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  • 1
    Electronic Resource
    Electronic Resource
    Nonlocality of the density functional for exchange and correlation: Physical origins and chemical consequences (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 1522-1531 
    Details
    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
    URL: http://dx.doi.org/10.1063/1.475524
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  • 2
    Electronic Resource
    Electronic Resource
    Ionization energy and electron affinity of a metal cluster in the stabilized jellium model: Size effect and charging limit (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 8182-8189 
    Details
    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
    URL: http://dx.doi.org/10.1063/1.476173
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  • 3
    Electronic Resource
    Electronic Resource
    Generalized gradient approximation to the angle- and system-averaged exchange hole (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 3313-3320 
    Details
    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
    URL: http://dx.doi.org/10.1063/1.476928
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  • 4
    Electronic Resource
    Electronic Resource
    Success of quantum mechanical approximations for molecular geometries and electron–nuclear attraction expectation values: Gift of the Coulomb potential? (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 84 (1986), S. 4519-4523 
    Details
    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
    URL: http://dx.doi.org/10.1063/1.450024
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  • 5
    Electronic Resource
    Electronic Resource
    Rationale for mixing exact exchange with density functional approximations (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 9982-9985 
    Details
    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
    URL: http://dx.doi.org/10.1063/1.472933
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  • 6
    Electronic Resource
    Electronic Resource
    Long-range asymptotic behavior of ground-state wave functions, one-matrices, and pair densities (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 2798-2803 
    Details
    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
    URL: http://dx.doi.org/10.1063/1.472142
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  • 7
    Electronic Resource
    Electronic Resource
    Energetics of small clusters of stabilized jellium: Continuum and shell-structure effects (1993)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 48 (1993), S. 249-261 
    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: We evaluate binding energies, ionization energies, and second-order energy differences as functions of valence electron number for small spherical clusters of stabilized jellium, using the Kohn-Sham equations with the local-spin-density (LSD) approximation. Cohesive energies are also reported. A comparison is made with semiclassical formulas (liquid drop model and Padé approximant, with surface and curvature coefficients derived from first principles). These formulas nicely average the shell-structure oscillations of the energy, which are found to be almost the same as for ordinary jellium. Spherical clusters with 1, 7, and 9 electrons have binding energies very close to those of the semiclassical predictions. © 1993 John Wiley & Sons, Inc.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560480827
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  • 8
    Electronic Resource
    Electronic Resource
    Density functionals for exchange and correlation energies: Exact conditions and comparison of approximations (1994)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 49 (1994), S. 539-548 
    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 set of exact conditions is compiled for the purpose of developing and testing approximations for the exchange-correlation energy as a functional of the electron density. Special emphasis is placed upon recently developed density-scaling relationships. Commonly used generalized gradient approximations are compared against several of these conditions. A direct tabular comparison of these functionals (not of calculated properties) with one another is also made. © 1994 John Wiley & Sons, Inc.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560490416
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  • 9
    Electronic Resource
    Electronic Resource
    Local density and gradient-corrected functionals for short-range correlation: Antiparallel-spin and non-RPA contributions (1993)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 48 (1993), S. 93-100 
    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: In many situations, the most long-ranged parts of the exchange and correlation holes surrounding an electron cancel one another. Apparently for this reason, local spin density and generalized gradient approximations are more accurate for exchange and correlation together than for either alone. A study is made of the ability of these density functionals, and also the unmodified second-order gradient expansion, to describe various short-range effects in atoms: the correlation contribution to the interacting kinetic energy, the antiparallel-spin correlation energy, and the correction to the random phase approximation. Generalized gradient approximations, constructed with no adjustable parameter from the electron gas of slowly varying density, are found to give results of useful accuracy for real atoms. Prospects are discussed for use of the new functionals to improve the accuracy of electronic-structure calculations. © 1993 John Wiley & Sons, Inc.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560480813
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  • 10
    Electronic Resource
    Electronic Resource
    Self-expansion and compression of charged clusters of stabilized jellium (1996)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 60 (1996), S. 1537-1548 
    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: In a positively charged metallic cluster, surface tension tends to enhance the ionic density with respect to its bulk value, while surface-charge repulsion tends to reduce it. Using the stabilized jellium model, we examine the self-expansion and compression of positively charged clusters of simply metals. Quantal results from the Kohn-Sham equations using the local density approximation are compared with continuous results from the liquid drop model. The positive background is constrained to a spherical shape. Numerical results for the equilibrium radius and the elastic stiffness are presented for singly and doubly positively charged aluminum, sodium, and cesium clusters of 1-20 atoms. Self-expansion occurs for small charged clusters of sodium and cesium, but not of aluminum. The effect of the expansion or compression on the ionization energies is analyzed. For Al6, we also consider net charges greater than 2+. The results of the stabilized jellium model for self-compression are compared with those of other models, including the SAPS (spherical averaged pseudopotential model). © 1996 John Wiley & Sons, Inc.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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