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The exact-exchange (EXX) potential, which is obtained by solving theoptimized-effective potential (OEP) equation, is compared to variousapproximate 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 linearizedaugmented plane-wave method, which allows for a very accurate all-electronsolution of electronic structure problems in solids. In order to assess theability of the semilocal potentials to approximate the EXX-OEP, we consideredthe EXX total energy, electronic structure, electric-field gradient, andmagnetic moment. An attempt to parameterize a semilocal exchange potential isalso reported.

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