  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.

Materials Science;Computational Physics