Excitons in solids from time-dependent density-functional theory: Assessing the Tamm-Dancoff approximation

TL;DR

This paper evaluates the impact of the Tamm-Dancoff approximation on exciton binding energy calculations in solids using TDDFT, highlighting its limitations especially for strongly bound excitons in insulators.

Contribution

It provides a systematic assessment of the TDA's effects on exciton energies in solids within TDDFT, emphasizing the need for full Casida solutions for accuracy.

Findings

TDA slightly underestimates exciton energies in semiconductors.

TDA significantly underestimates exciton energies in insulators by over 100%.

Full Casida equation is necessary for accurate strongly bound exciton descriptions.

Abstract

Excitonic effects in solids can be calculated using the Bethe-Salpeter equation (BSE) or the Casida equation of time-dependent density-functional theory (TDDFT). In both methods, the Tamm-Dancoff approximation (TDA), which decouples excitations and de-excitations, is widely used to reduce computational cost. Here, we study the effect of the TDA on exciton binding energies of solids obtained from the Casida equation using long-range corrected (LRC) exchange-correlation kernels. We find that the TDA underestimates TDDFT-LRC exciton binding energies of semiconductors slightly, but those of insulators significantly (i.e., by more than 100%), and thus it is essential to solve the full Casida equation to describe strongly bound excitons. These findings are relevant in the ongoing search for accurate and efficient TDDFT approaches for excitons.