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

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