Electron-vibron interactions in charged fullerenes. II. Pair energies and spectra

The ground-state energy shifts and excitation spectra of charged fullerenes ${\mathrm{C}}_{60}^{\mathit{n}\mathrm{-}}$, n=1,...,5 are calculated. The electron-vibron Hamiltonian of part I is extended to include all ${\mathit{A}}_{\mathit{g}}$ and ${\mathit{H}}_{\mathit{g}}$ modes with experimentally determined frequencies and theoretically estimated coupling constants. Complex splitting patterns of ${\mathit{H}}_{\mathit{g}}$ vibrational levels are found. Our results are relevant to EPR measurements of spin splittings in ${\mathrm{C}}_{60}^{2\mathrm{-}}$ and ${\mathrm{C}}_{60}^{3\mathrm{-}}$ in solution. Spectroscopic gas-phase experiments will be of interest for further testing of this theory. As found in part I, degeneracies in the electron and vibron Hamiltonians give rise to a dynamical Jahn-Teller effect, and to a considerable enhancement of the electronic pairing interaction. This helps to overcome repulsive Coulomb interactions and has important implications for superconductivity in ${\mathrm{K}}_3$${\mathrm{C}}_{60}$ and the insulating state in ${\mathrm{K}}_4$${\mathrm{C}}_{60}$.