# A finite field approach to solving the Bethe Salpeter equation

## TL;DR

This paper introduces a novel finite field method for solving the Bethe-Salpeter equation to efficiently compute optical spectra and exciton binding energies in large molecular and solid systems without needing dielectric matrices or virtual states.

## Contribution

The method simplifies BSE calculations by avoiding dielectric matrices and virtual states, utilizing localized orbitals, and enabling efficient use of hybrid functionals for large systems.

## Key findings

- Accurate exciton binding energies for various molecules.
- Optical spectra for large condensed systems like water and ice.
- Reduced computational complexity enabling larger system simulations.

## Abstract

We present a method to compute optical spectra and exciton binding energies of molecules and solids based on the solution of the Bethe-Salpeter equation (BSE) and the calculation of the screened Coulomb interaction in finite field. The method does not require the explicit evaluation of dielectric matrices nor of virtual electronic states, and can be easily applied without resorting to the random phase approximation. In addition it utilizes localized orbitals obtained from Bloch states using bisection techniques, thus greatly reducing the complexity of the calculation and enabling the efficient use of hybrid functionals to obtain single particle wavefunctions. We report exciton binding energies of several molecules and absorption spectra of condensed systems of unprecedented size, including water and ice samples with hundreds of atoms.