Nonadiabatic effects lead to the breakdown of the semiclassical phonon picture

Phonon properties of realistic materials are routinely calculated within the Density Functional Perturbation Theory (DFPT).This is a semi-classical approach where the atoms are assumed to oscillate along classical trajectories immersed in the electronic Kohn-Sham system.In this work I demonstrate that, in metals, non-adiabatic effects induce a deviation of the DFTP phonon frequencies from the quantistic solution of the Dyson equation.A deviation that increases with the phonon energy width reflecting the breakdown of the semi-classical DFPT description.The final message is that non-adiabatic phonon effects can be described only by using a fully quantistic approach.