Jahn-Teller effects in the fullerene anion ${\mathrm{C}}_{60}^{2-}$

The motion of the electrons in a fullerene molecule is strongly influenced by Jahn-Teller coupling to vibrations of the ${\mathrm{C}}_{60}$ molecular cage. Furthermore, cooperative vibronic coupling between molecules can result in different macroscopic phases. We investigate the linear Jahn-Teller (JT) effects applicable to isolated fullerene anions ${\mathrm{C}}_{60}^{2-}$ and ${\mathrm{C}}_{60}^{4-}.$ Analytical expressions for the energies of the quantum-mechanical states are derived as a function of the vibronic coupling constant. The results obtained will help the understanding of some of the wide range of structural, orientational, magnetic, and superconductive phase transitions seen in fullerene-based solids.