GWcalculations using the spectral decomposition of the dielectric matrix: Verification, validation, and comparison of methods

Abstract

In a recent paper [Nguyen et al., Phys. Rev. B 85, 081101(R) (2012)] we presented an approach to evaluate quasiparticle energies based on the spectral decomposition of the static dielectric matrix. This method does not require the calculation of unoccupied electronic states or the direct diagonalization of large dielectric matrices, and it avoids the use of plasmon-pole models. The numerical accuracy of the approach is controlled by a single parameter, i.e., the number of eigenvectors used in the spectral decomposition of the dielectric matrix. Here we present a comprehensive validation of the method, encompassing calculations of ionization potentials and electron affinities of various molecules and of band gaps for several crystalline and disordered semiconductors. We demonstrate the efficiency of our approach by carrying out $GW$ calculations for systems with several hundred valence electrons.