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  • 1
    Electronic Resource
    Electronic Resource
    Unambiguous exchange-correlation energy density (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 8161-8167 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: An exact exchange-correlation energy density is constructed using only knowledge of the density dependence of the exchange-correlation energy functional, EXC. The energy density does not depend on the choice of origin, and allows direct comparison between any functional approximation and the exact quantity. The asymptotic behavior of this energy density contains the exact ionization potential. The relative performance of approximation energy functionals is reflected in this energy density, i.e., the local approximation is moderately accurate, generalized gradient approximations work better, while hybrids with exact exchange work best. The intershell spike in atoms is highlighted in this energy density. The energy density can also be calculated for solids, and has implications for many areas of density-functional theory. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.477479
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  • 2
    Electronic Resource
    Electronic Resource
    Two phases of {[CsPH(η6-2,4,6-tBu3C6H2)]2(η3-toluene)0.5}x: their structures and interconversions (2000)
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 56 (2000), S. 210-214 
    Details
    ISSN: 1600-5740
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The solvent-bridged caesium phosphide {[CsPH(η6-2,4,6-tBu3C6H2)]2(η3-toluene)0.5}x, catena-[(μ-η3-toluene)-bis[caesium(2,4,6-tri-tert-butylphenylphosphide)]], undergoes a reversible solid-state, order–disorder phase transition characterized by the doubling of the unit-cell volume at low temperature achieved by doubling one unit-cell vector. The unit-cell parameters at 293 (2) K (form A) are: a = 11.147 (4), b = 14.615 (4), c = 14.806 (5) Å, α = 70.57 (3), β = 71.85 (3), γ = 72.93 (2)°, V = 2112.5 (12) Å3, Z = 2, ρcalc = 1.362 g cm−3, R1 = 0.0513 for 5462 reflections, wR2 = 0.0947 for all data. The unit-cell parameters at 173 (2) K (form B) are: a = 14.6241 (3), b = 14.7393 (3), c = 22.0720 (4) Å, α = 72.2117 (7), β = 73.3659 (8), γ = 70.2953 (7)°, V = 4174.8 (2) Å3, Z = 4, ρcalc = 1.379 g cm−3, R1 = 0.0405 for 14 010 reflections, wR2 = 0.1326 for all data. With a minor change, the key structural features discussed previously for form A [Rabe et al. (1998). Inorg. Chem. 37, 4235–4245] remain unchanged. The η3-toluene ligand is observed to be disordered at 293 (2) K and ordered at 173 (2) K, with the order–disorder phase transition occurring at approximately 278 (2) K.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108768199012677
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  • 3
    Electronic Resource
    Electronic Resource
    Unambiguous exchange-correlation energy density for Hooke's atom (1998)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 70 (1998), S. 583-589 
    Details
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Recently, we used Helmholtz's theorem to construct an unambiguous exchange-correlation energy density for use in density functional theory. This energy density requires only knowledge of the density dependence of the exchange-correlation energy functional, EXC, for its calculation. We calculate this energy density for Hooke's atom in three different regimes: the high-density (or weakly correlated) limit; a moderate density, comparable to that of the He atom; and a low density, in which the system is strongly correlated. We compare the exact unambiguous energy density with approximate energy densities found from approximate energy functionals. The exchange-correlation energy can be deduced directly from the density in the highly correlated limit and a new formula for the high-density limit of the correlation energy is given.   © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 583-589, 1998
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 4
    Electronic Resource
    Electronic Resource
    Virial exchange-correlation energy density in Hooke's atom (1998)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 69 (1998), S. 533-540 
    Details
    ISSN: 0020-7608
    Keywords: density functional ; exchange-correlation ; energy density ; Hooke's atom ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Application of the virial theorem to the interelectronic Coulomb repulsion shows that the virial of the exchange potential yields the exchange energy. However, the virial of the correlation potential does not yield the correlation energy. We have recently constructed a “hypercorrelated” potential whose virial is the correlation energy. We apply these ideas to a system which contains two interacting electrons in an external harmonic potential, Hooke's atom. This system can be solved analytically for a set of spring constants and numerically for any spring constant. By inverting the Kohn-Sham equations, the exact exchange and correlation potentials can be found. These exact values are compared with several popular approximate functionals, namely local spin density (LSD), Perdew, Burke, and Ernzerhof (PBE), and Becke and Lee-Yang-Parr (BLYP). We illustrate our results for two values of the spring constant. At a moderate value, the density is comparable to the He atom, while for a low spring constant, we explore extremely low densities.   © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 533-540, 1998
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
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