Large-Scale Benchmark of Exchange-Correlation Functionals for the Determination of Electronic Band Gaps of Solids

We compile a large data set designed for the efficient benchmarking of exchange-correlation functionals for the calculation of electronic band gaps. The data set comprises information on the experimental structure and band gap of 472 nonmagnetic materials and includes a diverse group of covalent-, ionic-, and van der Waals-bonded solids. We used it to benchmark 12 functionals, ranging from standard local and semilocal functionals, passing through meta-generalized-gradient approximations, and several hybrids. We included both general purpose functionals, like the Perdew-Burke-Ernzerhof approximation, and functionals specifically crafted for the determination of band gaps. The comparison of experimental and theoretical band gaps shows that the modified Becke-Johnson is at the moment the best available density functional, closely followed by the Heyd-Scuseria-Ernzerhof screened hybrid from 2006 and the high-local-exchange generalized-gradient approximation.