Density-Based Basis-Set Incompleteness Correction for GW Methods

Similar to other electron correlation methods, many-body perturbation theory methods based on Green's 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 the 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 toward the complete basis set limit. The performance of this density-based correction is illustrated by computing the ionization potentials of the 20 smallest atoms and molecules of the GW100 test set at the perturbative GW (or G₀W₀) 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.