Bound excitons in time-dependent density-functional-theory: optical and energy-loss spectra

TL;DR

This paper develops a new frequency-dependent exchange-correlation kernel in TDDFT that accurately reproduces excitonic effects in optical and energy-loss spectra, matching results from the Bethe-Salpeter approach.

Contribution

A novel, efficient, and easy-to-implement $f_{xc}$ kernel for TDDFT that captures excitonic effects in optical and energy-loss spectra.

Findings

TDDFT with the new $f_{xc}$ reproduces Bethe-Salpeter excitonic spectra

Accurate spectra for LiF, SiO2, and diamond

Effective for both bound and resonant excitons

Abstract

A robust and efficient frequency dependent and non-local exchange-correlation $f_{xc}(r,r';\omega)$ is derived by imposing time-dependent density-functional theory (TDDFT) to reproduce the many-body diagrammatic expansion of the Bethe-Salpeter polarization function. As an illustration, we compute the optical spectra of LiF, \sio and diamond and the finite momentum transfer energy-loss spectrum of LiF. The TDDFT results reproduce extremely well the excitonic effects embodied in the Bethe-Salpeter approach, both for strongly bound and resonant excitons. We provide a working expression for $f_{xc}$ that is fast to evaluate and easy to implement.