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We present a method to efficiently combine the computation ofelectron-electron and electron-phonon self-energies, which enables theevaluation of electron-phonon coupling at the $G_0W_0$ level of theory forsystems with hundreds of atoms. In addition, our approach, which is ageneralization of a method recently proposed for molecules [J. Chem. TheoryComput. 2018, 14, 6269-6275], enables the inclusion of non-adiabatic andtemperature effects at no additional computational cost. We present results fordiamond and defects in diamond and discuss the importance of numericallyaccurate $G_0W_0$ band structures to obtain robust predictions of zero pointrenormalization (ZPR) of band gaps, and of the inclusion of non-adiabaticeffect to accurately compute the ZPR of defect states in the band gap.

Combined first-principles calculations of electron-electron and electron-phonon self-energies in condensed systems