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

Abstract

The Bethe-Salpeter equation (BSE) is the standard computational method for optical excitations in solids, including excitonic effects. In this paper we explore ways to reduce the computational cost of the BSE by simplifying the dielectrically screened Coulomb interaction: Instead of calculating the dielectric function from first principles, we replace it by a momentum-dependent model dielectric function or just by a single parameter. Combined with a semilocal exchange-correlation kernel, this defines an alternative class of hybrid functionals for solids within generalized time-dependent density-functional theory. We perform a systematic assessment of these simplified approaches and find that they yield optical absorption spectra and exciton binding energies of semiconductors and wide-gap insulators in close agreement with the standard BSE and with experiment. We also present applications to the perovskite material CsPbBr 3 as an example of a more complex system.

Accurate optical spectra through time-dependent density functional theory based on screening-dependent hybrid functionals

“…In particular, we show that the off-diagonal elements of this matrix barely have any effect on the calculated spectrum (W diag ), in accordance with Ref. [30]. Next, we replace the inverse dielectric function with the model c DDH x (|q + G|) and find no discernible difference in the spectrum (W m ).…”

“…Several different approximations for the screening of the nonlocal exchange interaction have been investigated [26][27][28][29][30]. The results suggest that hybrid functionals yield spectra comparable to BSE-GW provided the adopted fraction of Fock exchange accounts for the screening in the long range.…”

“…Notice that we here consider isotropic screening and that the extension of this model to anisotropic materials remains to be investigated. The present treatment of the screening is equivalent to that of TD-DDH, where the local exchange-correlation kernel is neglected, i.e., f loc xc = 0, also referred to as model BSE (mBSE) [30,66]. To restore the full TD-DDH screening, we include the f loc…”

Hybrid functionals with system‐dependent parameters: Conceptual foundations and methodological developments

“…In the context of simplifying the GW approach 63,92,112 for semiconductors, Bechstedt et al proposed the following model dielectric function, 113,114 where ω pl = (4 πn val ) 1/2 is the plasmon frequency corresponding to the valence electron density n val , and α , taking the value of 1.563, is a fitting parameter introduced by Bechstedt et al to better reproduce directly calculated dielectric function for typical semiconductors 114 . We note that this model dielectric functional has recently attracted a lot of interest in the model Bethe–Salpeter equation (mBSE) or other related approaches in the framework of time‐dependent DFT (TDDFT) with hybrid functionals 115,116 as an effort to reduce the computational cost of the standard BSE calculations of optical properties of materials. The Bechstedt model dielectric function has the nice features that it reproduces the Thomas–Fermi screening model when ε ∞ is large and q is small, and in the long‐range limit ( q = 0), ε (0) = ε ∞ .…”

Machine learning dielectric screening for the simulation of excited state properties of molecules and materials

“…Another important advantage of the ML-derived dielectric screening is that it provides insight into the approximate screening parameters used in the derivation of hybrid functionals for time-dependent DFT (TDDFT) calculations, including dielectric-dependent hybrid (DDH) functionals. [44][45][46][47][48] We emphasize that the strategy adopted here is different in spirit from strategies that use ML to infer structure-property relationships [49][50][51][52][53][54][55][56][57] or relationships between computational and experimental data. 58 We do not seek to relate structural properties of a molecule or a solid to its absorption spectrum.…”