Hybrid functionals for periodic systems in the density functional tight-binding method

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van der Heide, Tammo and Aradi, Bálint and Hourahine, Ben and Frauenheim, Thomas and Niehaus, Thomas A. (2023) Hybrid functionals for periodic systems in the density functional tight-binding method. Physical Review Materials, 7 (6). 063802. ISSN 2475-9953 (https://doi.org/10.1103/PhysRevMaterials.7.063802)

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Abstract

Screened range-separated hybrid (SRSH) functionals within generalized Kohn-Sham density functional theory (GKS-DFT) have been shown to restore a general 1/(rɛ) asymptotic decay of the electrostatic interaction in dielectric environments. Major achievements of SRSH include an improved description of optical properties of solids and correct prediction of polarization-induced fundamental gap renormalization in molecular crystals. The density functional tight-binding method (DFTB) is an approximate DFT that bridges the gap between first-principles methods and empirical electronic structure schemes. While purely long-range corrected RSH are already accessible within DFTB for molecular systems, this work generalizes the theoretical foundation to also include screened range-separated hybrids, with conventional pure hybrid functionals as a special case. The presented formulation and implementation is also valid for periodic boundary conditions (PBC) beyond the Γ point. To treat periodic Fock exchange and its integrable singularity in reciprocal space, we resort to techniques successfully employed by DFT, in particular a truncated Coulomb operator and the minimum image convention. Starting from the first-principles Hartree-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 and demonstrated for the polyacene series as well as two- and three-dimensional materials. Benzene and pentacene molecular and crystalline systems show the correct polarization-induced gap renormalization by SRSH-DFTB at heavily reduced computational cost compared to first-principles methods.

ORCID iDs

van der Heide, Tammo, Aradi, Bálint, Hourahine, Ben ORCID logoORCID: https://orcid.org/0000-0002-7667-7101, Frauenheim, Thomas and Niehaus, Thomas A.;
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