Combined First-Principles Calculations of Electron-Electron and Electron-Phonon Self-Energies in Condensed Systems

We present a method to efficiently combine the computation of electron-electron and electron-phonon self-energies, which enables the evaluation of electron-phonon coupling at the G₀W₀ level of theory for systems with hundreds of atoms. In addition, our approach, which is a generalization of a method recently proposed for molecules [J. Chem. Theory Comput. 2018, 14, 6269-6275], enables the inclusion of nonadiabatic and temperature effects at no additional computational cost. We present results for diamond and defects in diamond and discuss the importance of numerically accurate G₀W₀ band structures to obtain robust predictions of zero point renormalization (ZPR) of band gaps, and of the inclusion of nonadiabatic effects to accurately compute the ZPR of defect states in the band gap.