Exciton levels in undoped, solid ${\mathrm{C}}_{60}$ are calculated using a model Hamiltonian. We find excitation energies of 1.58 and 1.30 eV for the lowest singlet and triplet exciton, respectively, in comparison with the measured energies of 1.83 and 1.55 eV. Singlet and triplet states have similar energy diagrams, wherein exciton states having ${\mathit{T}}_{2\mathit{g}}$, ${\mathit{T}}_{1\mathit{g}}$, ${\mathit{G}}_{\mathit{g}}$, and ${\mathit{H}}_{\mathit{g}}$ symmetries are separated by up to several tenths of an electron volt. As a function of crystal momentum, exciton energies exhibit dispersion from 20 to 40 meV. Theoretical pressure derivatives of exciton energies are presented. © 1996 The American Physical Society.

• Received 6 October 1995

DOI:https://doi.org/10.1103/PhysRevB.54.10970