Electronic excitation energies of molecular systems from the Bethe-Salpeter equation: Example of the H2 molecule

TL;DR

This paper reviews the Bethe-Salpeter equation method for calculating molecular electronic excitation energies, demonstrating its application to the H2 molecule and analyzing the effects of different Green's functions on the results.

Contribution

It provides a detailed application of the BSE approach to a simple molecule, highlighting the impact of the starting Green's function choice on excitation energy accuracy.

Findings

Using non-interacting Green's function yields incorrect energy curves.

Starting from the exact Green's function improves results but still has issues.

The method produces some spurious excitations, including a double excitation.

Abstract

We review the Bethe-Salpeter equation (BSE) approach to the calculation of electronic excitation energies of molecular systems. We recall the general Green's function many-theory formalism and give the working equations of the BSE approach within the static GW approximation with and without spin adaptation in an orbital basis. We apply the method to the pedagogical example of the H2 molecule in a minimal basis, testing the effects of the choice of the starting one-particle Green's function. Using the non-interacting one-particle Green's function leads to incorrect energy curves for the first singlet and triplet excited states in the dissociation limit. Starting from the exact one-particle Green's function leads to a qualitatively correct energy curve for the first singlet excited state, but still an incorrect energy curve for the triplet excited state. Using the exact one-particle Green's function in the BSE approach within the static GW approximation also leads to a number of additional excitations, all of them being spurious except for one which can be identified as a double excitation corresponding to the second singlet excited state.