Implementation of screened hybrid functionals based on the Yukawa potential within the LAPW basis set

The implementation of screened hybrid functionals into the wien2k code, which is based on the linearized augmented plane wave (LAPW) basis set, is reported. The Hartree-Fock exchange energy and potential are screened by means of the Yukawa potential as proposed by Bylander and Kleinman [D. M. Bylander and L. Kleinman, Phys. Rev. B 41, 7868 (1990)] for the calculation of the electronic structure of solids with the screened-exchange local density approximation. Details of the formalism, which is based on the method of Massidda, Posternak, and Baldereschi [S. Massidda, M. Posternak, and A. Baldereschi, Phys. Rev. B 48, 5058 (1993)] for the unscreened Hartree-Fock exchange are given. The results for the transition-energy and structural properties of several test cases are presented. The results of calculations of the Cu electric-field gradient in Cu${}_{2}$O are also presented, and it is shown that the hybrid functionals are much more accurate than the standard local-density or generalized gradient approximations.