The quadratic Jahn-Teller effect of ${\mathrm{C}}_{60}{}^{n-}$ ($n=1$–5) is investigated from the first principles. Employing the density functional theory calculations with hybrid functional, the quadratic vibronic coupling constants of ${\mathrm{C}}_{60}{}^{-}$ were derived. The warping of the adiabatic potential energy surface of ${\mathrm{C}}_{60}{}^{-}$ by the quadratic vibronic coupling is estimated to be about 2 meV, which is much smaller than the Jahn-Teller stabilization energy ($\approx 50\mathrm{meV}$). 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 ${\mathrm{C}}_{60}{}^{3-}$, 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 ${\mathrm{C}}_{60}{}^{n-}$ is of pseudorotational type.

• Received 21 May 2018

DOI:https://doi.org/10.1103/PhysRevB.98.035402