We compare the ability of four popular hybrid density functionals (B3LYP, B3PW91, HSE, and PBE0) for predicting band gaps of semiconductors and insulators over a large benchmark set using a consistent methodology. We observe no significant statistical dference in their overall performance although the screened hybrid HSE is more accurate for typical semiconductors. HSE can improve its accuracy for large large band gap materials --without affecting that of semiconductors-- by including a larger portion of Hartree-Fock exchange in its short range. Given that screened hybrids are computationally much less expensive than their global counterparts, we conclude that they are a better option for the black box prediction of band gaps.
@article{arxiv.1608.04796,
title = {Predicting Band Gaps with Hybrid Density Functionals},
author = {Alejandro J. Garza and Gustavo E. Scuseria},
journal= {arXiv preprint arXiv:1608.04796},
year = {2016}
}