Comparison between exact and semilocal exchange potentials: An all-electron study for solids

The exact-exchange (EXX) potential, which is obtained by solving the optimized-effective potential (OEP) equation, is compared to various approximate semilocal exchange potentials for a set of selected solids (C, Si, BN, MgO, Cu$_{2}$O, and NiO). This is done in the framework of the linearized augmented plane-wave method, which allows for a very accurate all-electron solution of electronic structure problems in solids. In order to assess the ability of the semilocal potentials to approximate the EXX-OEP, we considered the EXX total energy, electronic structure, electric-field gradient, and magnetic moment. An attempt to parameterize a semilocal exchange potential is also reported.