Validation of Pseudopotential Calculations for the Electronic Band Gap of Solids

Nowadays pseudopotential (PP) density functional theory calculations constitute the standard approach to tackle solid-state electronic problems. These rely on distributed PP tables that were built from all-electron atomic calculations using few popular semilocal exchange-correlation functionals, while PPs based on more modern functionals, such as meta-generalized gradient approximation and hybrid functionals, or for many-body methods, such as GW, are often not available. Because of this, employing PPs created with inconsistent exchange-correlation functionals has become a common practice. Our aim is to quantify systematically the error in the determination of the electronic band gap when cross-functional PP calculations are performed. To this end, we compare band gaps obtained with norm-conserving PPs or the projector-augmented wave method with all-electron calculations for a large data set of 473 solids. We focus, in particular, on density functionals that were designed specifically for band gap calculations. On average, the absolute error is about 0.1 eV, yielding absolute relative errors in the 5-10% range. Considering that typical errors stemming from the choice of the functional are usually larger, we conclude that the effect of choosing an inconsistent PP is rather harmless for most applications. However, we find specific cases where absolute errors can be larger than 1 eV or others where relative errors can amount to a large fraction of the band gap.