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We combine the renormalized singles (RS) Green's function with the T-Matrixapproximation for the single-particle Green's function to compute quasiparticleenergies for valence and core states of molecular systems. The$G_{\text{RS}}T_0$ method uses the RS Green's function that incorporatessingles contributions as the initial Green's function. The$G_{\text{RS}}T_{\text{RS}}$ method further calculates the generalizedeffective interaction with the RS Green's function by using RS eigenvalues inthe T-Matrix calculation through the particle-particle random phaseapproximation. The $G_{\text{RS}}T_{\text{RS}}$ method provides significantimprovements over the one-shot T-Matrix method $G_0T_0$ as demonstrated incalculations for GW100 and CORE65 test sets. It also systematically eliminatesthe dependence of $G_{0}T_{0}$ on the choice of density functionalapproximations (DFAs). For valence states, the $G_{\text{RS}}T_{\text{RS}}$method provides an excellent accuracy, which is better than $G_0T_0$ withHartree-Fock (HF) or other DFAs. For core states, the$G_{\text{RS}}T_{\text{RS}}$ method correctly identifies desired peaks in thespectral function and significantly outperforms $G_0T_0$ on core level bindingenergies (CLBEs) and relative CLBEs, with any commonly used DFAs.

Renormalized Singles Green's Function in the T-Matrix Approximation for Accurate Quasiparticle Energy Calculation