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Title: Derivative discontinuity and exchange-correlation potential of meta-GGAs in density-functional theory

We investigate fundamental properties of meta-generalized-gradient approximations (meta-GGAs) to the exchange-correlation energy functional, which have an implicit density dependence via the Kohn-Sham kinetic-energy density. To this purpose, we construct the most simple meta-GGA by expressing the local exchange-correlation energy per particle as a function of a fictitious density, which is obtained by inverting the Thomas-Fermi kinetic-energy functional. This simple functional considerably improves the total energy of atoms as compared to the standard local density approximation. The corresponding exchange-correlation potentials are then determined exactly through a solution of the optimized effective potential equation. These potentials support an additional bound state and exhibit a derivative discontinuity at integer particle numbers. We further demonstrate that through the kinetic-energy density any meta-GGA incorporates a derivative discontinuity. However, we also find that for commonly used meta-GGAs the discontinuity is largely underestimated and in some cases even negative.
Authors:
 [1] ;  [2]
  1. Department of Physics, University of Missouri-Columbia, Columbia, Missouri 65211 (United States)
  2. International School for Advanced Studies (SISSA), via Bonomea 265, 34136 Trieste (Italy)
Publication Date:
OSTI Identifier:
22413289
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 22; 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; BOUND STATE; DENSITY; DENSITY FUNCTIONAL METHOD; ELECTRON CORRELATION; KINETIC ENERGY; PARTICLES; SOLUTIONS; THOMAS-FERMI MODEL