Fig. 2: Band gaps obtained with various functionals.

Band edges as obtained with DFT + U and PBE0(α) as a function of U and α, respectively, for BiVO4, MgO, and α-SiO2. For MgO, we consider Uk and αk calculated for the self-trapped hole. The vertical red line denotes the choice of the parameter for which the piecewise linearity condition is retrieved. The energy levels are aligned with respect to the average electrostatic potential98.