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

TL;DR

This paper explores the fundamental properties of meta-GGA functionals in density-functional theory, focusing on their derivative discontinuities and how they influence exchange-correlation potentials, with implications for improving energy calculations.

Contribution

It introduces a simple meta-GGA model based on a fictitious density, demonstrating how kinetic-energy density affects derivative discontinuities in exchange-correlation potentials.

Findings

The simple meta-GGA improves atomic energy calculations compared to LDA.

Exchange-correlation potentials support an additional bound state.

Common meta-GGAs underestimate or negatively predict derivative discontinuities.

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.