Renormalized Singles with Correlation in $GW$ Green's Function Theory for Accurate Quasiparticle Energies

We apply the renormalized singles with correlation (RSc) Green's function in the $GW$ approximation to calculate accurate quasiparticle (QP) energies and orbitals. The RSc Green's function includes all orders of singles contributions from the associated density functional approximation (DFA) and treats higher order contributions in a perturbative manner. The $G_{\text{RSc}}W_{\text{RSc}}$ method uses the RSc Green's function as the new starting point and calculates the screened interaction with the RSc Green's function. The $G_{\text{RSc}}W_0$ methods fixes the screened interaction at the DFA level. For the calculations of ionization potentials in the GW100 set, $G_{\text{RSc}}W_{\text{RSc}}$ significantly reduces the dependence on the starting point of DFAs used and provides accurate results with the mean absolute error (MAE) of $0.34$ eV comparable to ev$GW$. For the calculations of core-level binding energies in the CORE65 set, $G_{\text{RSc}}W_{\text{RSc}}$ slightly overestimates the results because of underscreening, but $G_{\text{RSc}}W_0$ with GGA functionals provides the optimal accuracy of $0.40$ eV MAE comparable to ev$GW_0$. We also show that $G_{\text{RSc}}W_{\text{RSc}}$ predicts accurate dipole moments of small molecules. These two methods, $G_{\text{RSc}}W_{\text{RSc}}$ and $G_{\text{RSc}}W_0$, are computationally much favorable than any flavor of self-consistent $GW$ methods. Thus, the RSc approach is promising for making $GW$ and other Green's function methods efficient and robust.