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

Abstract

Screened range-separated hybrid (SRSH) functionals within generalized Kohn-Sham density functional theory (GKS-DFT) have been shown to restore a general $1/(r\epsilon )$ 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 $\Gamma$-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.

References in corpus (14)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Resolution-of-identity approach to Hartree-Fock, hybrid density functionals, RPA, MP2, and \textit{GW} with numeric atom-centered orbital basis functions
• Fundamental gaps of finite systems from the eigenvalues of a generalized Kohn-Sham method
• A density functional theory with correct long-range asymptotic behavior
• Quasiparticle spectra from a non-empirical optimally-tuned range-separated hybrid density functional
• Ideal regularization of the Coulomb singularity in exact exchange by Wigner-Seitz truncated interactions: towards chemical accuracy in non-trivial systems
• Range separated functionals in the density functional based tight binding method: Formalism
• Hybrid functionals within the all-electron FLAPW method: implementation and applications of PBE0
• Quantitative Molecular Orbital Energies within a $G_0{W}_0$ Approximation
• Importance of electronic self-consistency in the TDDFT based treatment of nonadiabatic molecular dynamics
• Quasiparticle energies for large molecules: a tight-binding GW approach
• The HSE hybrid functional within the FLAPW method and its application to GdN
• Linear scaling computation of the Fock matrix. VIII. Periodic boundaries for exact exchange at the $\Gamma$-point
• Fortnet, a software package for training Behler-Parrinello neural networks

Cited by in corpus (1)

• Density Functional Tight-Binding Enables Tractable Studies of Quantum Plasmonics