Predicting Complete Basis Set Limit Quasiparticle Energies from Triple-ζ Calculations

We present a simple linear model to estimate the basis set incompleteness errors (BSIEs) of (vertex-corrected) <i>GW</i> QP energies based on the kinetic energy of the corresponding orbital only. We parametrize the model for <i>G</i>₀<i>W</i>₀, quasi-particle self-consistent <i>GW</i> (qs<i>GW</i>), and vertex-corrected (Σ^BSE<i>@L</i>^BSE) QP energies on a large set of molecules containing 10 different elements for which we calculate complete basis set (CBS) limit extrapolated reference values with correlation-consistent basis sets ranging from triple to hextuple ζ (TZ/6Z). Based on these accurate reference values, we obtain model parameters for Gaussian- and Slater-type orbital (GTO and STO, respectively) basis sets that allow for the extrapolation of QP energies calculated with TZ basis sets to the CBS limit with errors of 20-30 meV. Analyzing extrapolation errors, we show the commonly used extrapolation method that assumes an inverse linear dependence of the BSIE on the inverse number of basis functions to be valid but to produce much larger errors, unless a quadruple-ζ calculation is used in the extrapolation.