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

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_RSW_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_RSW_RS approach significantly outperforms BSE/G₀W₀ 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_RSW_RS provides comparable accuracy to time-dependent density functional theory (TDDFT) and is slightly better than BSE starting from eigenvalue self-consistent GW (evGW). For the Stein CT test set, BSE/G_RSW_RS significantly outperforms BSE/G₀W₀ and TDDFT with the accuracy comparable to BSE/evGW. We also show that BSE/G_RSW_RS predicts Rydberg excitation energies of atomic systems well. Besides the excellent accuracy, BSE/G_RSW_RS largely eliminates the dependence on the choice of the density functional approximation. This work demonstrates that the BSE/G_RSW_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.

Figure 1.

MAEs and MSEs of excitation energies in the Truhlar–Gagliardi test set obtained from TDDFT, BSE/G₀W₀, BSE/G_RSW₀, BSE/G_RSW_RS, and BSE/evGW based on HF, BLYP, PBE, B3LYP, PBE0, and PBEh(0.75). Reference values for pNA and DMABN were taken from ref and for the remaining molecules from ref . The reference values are the theoretical best estimates. The aug-cc-pVDZ basis set was used for naphthalene, pNA, and DMABN, and the aug-cc-pVTZ basis set was used for the remaining systems. B-TCNE was excluded due to the high computational cost. Total MAEs and total MSEs were calculated by averaging all systems with equal weights. The error for system i is defined as ${\text{Error}}_i=E_i^{\text{calc}}-E_i^{\text{reference}}$.

Figure 2.

Signed errors of B⁺, Be and Mg obtained from TDDFT, BSE/G₀W₀, BSE/G_RSW₀, BSE/G_RSW_RS, and BSE/evGW with HF, BLYP, PBE, B3LYP, and PBE0. All values in eV. Experimental values were taken as the reference values. The aug-cc-pVQZ basis set was used. The signed error for system i is defined as ${\text{Error}}_i=E_i^{\text{calc}}-E_i^{\text{experiment}}$.