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 semiclassical approach where the atoms are assumed to oscillate along classical trajectories immersed in the electronic Kohn–Sham system. In this paper, we demonstrate that, in metals, nonadiabatic 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 semiclassical DFPT description. The final message is that nonadiabatic phonon effects can be described only by using a fully quantistic approach.