Computational protocol to evaluate electron-phonon interactions within density matrix perturbation theory

We present a computational protocol, based on density matrix perturbation theory, to obtain non-adiabatic, frequency-dependent electron-phonon self-energies for molecules and solids. Our approach enables the evaluation of electron-phonon interaction using hybrid functionals, for spin-polarized systems, and the computational overhead to include dynamical and non-adiabatic terms in the evaluation of electron-phonon self-energies is negligible. We discuss results for molecules, as well as pristine and defective solids.