Predicting complete basis set limit quasiparticle energies from triple-$ζ$ calculations

Abstract

We present a simple linear model to estimate the basis set incompleteness errors (BSIE) of (vertex-corrected) $GW$ QP energies based on the kinetic energy of the corresponding orbital only. We parametrise the model for $G_0W_0$, quasi-particle self-consistent $GW$ (qs$GW$), and vertex-corrected ($Σ^{BSE}@L^{BSE}$) 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-type and Slater-type orbital (GTO/STO) basis sets which allow for the extrapolation of QP energies calculated with TZ basis sets to the CBS limit with errors of 20 to 30 meV. Analysing extrapolation errors, we show the commonly used extrapolation method which assumes an inverse linear dependence of the BSIE on the inverse number of basis functions to be valid, but to produce larger errors, even when a quadruple-$ζ$ calculation is used in the extrapolation.

Figures (5)

• Figure 1: Basis set convergence with fits based on average exponent (“Fit”) and based on the individually optimal exponents (“Optimal Fit”) for $G_0W_0$@BHandHLYP (top row) and $\Sigma^{BSE}@L^{BSE}$ (bottom row) on the General set. Examples are shown for samples where, with respect to the average exponent, the fitted exponent exactly coincides (left column), deviates by one standard deviation (middle column) or deviates the most out of all samples in the set (right column).
• Figure 2: Linear correlation between the natural logarithm of the kinetic energy and the BSIE, based on the CBS limit (left) and based on a 5Z basis set (right).
• Figure 3: MAE of predicted BSIEs of QP energies on the Organic set using our extrapolation based on different GTO basis sets (left), STO basis sets (middle) and using standard two-point basis set extrapolation (right).
• Figure 4: Predicted BSIEs for the Organic set, in the top row using our proposed extrapolation method based on TZ calculations, in the bottom row using standard two-point extrapolation with TZ and QZ calculations.
• Figure 5: Predicted BSIE based on TZ3P calculations for the Organic set plotted against the corresponding reference BSIE based on converged QP energies (left) and based on first-iteration QP energies (right).