π-Molecular orbitals in fullerenes and the free electron model

π-Molecular orbitals (π-MOs) in fullerenes were characterized by reference to energy levels of the electron gas bound on the surface of a sphere. We plotted all π-MOs in many fullerene isomers on a single energy scale and obtained the quasi density-of-state (DOS) curve for the fullerene. The quasi DOS curve on the low-energy side consists of several distinct peaks, which were found to correspond to the electronic shells of the free electron model. The quasi DOS near the non-bonding level is small like that of a graphite sheet, indicating that fullerenes have a relatively large HOMO–LUMO gap energy.