Beyond time-dependent exact-exchange: the need for long-range correlation

TL;DR

This paper compares different theoretical frameworks for electron interactions in solids, highlighting the importance of long-range correlation and screening effects to accurately predict optical spectra, especially excitonic effects.

Contribution

It demonstrates that incorporating screening into time-dependent exact-exchange methods aligns them with many-body perturbation theory, improving agreement with experimental spectra.

Findings

All three frameworks overestimate excitonic effects in semiconductors.

Screening reduces the overestimated excitonic effects.

Adjusting the long-range Coulomb interaction yields spectra in good agreement with experiments.

Abstract

In the description of the interaction between electrons beyond the classical Hartree picture, bare exchange often yields a leading contribution. Here we discuss its effect on optical spectra of solids, comparing three different frameworks: time-dependent Hartree-Fock, a recently introduced combined density-functional and Green's functions approach applied to the bare exchange self-energy, and time-dependent exact-exchange within time-dependent density-functional theory (TD-EXX). We show that these three approximations give rise to identical excitonic effects in solids; these effects are drastically overestimated for semiconductors. They are partially compensated by the usual overestimation of the quasiparticle band gap within Hartree-Fock. The physics that lacks in these approaches can be formulated as screening. We show that the introduction of screening in TD-EXX indeed leads to a formulation that is equivalent to previously proposed functionals derived from Many-Body Perturbation Theory. It can be simulated by reducing the long-range part of the Coulomb interaction: this produces absorption spectra of semiconductors in good agreement with experiment.