Range-separated hybrid functionals for accurate prediction of band gaps of extended systems

In this work, we systematically evaluate the accuracy in band gap prediction of range-separated hybrid functionals on a large set of semiconducting and insulating materials and carry out comparisons with the performance of their global counterparts. We observe that all the range-separated hybrid functionals that correctly describe the long-range dielectric screening significantly improve from standard hybrid functionals such as PBE0 and HSE06. Among this group, the choice of the short-range Fock exchange fraction and the screening length can further reduce the predicted error. We then propose a universal expression for the selection of the inverse screening parameter as a function of the short-range and long-range Fock exchange fractions, which results in a mean absolute error as small as 0.15 eV for band gap prediction.