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 exchangecorrelation energy typically surpass the accuracy of the local spin density approximation and compete with standard quantumchemical methods in electronicstructure calculations. But the derivation and analytic expression for the integrand f tend to be complicated and overparametrized. We present a simple derivation of a simple but accurate expression for f, involving no parameter other than fundamentalconstants. The derivation invoices only general ideas (not details) of the realspace 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 highdensity limit. (2) The linear response of the uniform electron gas agrees with the accurate local spin density prediction. 96:006128*1 Paper TuI 6 Manybody effects are hidden in the universal density functional. The interaction of degenerate states via twobody operators, such as the electronelectron repulsion (for describing multiplets or the interaction of molecular fragments at large separations) are thus not explicitly considered in the KohnSham scheme. In practice the density functionals have to be approximated,more »
 Authors:

 Tulane Univ., New Orleans, LA (United States)
 Publication Date:
 OSTI Identifier:
 447535
 Report Number(s):
 CONF960343
TRN: 97:005432
 Resource Type:
 Conference
 Resource Relation:
 Conference: 2. international congress on theoretical chemical physics, New Orleans, LA (United States), 913 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 exchangecorrelation energy typically surpass the accuracy of the local spin density approximation and compete with standard quantumchemical methods in electronicstructure calculations. But the derivation and analytic expression for the integrand f tend to be complicated and overparametrized. We present a simple derivation of a simple but accurate expression for f, involving no parameter other than fundamentalconstants. The derivation invoices only general ideas (not details) of the realspace 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 highdensity limit. (2) The linear response of the uniform electron gas agrees with the accurate local spin density prediction. 96:006128*1 Paper TuI 6 Manybody effects are hidden in the universal density functional. The interaction of degenerate states via twobody operators, such as the electronelectron repulsion (for describing multiplets or the interaction of molecular fragments at large separations) are thus not explicitly considered in the KohnSham 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 twobody operators, which can be, but must not be, the physical electronelectron interaction.},
doi = {},
url = {https://www.osti.gov/biblio/447535},
journal = {},
number = ,
volume = ,
place = {United States},
year = {1996},
month = {12}
}