  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 density, treated quantistically. In this
work I demonstrate that, in metals, non--adiabatic effects induce a gap between
the DFTP phonon frequencies and the fully quantistic solution of the phonon
Dyson equation. A gap 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 included only by using a fully
quantistic approach.
