The Bethe-Salpeter Equation Formalism: From Physics to Chemistry

TL;DR

The Bethe-Salpeter equation formalism, combined with the GW approximation, offers a highly accurate and computationally efficient method for predicting optical excitations in molecular systems, bridging physics and chemistry.

Contribution

This paper provides a historical overview and critical review of the Bethe-Salpeter equation formalism's application in chemistry, highlighting its strengths and limitations.

Findings

BSE combined with GW yields accurate excitation energies.

BSE offers comparable accuracy to advanced hybrid functionals.

BSE effectively models charge-transfer excitations.

Abstract

The Bethe-Salpeter equation (BSE) formalism is steadily asserting itself as a new efficient and accurate tool in the ensemble of computational methods available to chemists in order to predict optical excitations in molecular systems. In particular, the combination of the so-called $GW$ approximation, giving access to reliable ionization energies and electron affinities, and the BSE formalism, able to model UV/Vis spectra, has shown to provide accurate singlet excitation energies with a typical error of $0.1$--$0.3$ eV. With a similar computational cost as time-dependent density-functional theory (TD-DFT), BSE is able to provide an accuracy on par with the most accurate global and range-separated hybrid functionals without the unsettling choice of the exchange-correlation functional, resolving further known issues (\textit{e.g.}, charge-transfer excitations). In this \textit{Perspective} article, we provide a historical overview of BSE, with a particular focus on its condensed-matter roots. We also propose a critical review of its strengths and weaknesses in different chemical situations.