Band gaps of crystalline solids from Wannier-localization based optimal tuning of a screened range-separated hybrid functional

Accurate prediction of fundamental band gaps of crystalline solid state systems entirely within density functional theory is a long standing challenge. Here, we present a simple and inexpensive method that achieves this by means of non-empirical optimal tuning of the parameters of a screened range-separated hybrid functional. The tuning involves the enforcement of an ansatz that generalizes the ionization potential theorem to the removal of an electron in an occupied state described by a localized Wannier function in a modestly sized supercell calculation. The method is benchmarked against experiment for a set of systems ranging from narrow band gap semiconductors to large band gap insulators, spanning a range of fundamental band gaps from 0.2 to 14.2 eV and is found to yield quantitative accuracy across the board, with a mean absolute error of $\sim$0.1 eV and a maximal error of $\sim$0.2 eV.