title: Derivative discontinuity and exchange-correlation potential of meta-GGAs in density-functional theory.
abstract: 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.affiliation: Department of Physics, University of Missouri-Columbia, Columbia, Missouri 65211, USA.
authors.forename: F G
authors.initials: FG
authors.lastname: Eich
authors.affiliation: International School for Advanced Studies (SISSA), via Bonomea 265, 34136 Trieste, Italy.
authors.forename: Maria
authors.initials: M
authors.lastname: Hellgren