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The band gap is an important parameter of semiconductor materials thatinfluences several functional properties, in particular optical properties.However, a fast and reliable first-principles prediction of band gaps remains achallenging problem. Standard DFT approximations tend to strongly underestimateband gaps, while the more accurate $GW$ and hybrid functionals are much morecomputationally demanding and unsuitable for high-throughput screening. In thiswork, we have performed an extensive benchmark of several approximations withdifferent computational complexity ($G_{0}W_{0}$@PBEsol, HSE06, PBEsol, mBJ,PBEsol$-1/2$, and ACBN0) to evaluate and compare their performance inpredicting the band gap of semiconductors. The benchmark is based on 114 binarysemiconductors of different compositions and crystal structures, where abouthalf of them have experimental band gaps. We find that, as expected,$G_{0}W_{0}$@PBEsol performs well relative to the experiment, with a noticeableunderestimation of the band gaps by about 14% on average. Surprisingly,$G_{0}W_{0}$@PBEsol is followed closely by the much computationally cheaperpseudo-hybrid ACBN0 functional, showing an excellent performance with respectto experimental data. The meta-GGA mBJ functional also performs well relativeto the experiment, even slightly better than $G_{0}W_{0}$@PBEsol in terms ofmean absolute (percentage) error. The HSE06 and PBEsol$-1/2$ schemes performoverall worse than ACBN0 and mBJ schemes but much better than PBEsol. Comparingthe calculated band gaps on the whole data set (including the samples with noexperimental band gap), we find that HSE06 and mBJ have excellent agreementwith respect to the reference $G_{0}W_{0}$@PBEsol band gaps. Thus, we proposethe mBJ band gaps as economic descriptors when developing artificialintelligence models for high-throughput screening of semiconductor band gaps.

A benchmark of first-principles methods for accurate prediction of semiconductor band gaps