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  • 1
    Electronic Resource
    Electronic Resource
    Analysis of electron interaction and atomic shell structure in terms of local potentials (1994)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 101 (1994), S. 8955-8963 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The Kohn–Sham potential vs of an N-electron system and the potential veff of the Euler–Lagrange equation for the square root of the electron density are expressed as the sum of the external potential plus potentials related to the electronic structure, such as the potential of the electron Coulomb repulsion, including the Hartree potential and the screening due to exchange and correlation, a potential representing the effect of Fermi–Dirac statistics and Coulomb correlation on the kinetic functional, and additional potentials representing "response'' effects on these potentials. For atoms several of these potentials have distinct atomic shell structure: One of them has peaks between the shells, while two others are step functions. In one of those step functions the steps represent characteristic shell energies. Examples of the potentials extracted from the optimized potential model (OPM) are presented for Kr and Cd. Correlation potentials, obtained by subtracting the exchange potential of the OPM from (nearly) exact Kohn–Sham potentials, are discussed for Be and Ne.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.468024
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  • 2
    Electronic Resource
    Electronic Resource
    Correlation energy density from ab initio first- and second-order density matrices: A benchmark for approximate functionals (1995)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 103 (1995), S. 10085-10094 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A procedure has been proposed to construct numerically the exchange-correlation εxc(r) and correlation εc(r) energy densities of density functional theory using the correlated first- and second-order density matrices from ab initio calculations. εc(r) as well as its kinetic and potential components have been obtained for the two-electron He atom and H2 molecule. The way various correlation effects manifest themselves in the form of εc(r) has been studied. The εc(r) have been compared with some density functional local and gradient-corrected models εcmod(r). The investigation of the shape of the model energy densities εcmod(r) has been extended to the Be2 and F2 molecules and the corresponding correlation energies Ec have been calculated and discussed for a number of atomic and molecular systems. The results show the importance of a proper modeling of εc(r) in the molecular bond midpoint region. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.469911
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  • 3
    Electronic Resource
    Electronic Resource
    Molecular exchange-correlation Kohn–Sham potential and energy density from ab initio first- and second-order density matrices: Examples for XH (X=Li, B, F) (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 104 (1996), S. 8535-8545 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The molecular Kohn–Sham exchange-correlation potential vxc and the energy density εxc have been constructed from ab initio first- and second-order density matrices for the series XH (X=Li, B, F). The way various effects of electronic structure and electron correlation manifest themselves in the shape of vxc and εxc has been analyzed by their decomposition into various components; the potential of the exchange-correlation hole, the kinetic component and (in the case of vxc) the "response'' component. The kinetic energy of noninteracting particles Ts, the kinetic part of the exchange-correlation energy Tc, and the energy of the highest occupied molecular orbital εN have been obtained with reasonable accuracy and the effect of bond formation on these functionals has been studied. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.471602
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  • 4
    Electronic Resource
    Electronic Resource
    CNDO-S2—a semiempirical SCF MO method for transition metal organometallics (1987)
    Springer
    Theoretical chemistry accounts 72 (1987), S. 211-222 
    Details
    ISSN: 1432-2234
    Keywords: S2 terms in CNDO ; Transition metal compounds
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract A new semiempirical SCF MO procedure available for prediction of the transition metal compounds energy and geometry is developed. The procedure takes an explicit account of the orthogonality of the basis set in the calculation of the core-Hamiltonian elements. A new formula for the resonance integral used in CNDO-S2 gives a physically correct treatment of diffuse orbital-localized orbital interaction. The parametrization for atoms H, C, N, O and Ni is presented, with one-center empirical parameters only used. The results of CNDO-S2 energy and geometry calculations performed for a number of organic compounds and some nickelorganics are compared with the experimental data. The average absolute errors for the binding energies of organic compounds and nickel complexes are 6.6 kcal/mol and 9.3 kcal/mol respectively.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00527664
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  • 5
    Electronic Resource
    Electronic Resource
    Electron correlation effects on the shape of the Kohn–Sham molecular orbital (1997)
    Springer
    Theoretical chemistry accounts 96 (1997), S. 44-50 
    Details
    ISSN: 1432-2234
    Keywords: Key words: Electronic structure theory of atoms and molecules ; Density functional theory ; One-electron model ; Local kinetic energy and effective one-electron potential ; Local effect of exchange and Coulomb correlation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract. Even systems in which strong electron correlation effects are present, such as the large near-degeneracy correlation in a dissociating electron pair bond exemplified by stretched H2, are represented in the Kohn–Sham (KS) model of non-interacting electrons by a determinantal wavefunction built from the KS molecular orbitals. As a contribution to the discussion on the status and meaning of the KS orbitals we investigate, for the prototype system of H2 at large bond distance, and also for a one-dimensional molecular model, how the electron correlation effects show up in the shape of the KS σ g orbital. KS orbitals φHL and φFCI obtained from the correlated Heitler-London and full configuration interaction wavefunctions are compared to the orbital φLCAO, the traditional linear combination of atomic orbitals (LCAO) form of the (approximate) Hartree-Fock orbital. Electron correlation manifests itself in an essentially non-LCAO structure of the KS orbitals φHL and φFCI around the bond midpoint, which shows up particularly clearly in the Laplacian of the KS orbital. There are corresponding features in the kinetic energy density t s of the KS system (a well around the bond midpoint) and in the one-electron KS potential v s (a peak). The KS features are lacking in the Hartree-Fock orbital, in a minimal LCAO approximation as well as in the exact one.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002140050202
