Screened range-separated hybrid functionals in the density functional tight-binding method: theory and implementation for periodic systems*

Screened range-separated hybrid (SRSH) functionals within generalized Kohn-Sham density functional theory (GKS-DFT) have been shown to restore the correct 1/(rε) asymptotic decay of the screened Coulomb interaction in a dielectric environment (ε). Major achievements of SRSH include an improved description of optical properties and correct prediction of polarization-induced fundamental gap renormalization in molecular crystals [1]. The density functional tight-binding method (DFTB) is an approximate DFT that bridges the gap between first principles methods and empirical schemes. While RSH have already been accessible within DFTB for molecular systems [2], effort has been made to generalize the theoretical foundation to extended systems beyond the Γ-point. For treating the periodic Fock exchange and its integrable singularity in reciprocal space, we resort to techniques successfully employed by DFT. Starting from the first principles Fock operator, we derive suitable expressions for the DFTB method, using standard integral approximations and their efficient implementation in the DFTB+ software package. Convergence behavior is investigated for, among others, one-dimensional acene chains and three-dimensional bulk systems.

[1] Sivan Refaely-Abramson et al. (2013), Phys. Rev. B 88, p. 081204.

[2] Niehaus, T.A. and Della Sala, F. (2012), Phys. Status Solidi B, 249: 237-244.