Nonempirical dielectric-dependent hybrid functional with range separation for semiconductors and insulators

Abstract

We present a general scheme of range-separated hybrid functionals in which the mixing parameters of Fock exchange are fully nonempirical and determined solely from the dielectric function.We showthat the full dielectric dependence leads to an unscreened Fock exchange in the short range, while in the long range the Fock exchange is correctly screened by the macroscopic dielectric constant. The range separation is obtained by fitting to the calculated static dielectric function in the long-wavelength limit. The resulting hybrid functional accurately accounts for electronic and structural properties of various semiconductors and insulators spanning a wide range of band gaps. We present a general scheme of range-separated hybrid functionals in which the mixing parameters of Fock exchange are fully nonempirical and determined solely from the dielectric function. We show that the full dielectric dependence leads to an unscreened Fock exchange in the short range, while in the long range the Fock exchange is correctly screened by the macroscopic dielectric constant. The range separation is obtained by fitting to the calculated static dielectric function in the long-wavelength limit. The resulting hybrid functional accurately accounts for electronic and structural properties of various semiconductors and insulators spanning a wide range of band gaps.

Low-cost alternatives to the Bethe-Salpeter equation: Towards simple hybrid functionals for excitonic effects in solids

“…While hybrid functionals have found widespread application for periodic solids due mainly to their excellent performance for calculating band gaps [37][38][39][40][41][42][43][44][45][46][47][48][49], there have so far been relatively few applications of hybrid functionals for optical spectra in semiconductors and insulators [50][51][52][53][54][55][56][57].…”

“…A very widely used generalization of (TD)DFT [29][30][31] is based on hybrid functionals, where a fraction of nonlocal (Hartree-Fock) exchange is combined with semilocal exchange and correlation [32][33][34][35][36]. In ground-state DFT, hybrid xc functionals have gained increased popularity for calculating electronic band structures, since they offer a practical solution to DFT's band-gap problem [37][38][39][40][41][42][43][44][45][46][47][48][49]. There also are a few applications of hybrid xc functionals to describe excitations in periodic solids [50][51][52][53].…”

Nonempirical hybrid functionals for band gaps of inorganic metal-halide perovskites

“…The connection between these quantities was first observed for the fraction of Fock exchange α and the inverse macroscopic dielectric constant 1/ε ∞ [18,25]. Various authors contributed to the further development of this basic idea, in particular through the use of self-consistent update schemes [23,27,28] and the extension to range-separated hybrid functionals [30,32]. In particular, in Ref.…”

“…In particular, in Ref. [32], all the parameters of the DDH functional are extracted from the static dielectric response function.…”

“…However, hybrid functionals remain unsatisfactory because they contain undetermined parameters, such as the amount of incorporated Fock exchange. To overcome this deficiency, two different nonempirical determination schemes are being investigated at present, namely, * thomas.bischoff@epfl.ch dielectric-dependent hybrid (DDH) functionals [22][23][24][25][26][27][28][29][30][31][32] and hybrid functionals enforcing Koopmans' condition [33][34][35][36][37][38][39][40]. Both approaches exhibit great potential due to their promising combination of accuracy and computational cost.…”