  The fine structure and temperature evolution of infrared spectra have been
intensively used to probe the nature of Jahn-Teller dynamics in correlated
materials. At the same time, theoretical framework to adequately extract the
information on the complicated vibronic dynamics from infrared spectra is still
lacking. In this work, the first-principles theory of the infrared spectra of
dynamical Jahn-Teller system is developed and applied to the Mott-insulating
Cs$_3$C$_{60}$. With the calculated coupling parameters for Jahn-Teller and
infrared active vibrational modes, the manifestation of the dynamical
Jahn-Teller effect in infrared spectra is elucidated. In particular, the
temperature evolution of the infrared line shape is explained. The
transformation of the latter into Fano resonance type in metallic fulleride is
discussed on the basis of obtained results.
