Effects of Doping on the Vibrational Properties of C(sub 60) from First Principles: K(sub 6)C(sub 60)

{\it Ab initio\/} calculations of the phonon spectrum of K$_6$C$_{60}$ are presented, based on the local-density approximation of density-functional theory and on linear response theory. The effects of doping on frequencies and infrared intensities are identified and their physical origin discussed in detail for the optically allowed modes. Whereas structural relaxation is primarily responsible for the frequency changes, and especially for the softening of the tangential modes, the change in infrared relative intensities is merely a direct consequence of the electron transfer. The potassium vibrations are found to lie within the range 68--125~cm$^{-1}$ and are well decoupled from the C$_{60}$ intramolecular modes.