Combining Renormalized Singles $GW$ Methods with the Bethe-Salpeter Equation for Accurate Neutral Excitation Energies

TL;DR

This paper introduces a combined renormalized singles $GW$ and Bethe-Salpeter equation method that significantly improves the accuracy of neutral excitation energy predictions across various molecular systems, outperforming many existing approaches.

Contribution

The study develops and validates a new BSE/$G_{ ext{RS}}W_{ ext{RS}}$ approach that enhances accuracy and reduces dependence on density functional choices for excitation energy calculations.

Findings

Outperforms BSE/$G_0W_0$ in predicting excitation energies.

Achieves accuracy comparable to or better than TDDFT and ev$GW$.

Effectively predicts Rydberg and charge transfer excitations.

Abstract

We apply the renormalized singles (RS) Green's function in the Bethe-Salpeter equation (BSE)/$GW$ approach to predict accurate neutral excitation energies of molecular systems. The BSE calculations are performed on top of the $G_{\text{RS}}W_{\text{RS}}$ method, which uses the RS Green's function also for the computation of the screened Coulomb interaction $W$. We show that the BSE/$G_{\text{RS}}W_{\text{RS}}$ approach significantly outperforms BSE/$G_0W_0$ for predicting excitation energies of valence, Rydberg and charge transfer (CT) excitations by benchmarking the Truhlar-Gagliardi set, Stein CT set and an atomic Rydberg test set. For the Truhlar-Gagliardi test set, BSE/$G_{\text{RS}}W_{\text{RS}}$ provides comparable accuracy to time-dependent density functional theory (TDDFT) and is slightly better than BSE starting from eigenvalue self-consistent $GW$ (ev$GW$). For the Stein CT test set, BSE/$G_{\text{RS}}W_{\text{RS}}$ significantly outperforms BSE/$G_0W_0$ and TDDFT with the accuracy comparable to BSE/ev$GW$. We also show that BSE/$G_{\text{RS}}W_{\text{RS}}$ predicts Rydberg excitation energies of atomic systems well. Besides the excellent accuracy, BSE/$G_{\text{RS}}W_{\text{RS}}$ largely eliminates the dependence on the choice of the density functional approximation. This work demonstrates that the BSE/$G_{\text{RS}}W_{\text{RS}}$ approach is accurate and efficient for predicting excitation energies for a broad range of systems, which expands the applicability of the BSE/$GW$ approach.