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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 8161-8167 
    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
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 3760-3771 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Gradient-corrected density functionals provide a common tool for electronic structure calculations in quantum chemistry and condensed matter physics. This article explains why local and semilocal approximations work for the exchange-correlation energy. We demonstrate the high accuracy of the local spin-density (LSD) approximation for the on-top pair density, which provides the missing link between real atoms and molecules and the uniform electron gas. Special attention is devoted to the leading correction to exchange in the high-density (or weakly correlated) limit. We give an improved analytic expression for the on-top pair density in the uniform electron gas, calculating its spin-polarization dependence exactly in the high-density limit. We find the exact form of the gradient expansion for the on-top pair density, using Levy's scaling of the interacting wave function. We also discuss the importance of system averaging, which unweights spatial regions where the density varies most rapidly. We show how the depth of the on-top hole correlates with the degree of locality of the exchange-correlation energy. Finally, we discuss how well fully nonlocal approximations (weighted-density, self-interaction correction, and hybrid-exchange) reproduce the on-top hole. © 1998 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 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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  • 5
    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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  • 6
    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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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 61 (1997), S. 197-205 
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The on-top pair density P(r, r) gives the probability that one electron will be found on top of another at position r. We find that the local spin density (LSD) and generalized gradient (GGA) approximations for exchange and correlation predict this quantity with remarkable accuracy. We show how this fact and the usual sum-rule arguments explain the success of these approximations for real atoms, molecules, and solids, where the electron spin densities do not vary slowly over space. Self-consistent LSD or GGA calculations make realistic predictions for the total energy E, the total density n(r), and the on-top pair density P(r,r), even in those strongly “abnormal” systems (such as stretched H2) where these approximations break symmetries and yield unrealistic spin magnetization densities m(r). We then suggest that ground-state ferromagnetic iron is a “normal” system, for which for LSD or GGA m(r) and the related local spin moment are trustworthy, but that iron above the Curie temperature and antiferromagnetic clusters at all temperatures are abnormal system for which the on-top pair density interpretation is more viable than the standard physical interpretation. As an example of a weakly abnormal system, we consider the four-electron ion with nuclear charge Z → ∞ © 1997 John Wiley & Sons, Inc.
    Additional Material: 3 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 70 (1998), S. 583-589 
    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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  • 9
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 56 (1995), S. 199-210 
    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 exchange-correlation energy of a many-electron system may be written as the electrostatic interaction between the electron density at position r and the density of the exchange-correlation hole at position r + u. If we average the hole over the entire system, we find that the energy is uniquely decomposed into contributions from various electronic separations u. We may also decompose the hole into contributions from parallel and antiparallel spins. We give several exact conditions which this system-averaged, spindecomposed exchange-correlation hole satisfies. Local spin density (LSD) and generalized gradient approximations (GGAS), are more appropriate for u → 0 than for large u and more trustworthy for antiparallel spins than for parallel spins. We illustrate how good LSD is as u = 0 with explicit examples, but also note that, contrary to expectation, LSD is not exact for u=0, except in certain limiting cases. We show that the dramatic failure of the second-order gradient expansion for large u can be cured by a real-space cutoff procedure which generates a nonempirical GGA, the Pw91 functional. We conclude with some thoughts about the search for greater accuracy in the next 30 years of density functional theory. © 1995 John Wiley & Sons, Inc.
    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 57 (1996), S. 309-319 
    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: Gradient corrections to the local spin density (LSD) approximation for the exchange-correlation energy are making density functional theory as useful in quantum chemistry as it is in solid-state physics. But which of the many gradient-corrected density functionals should be preferred a priori? We make a graphical comparison of the gradient dependencies of some popular approximations, discussing the exact formal conditions which each obeys and identifying which conditions seem most important. For the exchange energy, there is little formal or practical reason to choose among the Perdew-Wang 86, Becke 88, or Perdew-Wang 91 functionals. But, for the correlation energy, the best formal properties are displayed by the nonempirical PW91 correlation functional. Furthermore, the real-space foundation of PW91 yields an insight into the character of the gradient expansion which suggests that PW91 should work especially well for solids. Indeed, while improving dissociation energies over LSD, PW91 remains the most “local” of the gradient-corrected exchange-correlation functionals and, thus, the least likely to overcorrect the subtle errors of LSD for solids. To show that our analysis of spin-unpolarized functionals is sufficient, we also compute spin-polarization energies for atoms, finding PW91 values only slightly more negative than LSD values. © 1996 John Wiley & Sons, Inc.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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