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

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