Self-consistent hybrid functional for condensed systems

A self-consistent scheme for determining the optimal fraction of exact exchange for full-range hybrid functionals is presented and applied to the calculation of band gaps and dielectric constants of solids. The exchange-correlation functional is defined in a similar manner to the PBE0 functional, but the mixing parameter is set equal to the inverse macroscopic dielectric function and it is determined self-consistently by computing the optimal dielectric screening. We found excellent agreement with experiments for the properties of a broad class of systems, with band gaps ranging between 0. 7 and 21. 7 eV and dielectric constants within 1. 23 and 15. 9. We propose that the eigenvalues and eigenfunctions obtained with the present self-consistent hybrid scheme may be excellent inputs for G₀W₀ calculations.