Quadratic Jahn-Teller effect of fullerene anions

The quadratic Jahn-Teller effect of ${\mathrm{C}}₆₀{\phantom{\rule{0.16em}{0ex}}}^{n\ensuremath{-}}$ ($n=1$--5) is investigated from the first principles. Employing the density functional theory calculations with hybrid functional, the quadratic vibronic coupling constants of ${\mathrm{C}}₆₀{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{-}}$ were derived. The warping of the adiabatic potential energy surface of ${\mathrm{C}}₆₀{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{-}}$ by the quadratic vibronic coupling is estimated to be about 2 meV, which is much smaller than the Jahn-Teller stabilization energy ($\ensuremath{\approx}50\phantom{\rule{4pt}{0ex}}\mathrm{meV}$). Because of the selection rule and the vibronic reduction, the quadratic coupling slightly modifies the vibronic states of ${\mathrm{C}}₆₀$ anions. Particularly, in the case of ${\mathrm{C}}₆₀{\phantom{\rule{0.16em}{0ex}}}^{3\ensuremath{-}}$, parity and symmetry selection rule significantly reduces the effect of quadratic coupling on vibronic states. The present results confirm that the low-energy vibronic dynamics of ${\mathrm{C}}₆₀{\phantom{\rule{0.16em}{0ex}}}^{n\ensuremath{-}}$ is of pseudorotational type.