Kohn-Sham band gaps and potentials of solids from the optimised effective potential method within the random phase approximation

TL;DR

This paper implements the optimised effective potential method with RPA and EXX functionals to compute Kohn-Sham potentials and band gaps of solids, showing improved consistency over local functionals but still requiring G0W0 corrections for accurate quasiparticle gaps.

Contribution

It introduces an implementation of the OEP scheme with RPA and EXX functionals for solids, providing a more consistent approach to band gap calculations.

Findings

Kohn-Sham gaps increase from LDA to RPA-OEP and EXX-OEP.

G0W0 corrections are needed for true quasiparticle gaps.

RPA-OEP G0W0 gaps are about 5% larger than experimental values.

Abstract

We present an implementation of the optimised effective potential (OEP) scheme for the exact-exchange (EXX) and random phase approximation (RPA) energy functionals and apply these methods to a range of bulk materials. We calculate the Kohn-Sham (KS) potentials and the corresponding band gaps and compare them to the potentials obtained by standard local density approximation (LDA) calculations. The KS gaps increase upon going from the LDA to the OEP in the RPA and finally to the OEP for EXX. This can be explained by the different depth of the potentials in the bonding and interstitial regions. To obtain the true quasi-particle gaps the derivative discontinuities or $G_0W_0$ corrections need to be added to the RPA-OEP KS gaps. The predicted $G_0W_0$@RPA-OEP quasi-particle gaps are about 5% too large compared to the experimental values. However, compared to $G_0W_0$ calculations based on local or semi-local functionals, where the errors vary between different materials, we obtain a rather consistent description among all the materials.