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  • 1
    Electronic Resource
    Electronic Resource
    Kinetic energy density dependent approximations to the exchange energy (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 911-915 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Two nonempirical kinetic energy density dependent approximations are introduced. First, the local τ approximation (LTA) is proposed in which the exchange energy Ex depends only on a kinetic energy density τ. This LTA scheme appears to be complementary to the local spin density (LSD) approximation in the sense that its exchange contribution to the atomization energy ΔEx=Exatoms−Exmolecule is fairly accurate for systems where LSD fails. On the other hand, in cases where LSD works well LTA results for ΔEx are worse. Secondly, the τPBE approximation to Ex is developed which combines some of the advantages of LTA and of the Perdew–Burke–Ernzerhof (PBE) exchange functional. Like the PBE exchange functional, τPBE is free of empirical parameters. Furthermore, it yields improved atomization energies compared to the PBE approximation. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.479374
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  • 2
    Electronic Resource
    Electronic Resource
    Functionals of quantities other than the electron density: Approximations to the exchange energy (2002)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 116 (2002), S. 3980-3984 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A new method is proposed for constructing approximations to the electron–electron interaction. In this approach tools of density functional theory, such as the gradient expansion, are employed. Traditional gradient expansions depend on the electron density ρ. Here, however, we propose an alternative route to ρ functionals, we derive functionals that depend solely on the noninteracting kinetic energy density τ(r) defined by τ(r)=〈fraction SHAPE="CASE"〉12∑iocc|∇cursive-phii(r)|2, where cursive-phii is a single-particle orbital. We demonstrate the potential of our approach by constructing an approximation to the exchange energy (EX) of electrons that rivals the accuracy of generalized gradient approximations of density functional theory. The strategy presented here is quite general and suitable to construct a variety of nonelectron-density functionals. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1446022
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  • 3
    Electronic Resource
    Electronic Resource
    The slowly-varying noninteracting electron gas in terms of its kinetic energy density (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 112 (2000), S. 5270-5274 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The noninteracting kinetic energy density τ(r)=〈fraction SHAPE="CASE"〉12∑iocc|∇cursive-phii(r)|2, calculated from the Kohn–Sham orbitals cursive-phii, has recently been used to model the exchange energy (EX). The question arises whether it is in principle possible to obtain EX or, more general, all the properties of a noninteracting ground-state system exclusively in terms of τ(r). We produce evidence to counter this possibility by showing that a one-to-one correspondence between local potentials v(r), which differ by more than a constant, and τ(r) does not exist. Furthermore, we show that EX cannot be obtained exactly in terms of τ. However, in the slowly varying limit a one-to-one mapping between τ and v can be established. Thus we are able to derive the gradient expansion of the electron density and of EX in terms of τ. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.481097
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  • 4
    Electronic Resource
    Electronic Resource
    Assessment of the Perdew–Burke–Ernzerhof exchange-correlation functional (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 5029-5036 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In order to discriminate between approximations to the exchange-correlation energy EXC[ρ↑,ρ↓], we employ the criterion of whether the functional is fitted to a certain experimental data set or if it is constructed to satisfy physical constraints. We present extensive test calculations for atoms and molecules, with the nonempirical local spin-density (LSD) and the Perdew–Burke–Ernzerhof (PBE) functional and compare our results with results obtained with more empirical functionals. For the atomization energies of the G2 set, we find that the PBE functional shows systematic errors larger than those of commonly used empirical functionals. The PBE ionization potentials, electron affinities, and bond lengths are of accuracy similar to those obtained from empirical functionals. Furthermore, a recently proposed hybrid scheme using exact exchange together with PBE exchange and correlation is investigated. For all properties studied here, the PBE hybrid gives an accuracy comparable to the frequently used empirical B3LYP hybrid scheme. Physical principles underlying the PBE and PBE hybrid scheme are examined and the range of their validity is discussed. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.478401
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  • 5
    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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  • 6
    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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  • 7
    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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  • 8
    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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  • 9
    Electronic Resource
    Electronic Resource
    Perspective on “Inhomogeneous electron gas” (2000)
    Springer
    Theoretical chemistry accounts 103 (2000), S. 259-262 
    Details
    ISSN: 1432-2234
    Keywords: Key words: Density functional theory – Hohenberg–Kohn theorems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract. The Hohenberg–Kohn theorems in “Inhomogeneous electron gas” established a whole new perspective for the study of electronic structure theory and marked the birth of modern density functional theory (DFT). In our view, DFT and wavefunction theories complement each other. Starting with the invention of the Kohn–Sham method a fruitful synthesis of DFT and wavefunction theories took place and the most powerful computational tools currently available are combinations of both methods. The Hohenberg–Kohn theorems inspire the quest for simple density functionals of increased accuracy. We believe that the synthesis of accurate density functionals and computationally efficient wavefunction methods will continue to dominate electronic structure theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002149900030
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  • 10
    Electronic Resource
    Electronic Resource
    Coupling-constant dependence of atomization energies (1997)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 64 (1997), S. 285-295 
    Details
    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.
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