Exact exchange Kohn-Sham formalism applied to semiconductors

We present a Kohn-Sham method that allows one to treat exchange interaction s exactly within density-functional theory. The method is used to calculate lattice constants, cohesive energies, Kohn-Sham eigenvalues, dielectric fu nctions, and effective masses of various zinc-blende semiconductors (Si, Ge , C, SiC, GaAs, AIAs, GaN, and AIN). The results are compared with values o btained within the local-density approximation, generalized gradient approx imations, the Krieger-Li-Iafrate approximation for the Kohn-Sham exchange p otential, and the Hartree-Fock method. We find that the exact exchange form alism, augmented by local density or generalized gradient correlations, yie lds both structural and optical properties in excellent agreement with expe riment. Exact exchange-only calculations are found to lead to densities and energies that are close to Hartree-Fock values but to eigenvalue gaps that agree with experiment within 0.2 eV. The generalized gradient approximatio ns for exchange yield energies that are much improved compared to local-den sity values. The exact exchange contribution to the discontinuity of the ex change-correlation potential is computed and discussed in the context of th e band-gap problem. [S01631-1829(99)05515-0].