Gedanken densities and exact constraints in density functional theory
Abstract
Approximations to the exact density functional for the exchangecorrelation energy of a manyelectron ground state can be constructed by satisfying constraints that are universal, i.e., valid for all electron densities. Gedanken densities are designed for the purpose of this construction, but need not be realistic. The uniform electron gas is an old gedanken density. Here, we propose a spherical twoelectron gedanken density in which the dimensionless density gradient can be an arbitrary positive constant wherever the density is nonzero. The LiebOxford lower bound on the exchange energy can be satisfied within a generalized gradient approximation (GGA) by bounding its enhancement factor or simplest GGA exchangeenergy density. This enhancementfactor bound is well known to be sufficient, but our gedanken density shows that it is also necessary. The conventional exact exchangeenergy density satisfies no such local bound, but energy densities are not unique, and the simplest GGA exchangeenergy density is not an approximation to it. We further derive a strongly and optimally tightened bound on the exchange enhancement factor of a twoelectron density, which is satisfied by the local density approximation but is violated by all published GGA's or metaGGA’s. Finally, some consequences of the nonuniform densityscaling behavior for the asymptotics ofmore »
 Authors:
 Department of Physics, Temple University, Philadelphia, Pennsylvania 19122 (United States)
 (United States)
 Department of Chemistry and Department of Physics, University of California, Irvine, California 92697 (United States)
 Publication Date:
 OSTI Identifier:
 22253098
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Chemical Physics; Journal Volume: 140; Journal Issue: 18; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; APPROXIMATIONS; DENSITY; DENSITY FUNCTIONAL METHOD; ELECTRON DENSITY; ELECTRON GAS; ELECTRONS; ENERGY DENSITY; GROUND STATES
Citation Formats
Perdew, John P., Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, Ruzsinszky, Adrienn, Sun, Jianwei, and Burke, Kieron. Gedanken densities and exact constraints in density functional theory. United States: N. p., 2014.
Web. doi:10.1063/1.4870763.
Perdew, John P., Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, Ruzsinszky, Adrienn, Sun, Jianwei, & Burke, Kieron. Gedanken densities and exact constraints in density functional theory. United States. doi:10.1063/1.4870763.
Perdew, John P., Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, Ruzsinszky, Adrienn, Sun, Jianwei, and Burke, Kieron. 2014.
"Gedanken densities and exact constraints in density functional theory". United States.
doi:10.1063/1.4870763.
@article{osti_22253098,
title = {Gedanken densities and exact constraints in density functional theory},
author = {Perdew, John P. and Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122 and Ruzsinszky, Adrienn and Sun, Jianwei and Burke, Kieron},
abstractNote = {Approximations to the exact density functional for the exchangecorrelation energy of a manyelectron ground state can be constructed by satisfying constraints that are universal, i.e., valid for all electron densities. Gedanken densities are designed for the purpose of this construction, but need not be realistic. The uniform electron gas is an old gedanken density. Here, we propose a spherical twoelectron gedanken density in which the dimensionless density gradient can be an arbitrary positive constant wherever the density is nonzero. The LiebOxford lower bound on the exchange energy can be satisfied within a generalized gradient approximation (GGA) by bounding its enhancement factor or simplest GGA exchangeenergy density. This enhancementfactor bound is well known to be sufficient, but our gedanken density shows that it is also necessary. The conventional exact exchangeenergy density satisfies no such local bound, but energy densities are not unique, and the simplest GGA exchangeenergy density is not an approximation to it. We further derive a strongly and optimally tightened bound on the exchange enhancement factor of a twoelectron density, which is satisfied by the local density approximation but is violated by all published GGA's or metaGGA’s. Finally, some consequences of the nonuniform densityscaling behavior for the asymptotics of the exchange enhancement factor of a GGA or metaGGA are given.},
doi = {10.1063/1.4870763},
journal = {Journal of Chemical Physics},
number = 18,
volume = 140,
place = {United States},
year = 2014,
month = 5
}

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