Gedanken densities and exact constraints in density functional theory

Journal Article · Wed May 14 04:00:00 EDT 2014 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4870763· OSTI ID:22253098

Perdew, John P. ^[1]; Ruzsinszky, Adrienn; Sun, Jianwei ^[1]; Burke, Kieron ^[2]

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1. Department of Physics, Temple University, Philadelphia, Pennsylvania 19122 (United States)
2. Department of Chemistry and Department of Physics, University of California, Irvine, California 92697 (United States)

Approximations to the exact density functional for the exchange-correlation energy of a many-electron 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 two-electron gedanken density in which the dimensionless density gradient can be an arbitrary positive constant wherever the density is non-zero. The Lieb-Oxford lower bound on the exchange energy can be satisfied within a generalized gradient approximation (GGA) by bounding its enhancement factor or simplest GGA exchange-energy density. This enhancement-factor bound is well known to be sufficient, but our gedanken density shows that it is also necessary. The conventional exact exchange-energy density satisfies no such local bound, but energy densities are not unique, and the simplest GGA exchange-energy density is not an approximation to it. We further derive a strongly and optimally tightened bound on the exchange enhancement factor of a two-electron density, which is satisfied by the local density approximation but is violated by all published GGA's or meta-GGA’s. Finally, some consequences of the non-uniform density-scaling behavior for the asymptotics of the exchange enhancement factor of a GGA or meta-GGA are given.

• OSTI ID: 22253098
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 18 Vol. 140; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
APPROXIMATIONS
DENSITY
DENSITY FUNCTIONAL METHOD
ELECTRON DENSITY
ELECTRON GAS
ELECTRONS
ENERGY DENSITY
GROUND STATES