  We apply the density functional theory for superconductors (SCDFT) based on
the local-density approximation (LDA) to alkali-doped fullerides A3C60 with the
face-centered cubic structure. We evaluate the superconducting transition
temperature (Tc) from first principles considering energy dependence of
electron-phonon coupling, the mass renormalization, and the retardation effect.
The calculated Tc=7.5, 9.0 and 15.7 K for A=K, Rb, Cs are approximately 60 %
smaller than the experimentally observed values. Our results strongly suggest
necessity to go beyond the framework of the Migdal-Eliashberg theory based on
the LDA.
