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

We combine the renormalized singles (RS) Green's function with the T-matrix approximation for the single-particle Green's function to compute quasiparticle energies for valence and core states of molecular systems. The GRST0 method uses the RS Green's function that incorporates singles contributions as the initial Green's function. The GRSTRS method further calculates the generalized effective interaction with the RS Green's function by using RS eigenvalues in the T-matrix calculation through the particle-particle random phase approximation. The GRSTRS method provides significant improvements over one-shot methods G0T0 and G0W0 as demonstrated in calculations for GW100 and CORE65 test sets. It also systematically eliminates the dependence of G0T0 on the choice of density functional approximations. For valence states, the GRSTRS method provides excellent accuracy, which is better than that of G0T0 and G0W0. For core states, the GRSTRS method identifies correct peaks in the spectral function and significantly outperforms G0T0 on core-level binding energies (CLBEs) and relative CLBEs.