Vibronic interactions in the visible and near-infrared spectra of ${\mathrm{C}}_{60}^{-}$ anions

Electron-phonon coupling is an important factor in understanding many properties of the ${\mathrm{C}}_{60}$ fullerides. However, there has been little success in quantifying the strength of the vibronic coupling in ${\mathrm{C}}_{60}$ ions, with considerable disagreement between experimental and theoretical results. We will show that neglect of quadratic coupling in previous models for ${\mathrm{C}}_{60}^{-}$ ions results in a significant overestimate of the linear coupling constants. Including quadratic coupling allows a coherent interpretation to be made of earlier experimental and theoretical results which at first sight are incompatible.

Figure 1

Electronic spectrum of ${\mathrm{C}}_{60}^{-}$ ions in solution. The data has been fitted to four Gaussians labeled 0-III (dotted lines), giving a very good overall fit (solid line).

Figure 2

Allowed vibronic transitions associated with the electronic transition $T_{1g}\leftarrow T_{1u}$ for $D_{3d}$ distorted ${\mathrm{C}}_{60}^{-}$ ions. The transitions shown correspond to the peaks observed in the NIR spectrum (Fig. 1). The inset shows the comparable picture if transitions were to occur between $D_{5d}$ distorted ${\mathrm{C}}_{60}^{-}$ ions.

Figure 3

Effective dimensionless linear $\left(V_1\right)$ and quadratic ($V_2$, $V_3$) vibronic coupling constants consistent with the data and assignment shown in Figs. 1, 2 for varying phonon overlap $S$. Ions with $D_{3d}$ symmetry occur when $S>0.635$.