# Accurate optical spectra of solids from pure time-dependent density-functional theory

## TL;DR

This paper demonstrates that accurate optical spectra of semiconductors and insulators can be obtained using a pure time-dependent density-functional theory approach without empirical corrections or advanced methods like GW, by leveraging the exchange-correlation kernel.

## Contribution

The authors establish a direct link between the exchange-correlation kernel and the derivative discontinuity, enabling accurate optical spectra calculations within pure TDDFT.

## Key findings

- Accurate optical absorption onset matches experimental data.
- No need for empirical parameters or GW corrections.
- Effective for various semiconductors and insulators.

## Abstract

We present accurate optical spectra of semiconductors and insulators within a pure Kohn-Sham time-dependent density-functional approach. In particular, we show that the onset of the absorption is well reproduced when comparing to experiment. No empirical information nor a theory beyond Kohn-Sham density-functional theory, such as $GW$, is invoked to correct the Kohn-Sham gap. Our approach relies on the link between the exchange-correlation kernel of time-dependent density functional theory and the derivative discontinuity of ground-state density-functional theory. We show explicitly how to relate these two quantities. We illustrate the accuracy and simplicity of our approach by applying it to various semiconductors (Si, GaP, GaAs) and wide-gap insulators (C, LiF, Ar).