First Principles Excitons in Periodic Systems with Gaussian Density Fitting and Ewald Potential Functions

TL;DR

This paper introduces a computational approach using Gaussian basis functions and Ewald potentials to efficiently solve the Bethe-Salpeter equation for excitons in non-metallic solids, enabling accurate optical property predictions.

Contribution

It presents a novel method combining Gaussian density fitting and Ewald potentials to calculate excitonic effects from first principles in periodic systems.

Findings

Successfully computed exciton spectra in 2D and 3D materials.

Demonstrated the method's ability to handle systems where single-particle approximations fail.

Provided optical absorption results consistent with experimental observations.

Abstract

Excitons, namely neutral excitations in a system of electrons arising from the electron-hole interaction, are often essential to explain optical measurements in materials. They are governed by the Bethe-Salpeter equation, which can be cast into a matrix form that is formally analogous to the one for electrons at the mean-field level. However, constructing the corresponding excitonic Hamiltonian in practice is challenging, specially from a computational perspective if one wishes to surpass effective models. Methods that enable such calculations from the different density-functional theory frameworks currently available are, therefore, convenient. In this work we present an approach to solve the BSE employing Gaussian basis functions starting from a self-consistent, possibly hybrid calculation in any non-metallic solid. It is based on the Gaussian density fitting or resolution of the identity approximation to reduce the initial quartic scaling in the basis dimension, in combination with the use of Ewald-type potential functions to automatically sum the conditionally convergent lattice series. As an illustration of the computational implementation, we provide examples of exciton spectra and optical absorption in some paradigmatic 2D and 3D materials where the single-particle approximation fails qualitatively.