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Title: Generalized gradient approximation made simple

Abstract

Generalized gradient approximations E{sub xc} = {integral} d{sup 3} r f(n{sub {up_arrow}}, n{sub {down_arrow}}, {triangledown}n{sub {up_arrow}}, {triangledown}n{sub {down_arrow}}) for the exchange-correlation energy typically surpass the accuracy of the local spin density approximation and compete with standard quantum-chemical methods in electronic-structure calculations. But the derivation and analytic expression for the integrand f tend to be complicated and over-parametrized. We present a simple derivation of a simple but accurate expression for f, involving no parameter other than fundamental-constants. The derivation invoices only general ideas (not details) of the real-space cutoff construction, and agrees closely with the result of this construction. Besides its greater simplicity, this PBE96 functional has other advantages over PW91: (1) The correct behavior of the correlation energy is recovered under uniform scaling to the high-density limit. (2) The linear response of the uniform electron gas agrees with the accurate local spin density prediction. 96:006128*1 Paper TuI 6 Many-body effects are hidden in the universal density functional. The interaction of degenerate states via two-body operators, such as the electron-electron repulsion (for describing multiplets or the interaction of molecular fragments at large separations) are thus not explicitly considered in the Kohn-Sham scheme. In practice the density functionals have to be approximated,more » and there is a fundamental difficulty which arises in the case of degeneracy. While density functionals should be universal, the effect of degeneracy is linked to the potential characteristic to the atom, molecule, or crystal. There are, however, several possibilities to treat degeneracy effects within density functional theory, a few of which will be discussed. These take profit of the use of two-body operators, which can be, but must not be, the physical electron-electron interaction.« less

Authors:
; ;  [1]
  1. Tulane Univ., New Orleans, LA (United States)
Publication Date:
OSTI Identifier:
447535
Report Number(s):
CONF-960343-
TRN: 97:005432
Resource Type:
Conference
Resource Relation:
Conference: 2. international congress on theoretical chemical physics, New Orleans, LA (United States), 9-13 Mar 1996; Other Information: PBD: 1996; Related Information: Is Part Of Second international congress on theoretical chemical physics - ICTCP II; PB: 90 p.
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; ELECTRONIC STRUCTURE; CALCULATION METHODS; ELECTRON CORRELATION; SPIN; ELECTRON EXCHANGE

Citation Formats

Perdew, J P, Burke, K, and Ernzerhof, M. Generalized gradient approximation made simple. United States: N. p., 1996. Web.
Perdew, J P, Burke, K, & Ernzerhof, M. Generalized gradient approximation made simple. United States.
Perdew, J P, Burke, K, and Ernzerhof, M. 1996. "Generalized gradient approximation made simple". United States.
@article{osti_447535,
title = {Generalized gradient approximation made simple},
author = {Perdew, J P and Burke, K and Ernzerhof, M},
abstractNote = {Generalized gradient approximations E{sub xc} = {integral} d{sup 3} r f(n{sub {up_arrow}}, n{sub {down_arrow}}, {triangledown}n{sub {up_arrow}}, {triangledown}n{sub {down_arrow}}) for the exchange-correlation energy typically surpass the accuracy of the local spin density approximation and compete with standard quantum-chemical methods in electronic-structure calculations. But the derivation and analytic expression for the integrand f tend to be complicated and over-parametrized. We present a simple derivation of a simple but accurate expression for f, involving no parameter other than fundamental-constants. The derivation invoices only general ideas (not details) of the real-space cutoff construction, and agrees closely with the result of this construction. Besides its greater simplicity, this PBE96 functional has other advantages over PW91: (1) The correct behavior of the correlation energy is recovered under uniform scaling to the high-density limit. (2) The linear response of the uniform electron gas agrees with the accurate local spin density prediction. 96:006128*1 Paper TuI 6 Many-body effects are hidden in the universal density functional. The interaction of degenerate states via two-body operators, such as the electron-electron repulsion (for describing multiplets or the interaction of molecular fragments at large separations) are thus not explicitly considered in the Kohn-Sham scheme. In practice the density functionals have to be approximated, and there is a fundamental difficulty which arises in the case of degeneracy. While density functionals should be universal, the effect of degeneracy is linked to the potential characteristic to the atom, molecule, or crystal. There are, however, several possibilities to treat degeneracy effects within density functional theory, a few of which will be discussed. These take profit of the use of two-body operators, which can be, but must not be, the physical electron-electron interaction.},
doi = {},
url = {https://www.osti.gov/biblio/447535}, journal = {},
number = ,
volume = ,
place = {United States},
year = {1996},
month = {12}
}

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