Abstract
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.
Highlights
Since its origin more than 50 years ago, density functional theory[1,2] (DFT) has become the standard approach to tackle the electronic structure of solids
We start our analysis by looking at the results computed with the generally available local density approximation (LDA) and Perdew− Burke−Ernzerhof (PBE) data sets
In order to illustrate the effect of an inaccurate value of c on the band gap more concretely, we show, in Table 5, the Vienna ab initio simulation package (VASP) (c = cWIEN2k) aThe second set of VASP results were obtained with the parameter c in eq 2 fixed to the value obtained from the WIEN2k calculation
Summary
Since its origin more than 50 years ago, density functional theory[1,2] (DFT) has become the standard approach to tackle the electronic structure of solids. A basic distinction exists between allelectron and pseudopotential (PP) (or effective-core potential) methods In the former, all electrons are explicitly included in the calculation, and the electron−nuclear attraction is described by the standard Coulomb potential. The projector-augmented wave (PAW) method[12,13] was developed, combining the advantages of PPs with a reconstruction of the all-electron wave function. Another alternative, the hybrid Gaussian and plane-wave densityfunctional scheme,[14,15] can be considered intermediate between PP and all-electron methods. PPs and PAW setups are normally calculated from atomic density-functional calculations performed with a specific xc functional and should be only used in calculations performed with the same functional
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