Using a tight-binding model with electron-phonon coupling, we have studied several ground and excited states of the neutral and ionic ${\mathrm{C}}_{60}$ cluster, hypothesized to have the structure of a soccer ball. We find that the presence of pentagons weakens the resonant π-bonding structure compared to graphite, and we present an analysis of this effect. The ionic ground state and low-lying neutral excited electronic states undergo Jahn-Teller instabilities which we classify. No localized self-trapped electronic states occur as excited states of the neutral structure or as ground states of singly ionic structures.

• Received 5 November 1986

DOI:https://doi.org/10.1103/PhysRevB.36.5010