A Density-Based Basis-Set Incompleteness Correction for GW Methods

TL;DR

This paper introduces a density-based correction method that accelerates the convergence of GW calculations towards the complete basis set limit, improving accuracy in ionization potential predictions for atoms, molecules, and nucleobases.

Contribution

It presents a novel, efficient density functional correction for GW methods that addresses basis set incompleteness, enhancing computational accuracy without significant additional cost.

Findings

Significant speed-up in basis set convergence for GW ionization potentials.

Improved accuracy in predicting ionization potentials of atoms and molecules.

Effective correction applied to nucleobases, demonstrating broad applicability.

Abstract

Similar to other electron correlation methods, many-body perturbation theory methods based on Green functions, such as the so-called $GW$ approximation, suffer from the usual slow convergence of energetic properties with respect to the size of the one-electron basis set. This displeasing feature is due to lack of explicit electron-electron terms modeling the infamous Kato electron-electron cusp and the correlation Coulomb hole around it. Here, we propose a computationally efficient density-based basis set correction based on short-range correlation density functionals which significantly speeds up the convergence of energetics towards the complete basis set limit. The performance of this density-based correction is illustrated by computing the ionization potentials of the twenty smallest atoms and molecules of the GW100 test set at the perturbative $GW$ (or $G_0W_0$) level using increasingly large basis sets. We also compute the ionization potentials of the five canonical nucleobases (adenine, cytosine, thymine, guanine, and uracil) and show that, here again, a significant improvement is obtained.