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.