Molecular cluster calculations within the local density approximation have been performed in a study of the electronic structure of the truncated icosahedral C60 also known as “Buckminsterfullerene” and C60 doped with K, B and N. Evaluated ionisation energies for C60 are found to be in good agreement with recently observed gas phase and solid-state photoelectron spectra. Excitation energies evaluated in the 1–10 eV energy range are also found to reproduce UV, IR and HREELS spectra. Calculations for the KC60 molecule, with the K atom located at the centre of the cage, show how the valence electron from K is transferred to the LUMO state of the bare C60 molecule. Doping with a B or N atom in the centre of the cage creates a different structure with a partly occupied level in the band gap, similar to the donor and acceptor levels in traditionally doped semiconductors. Doping by substitution of two of the carbon atoms in the cage with X = B or N, as modelled with the C58X2 cluster, gives a different structure with a splitting of the HOMO and LUMO levels in the bare C60 molecule.