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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 8182-8189 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We report the first reliable theoretical calculation of the quantum size correction c which yields the asymptotic ionization energy I(R)=W+(〈fraction SHAPE="CASE"〉12+c)/R+O(R−2) of a simple-metal cluster of radius R. Restricted-variational electronic density profiles are used to evaluate two sets of expressions for the bulk work function W and quantum size correction c: the Koopmans expressions, and the more accurate and profile-insensitive ΔSCF expressions. We find c(approximate)−0.08 for stabilized (as for ordinary) jellium, and thus for real simple metals. We present parameters from which the density profiles may be reconstructed for a wide range of cluster sizes, including the planar surface. We also discuss how many excess electrons can be bound by a neutral cluster of given size. Within a continuum picture, the criterion for total-energy stability of a negatively charged cluster is less stringent than that for existence of a self-consistent solution. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 2798-2803 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The asymptotic behavior of an N-electron ground-state wave function is analyzed, as one electron wanders far from the system. Implications for the one-matrix and pair density are described. The asymptotic behavior currently discussed in the literature, in which the remaining (N−1) electrons relax to their ground state, is generalized to the case where the (N−1)-electron ground state is degenerate. Infinitely long-ranged correlations are reported, in which the selected (N−1)-electron ground state depends upon the direction along which one electron wandered off. We correct a standard limit for the one matrix. Numerical and analytic studies of accurate correlated wave functions illustrate and support the standard asymptotic behavior for the nondegenerate case and its generalization derived here. We extract the (N−1)-electron density from the correlated N-electron wave function. We also discuss the question how large the separation of one electron must be to realize the limiting behavior. © 1996 American Institute of Physics.
    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 105 (1996), S. 9982-9985 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Density functional approximations for the exchange-correlation energy EDFAxc of an electronic system are often improved by admixing some exact exchange Ex: Exc≈EDFAxc+(1/n)(Ex−EDFAx). This procedure is justified when the error in EDFAxc arises from the λ=0 or exchange end of the coupling-constant integral ∫10 dλ EDFAxc,λ. We argue that the optimum integer n is approximately the lowest order of Görling–Levy perturbation theory which provides a realistic description of the coupling-constant dependence Exc,λ in the range 0≤λ≤1, whence n≈4 for atomization energies of typical molecules. We also propose a continuous generalization of n as an index of correlation strength, and a possible mixing of second-order perturbation theory with the generalized gradient approximation. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 3313-3320 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A simple analytic model is proposed for the angle- and system-averaged exchange hole of a many-electron system. The model hole depends on the local density and density gradient. It recovers a nonoscillatory local-spin density (LSD) approximation to the exchange hole for a vanishing density gradient. The model hole reproduces the exchange energy density of the Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation (GGA) for exchange, and facilitates a detailed understanding of the PBE GGA. The hole model is applied to atoms and molecules, and a comparison is made to exact and LSD angle- and system-averaged exchange holes. We find that the GGA hole model significantly improves upon the LSD model. Furthermore, the GGA hole model accurately describes the change in the exchange hole upon the formation of single bonds, but is less accurate for the formation of multiple bonds, where it misses the appearance of a long-range tail. © 1998 American Institute of Physics.
    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 108 (1998), S. 1522-1531 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Gradient corrections to the local spin density approximation for the exchange-correlation energy Exc are increasingly useful in quantum chemistry and solid state physics. We present elementary physical arguments which explain the qualitative dependencies of the exchange and correlation energies upon the local density, local spin polarization, and reduced density gradient. The nearly local behavior of the generalized gradient approximation for Exc at valence-electron densities, due to strong cancellation between the nonlocalities of exchange and correlation, is shared by the exact linear response of the uniform electron gas. We further test and develop our rationale for the chemical and solid-state consequences of gradient corrections. We also partially explain the "conjointness" between the exchange energy and the noninteracting kinetic energy, whose generalized gradient approximation is tested here. An appendix presents the full expression for the gradient-corrected correlation potential. © 1998 American Institute of Physics.
    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 84 (1986), S. 4519-4523 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A perturbation theory is derived for the study of molecular structure. For a large class of approximate formulations (including Hartree–Fock and higher-level schemes and exact exchange-only density-functional theory), it is proved that the change in the error of the energy, upon geometry change, is zero through the second-order perturbation term, thus helping to explain why approximate energy curves often closely parallel exact curves and give accurate geometries. In contrast, for each non-Coulomb potential considered, the error change is not zero through second order, suggesting that accurate geometries are due, in part, to a special quality of the Coulomb potential. Comparable results are obtained for atomic electron–nuclear attraction expectation values (isoelectronic energy changes), which are exact through second order in the Coulomb cases. The conclusions are supported by a nonperturbative argument and by a numerical example.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 61 (1997), S. 835-845 
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We present an analysis of local or semilocal density functionals for the exchange-correlation energy by decomposing them into their gradients rs (local Seitz radius), ζ (relative spin polarization), and s (reduced density gradient). We explain the numerical method pertaining to this kind of analysis and present results for a few atoms and ions. The atomic shell structure is prominent, and only the ranges 0 〈 rs 〈 10 and 0 〈 s 〈 3 are important. The low-density and large-gradient domains, where the approximations for the exchange-correlation energy are least trustworthy, have very little weight. © 1997 John Wiley & Sons, Inc.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 61 (1997), S. 935-941 
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Correlation of a quantum many-body state makes the one-particle density matrix nonidempotent. Therefore, the Shannon entropy of the natural occupation numbers measures the correlation strength on the one-particle level. Here, it is shown how this general idea of a correlation entropy must be adapted for two-electron systems in view of conservation laws which mix Slater determinants even in the noninteracting limit. Results are presented for the correlation entropy s of H2 as a function of the nucleus-nucleus separation R. In the ground state, the entropy of the spatial factor of the wave function maximizes 1.7 bohr beyond the Coulson-Fischer separation. The role of the correlation entropy in density functional theory is also discussed. © 1997 John Wiley & Sons, Inc.
    Additional Material: 2 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 64 (1997), S. 285-295 
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The local spin-density (LSD) functional and Perdew-Wang 91 (PW91) generalized gradient approximations to atomization energies of molecules are investigated. We discuss the coupling-constant dependence of the atomization energy and why exchange errors of the functionals are greater than exchange-correlation errors. This fact helps to justify hybrid schemes which mix some exact exchange with density functional approximations for exchange and correlation. It is shown that the biggest errors in the atomization energies occur when there is a strong interaction between different electron pairs, which vanishes upon atomization. We argue that the amount of exchange character of a molecular property, such as the atomization energy, depends on the property itself. We define an exact mixing coefficient b, which measures this exchange character, and show that both LSD and PW91 typically overestimate this quantity. Thus, nonempirical hybrid schemes which approximate this quantity by its LSD or PW91 value typically do not improve the exchange-correlation energy.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64: 285-295, 1997
    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 30 (1986), S. 451-451 
    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
    Type of Medium: Electronic Resource
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