Improving the efficiency of $G_0W_0$ calculations with approximate spectral decompositions of dielectric matrices

TL;DR

This paper introduces an efficient method for $G_0W_0$ calculations by approximating dielectric matrices using a subset of eigenvectors, significantly reducing computational cost without sacrificing accuracy.

Contribution

It proposes a novel approximation of dielectric response functions using eigenvectors from the kinetic operator, enhancing $G_0W_0$ calculation efficiency for molecules and solids.

Findings

Significant computational savings for larger systems.

No substantial loss of accuracy in quasiparticle energies.

Efficiency improves with increasing system size.

Abstract

Recently it was shown that the calculation of quasiparticle energies using the $G_0W_0$ approximation can be performed without computing explicitly any virtual electronic states, by expanding the Green function and screened Coulomb interaction in terms of the eigenstates of the static dielectric matrix. Avoiding the evaluation of virtual electronic states leads to improved efficiency and ease of convergence of $G_0W_0$ calculations. Here we propose a further improvement of the efficiency of these calculations, based on an approximation of density-density response functions of molecules and solids. The approximation relies on the calculation of a subset of eigenvectors of the dielectric matrix using the kinetic operator instead of the full Hamiltonian, and it does not lead to any substantial loss of accuracy for the quasiparticle energies. The computational savings introduced by this approximation depend on the system, and they become more substantial as the number of electrons increases.