More-Realistic Band Gaps from Meta-Generalized Gradient Approximations: Only in a Generalized Kohn-Sham Scheme

TL;DR

This paper develops an implementation of the optimized effective potential (OEP) for meta-GGA functionals, enabling consistent Kohn-Sham band structure calculations and revealing differences between KS gaps and gKS gaps.

Contribution

It introduces an OEP approach for meta-GGAs, allowing their band structures to be computed within a standard KS framework, which was previously challenging.

Findings

KS gaps of meta-GGAs are close to GGA gaps

KS gaps are smaller than gKS gaps of meta-GGAs

OEP calculations exhibit high grid sensitivity

Abstract

Unlike the local density approximation (LDA) and the generalized gradient approximation (GGA), calculations with meta-generalized gradient approximations (meta-GGA) are usually done according to the generalized Kohn-Sham (gKS) formalism. The exchange-correlation potential of the gKS equation is non-multiplicative, which prevents systematic comparison of meta-GGA bandstructures to those of the LDA and the GGA. We implement the optimized effective potential (OEP) of the meta-GGA for periodic systems, which allows us to carry out meta-GGA calculations in the same KS manner as for the LDA and the GGA. We apply the OEP to several meta-GGAs, including the new SCAN functional [Phys. Rev. Lett. 115, 036402 (2015)]. We find that the KS gaps and KS band structures of meta-GGAs are close to those of GGAs. They are smaller than the more realistic gKS gaps of meta-GGAs, but probably close to the less-realistic gaps in the band structure of the exact KS potential, as can be seen by comparing with the gaps of the EXX+RPA OEP potential. The well-known grid sensitivity of meta-GGAs is much more severe in OEP calculations.