Several properties of the lowest excited singlet state of the ${\mathrm{C}}_{60}$ molecule are investigated with reference to the Jahn-Teller distortion. We find that the symmetry of the molecular structure in the relaxed excited state is approximately the ${\mathit{C}}_{2\mathit{h}}$ symmetry, though the strict symmetry is that of the inversion group ${\mathit{C}}_{\mathit{i}}$. Also it is found that the most remarkable contribution to the Jahn-Teller distortion is given by the ${\mathit{h}}_{\mathit{g}}$ mode of the lowest frequency and the next by the ${\mathit{h}}_{\mathit{g}}$ mode of the fourth-lowest frequency. Furthermore, we calculate the frequencies of the normal modes in the relaxed excited state. It is shown that the frequency splittings of the ${\mathit{h}}_{\mathit{g}}$ modes of the lowest and the fourth-lowest frequency reach several tens of ${\mathrm{cm}}^{\mathrm{-}1}$. Also it is pointed out that the two ${\mathit{h}}_{\mathit{g}}$ modes are the radial and the tangential mode described by the second-order vector spherical harmonics.

• Received 13 July 1993

DOI:https://doi.org/10.1103/PhysRevB.48.14615