  We develop an ab initio method to simulate the infrared vibrational response
of metallic systems in the framework of time-dependent density functional
perturbation theory. By introducing a generalized frequency-dependent Born
effective charge tensor, we show that phonon peaks in the reflectivity of
metals can be always described by a Fano function, whose shape is determined by
the complex nature of the frequency-dependent effective charges and electronic
dielectric tensor. The IR vibrational properties of graphite, chosen as a
representative test case to benchmark our method, are found to be accurately
reproduced. Our approach offers a first-principle scheme for the prediction and
understanding of IR reflectance spectra of metals, that may represent one of
the few available tools of investigation of these materials when subjected to
extremely high-pressure conditions.
