations on the N-electron and the (N−1)-electron systems. The differences between the two IP calculations for a series of increasingly larger basis sets are 0.0017, 0.0004, and 0.0001 eV for LiH and are 0.0154, 0.0018, and 0.0007 eV for He2. The implication is that the lowest IP can be calculated to arbitrary accuracy. The EKT method is easily implemented as part of a multiconfigurational self-consistent-field calculation by diagonalizing the matrix of Lagrange multipliers with the first-order reduced density matrix as the metric.
    Type of Medium: Electronic Resource
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  • 7
    ISSN: 1432-2234
    Keywords: Reduced density matrices ; Natural orbitals ; Extended Koopmans' theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary The completeness of the natural orbitals with nonzero occupation numbers is examined for several model Hamiltonians and for the helium atom. It is demonstrated that whether the occupied natural orbitals form complete sets depends on the nature of the electron-electron interaction in the model Hamiltonian. Discrepancies in the extant proofs of the exactness and inexactness of the extended Koopmans' theorem are resolved.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 60 (1996), S. 421-431 
    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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  • 9
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 39 (1991), S. 823-837 
    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 entropy of an electronic system is defined in terms of the Husimi function, a nonnegative distribution function in phase space. The Husimi function is calculated by maximizing the entropy subject to the constraints that the Husimi function give a Gaussian convolution of the desity when integrating over the momentum coordinates and that its second moment with respect to momentum give a sum of Gaussian convolutions of the density and the kinetic energy density. The result is compared with the Wigner function. Equations are given for calculating the density matrix from the Husimi function. The resulting equation for the exchange energy requires a difficult numerical integration. An alternate method is used to obtain the density matrix from an approximate partially collapsed Husimi matrix that gives the maximum entropy Husimi function as its diagonal. The results are exact for the harmonic oscillator ground state. Exchange energies calculated for H and the He isoelectronic series through C+4 show slight improvements over those calculated using a maximum entropy Wigner function.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 38 (1990), S. 819-830 
    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 Wigner distribution function and the corresponding density matrix are calculated using a form for the distribution function suggested by maximization of the entropy. Wigner functions and density matrices are determined by imposing conditions of idempotency on the density matrix. Exchange energies and Compton profiles calculated from density matrices obtained by imposing the idempotency constraints are compared with the results of calculations using the Hartree-Fock density matrix and a Gaussian approximation for the density matrix for H and the noble gases He through Xe. Compton profiles from Wigner functions with idempotency constraints show improvements over the Gaussian approximation for the lighter atoms, but do not show significant changes for the heavier atoms. Exchange energies from density matrices with idempotency constraints show improvements over the Gaussian approximation except for the heavier atoms Kr and Xe.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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