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

We present a rigorous approach for constructing norm-conserving pseudopoten tials within the exact-exchange (EXX) Kohn-Sham density functional formalis m. The approach is based on the relativistic EXX scheme within the framewor k of the optimized potential method. We derive an integral equation that yi elds the exact local Kohn-Sham exchange potential due to valence electrons. This valence exchange potential is used for constructing ionic pseudopoten tials and replaces the standard procedure of unscreening atomic pseudopoten tials that is shown to be not applicable in the EXX formalism. The Wt pseud opotentials excellently reproduce the experimental atomic ionization energi es and they show a better transferability than the standard pseudopotential s based on the local density approximation (LDA). The relativistic EXX pseu dopotentials are shown to lead to the correct ordering of conduction band m inima in diamond-structure Ge and reduce the LDA errors in the energetic po sitions of d bands in solids.