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  • 6
    Electronic Resource
    Electronic Resource
    Step structure in the atomic Kohn-Sham potential (1995)
    Springer
    The European physical journal 33 (1995), S. 229-238 
    Details
    ISSN: 1434-6079
    Keywords: 31.20.Sy ; 31.20.Tz
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this work we analyze the exchange-correlation potentialv xc within the Kohn-Sham approach to density functional theory for the case of atomic systems. The exchange-correlation potential is written as the sum of two potentials. One of these potentialsv xc,scr is the long-range. Coulombic potential of the coupling constant integrated exchange-correlation hole which represents the screening of the two-particle interactions due to exchange-correlation effects. The other potentialv xc,scr resp contains the functional derivative with respect to the electron density of the coupling constant integrated pair-correlation function representing the sensitivity of this exchange-correlation screening to density variations. As explicit expression of the exchange-part of this functional derivative is derived using an approximation for the Greens function of the Kohn-Sham system and is shown to display a distinct atomic shell structure. The corresponding potentialv xc,scr resp has a clear step structure and is constant within the atomic shells and changes rapidly at the atomic shell boundaries. Numerical examples are presented for the Be and Kr atoms using the Optimized Potential Model (OPM).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01437503
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  • 7
    Electronic Resource
    Electronic Resource
    Structure of the optimized effective Kohn - Sham exchange potential and its gradient approximations (1996)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 57 (1996), S. 17-33 
    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 analysis of the structure of the optimized effective Kohn-Sham exchange potential vx and its gradient approximations is presented. The potential is decomposed into the Slater potential vs and the response of vs to density variations, vresp. The latter exhibits peaks that reflect the atomic shell structure. Kohn - Sham exchange potentials derived from current gradient approaches for the exchange energy are shown to be quite reasonable for the Slater potential, but they fail to approximate the response part, which leads to poor overall potentials. Improved potentials are constructed by a direct fit of vx with a gradient-dependent Padé approximant form. The potentials obtained possess proper asymptotic and scaling properties and reproduce the shell structure of the exact vx. © 1996 John Wiley & Sons, Inc.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Direct approximation of the long- and short-range components of the exchange-correlation Kohn-Sham potential (1997)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 61 (1997), S. 231-243 
    Details
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An approximation scheme was developed for the Kohn-Sham exchange-correlation potential vxcσ, making use of a partitioning of vxcσ into a long-range screening vscrσ and a short-range response vresp component. For the response part, a model vmodrespσ was used, which represents vresp as weighted orbital density contributions, the weights being determined by the orbital energies. vmodrespσ possesses the proper short-range behavior and the atomic-shell stepped structure characteristic for vresp. For the screening part, two model potentials vmodscrσ were used, one with the accurate Slater potential; the other one with the generalized gradient approximation (GGA) for the exchange part. Both use the GGA for the Coulomb correlation contribution to vscrσ. The scheme provides an adequate approximation to vxcσ in the outer-valence region with both the proper asymptotics and a rather accurate estimate of the ionization potential from the highest one-electron energy and a reasonable estimate of atomic Exc and total energies Etot. © 1997 John Wiley & Sons, Inc.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    On the optimal mixing of the exchange energy and the electron-electron interaction part of the exchange-correlation energy (1996)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 60 (1996), S. 1375-1384 
    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 optimal mixing coefficient C of the exchange energy Ex and the electron-electron interaction part of the exchange-correlation energy W1xc in the formula for the total exchange-correlation energy Exc was expressed through the ratio of the kinetic Tc and potential Wc contributions to the correlation energy Ec. This expression can be derived from a Heavyside step function model of the dependence of Wλxc on the coupling parameter of the electron interaction λ. Values of Tc and Wc obtained from ab initio wave functions were used to estimate C for a number of atoms and molecules. A strong dependence of Tc, Wc, and C on the bond distance was demonstrated for the case of the H2 molecule. Tc and C approach zero in the bond-dissociation limit; so for an electron-pair bond, the admixing of exact exchange to obtain an accurate Exc is strongly dependent on the bond length and has to disappear for weak interaction/large bond distances. The potential of the exchange-correlation hole constructed for H2 from an ab initio second-order density matrix was compared with its generalized gradient approximation (GGA). © 1996 John Wiley & Sons, Inc.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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