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

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 RS W 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 RS W RS approach significantly outperforms BSE/ G 0 W 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 RS W 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 RS W RS significantly outperforms BSE/ G 0 W 0 and TDDFT with the accuracy comparable to BSE/ev GW . We also show that BSE/ G RS W RS predicts Rydberg excitation energies of atomic systems well. Besides the excellent accuracy, BSE/ G RS W RS largely eliminates the dependence on the choice of the density functional approximation. This work demonstrates that the BSE/ G RS W 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.