Norm-conserving pseudopotentials in the exact-exchange Kohn-Sham formalism

We present a rigorous approach for constructing norm-conserving pseudopotentials within the exact-exchange (EXX) Kohn-Sham density functional formalism. The approach is based on the relativistic EXX scheme within the framework of the optimized potential method. We derive an integral equation that yields the exact local Kohn-Sham exchange potential due to valence electrons. This valence exchange potential is used for constructing ionic pseudopotentials and replaces the standard procedure of unscreening atomic pseudopotentials that is shown to be not applicable in the EXX formalism. The Wt pseudopotentials excellently reproduce the experimental atomic ionization energies and they show a better transferability than the standard pseudopotentials based on the local density approximation (LDA). The relativistic EXX pseudopotentials are shown to lead to the correct ordering of conduction band minima in diamond-structure Ge and reduce the LDA errors in the energetic positions of d bands in solids.