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A modified version of the exchange potential proposed by Becke and Johnson [ J. Chem. Phys. 124 221101 (2006)] is tested on solids for the calculation of band gaps. The agreement with experiment is very good for all types of solids we considered (e.g., wide band gap insulators, sp semiconductors, and strongly correlated 3d transition-metal oxides) and is of the same order as the agreement obtained with the hybrid functionals or the GW methods. This semilocal exchange potential, which recovers the local-density approximation (LDA) for a constant electron density, mimics very well the behavior of orbital-dependent potentials and leads to calculations which are barely more expensive than LDA calculations. Therefore, it can be applied to very large systems in an efficient way.
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