Jahn-Teller effects in the ${\mathrm{C}}_{60}^{2+}$ cation undergoing $D_{2h}$ distortion

It has recently been shown that the high-spin, doubly hole-doped fullerene cation ${\mathrm{C}}_{60}^{2+}$ is likely to undergo a Jahn-Teller (JT) distortion, which reduces the molecular symmetry from $I_h$ to $D_{2h}$. A theoretical model for the JT effect describing this situation is presented. The model includes parameters for the energy differences between molecular terms that arise from Coulomb interactions between the holes. Although the magnitudes of these parameters are not known to any degree of certainty for the ${\mathrm{C}}_{60}^{2+}$ cation, they are likely to have an important effect. Results are given for both the static JT effect, where the motion of the system can be considered in terms of vibrations in a potential well, and the dynamic JT effect, where tunneling between equivalent wells must be taken into account.

Figure 1

(Color online) (a) Fullerene ${\mathrm{C}}_{60}$ showing the location of the C-C double bonds, the centers of which coincide with the positions of the $D_{2h}$ wells. (b) An icosidodecahedron formed by connecting the points where the axes of the $D_{2h}$ distortions cut the surface of a sphere. The vertices are labeled $A,B,C,\dots ,O,$ as used in Table .

Figure 2

(Color online) Energies of the symmetry-adapted states when ${\mathcal{H}}_{\mathit{\text{term}}}^{\prime }=0$. The energies are given relative to $-E_{\mathrm{JT}}$, where $E_{\mathrm{JT}}=9V^{\prime 2}\hslash \omega ∕16$.

Figure 3

(Color online) Energies of the symmetry-adapted states in the presence of the term energies as calculated by different authors. The graphs are labeled according to the cases defined in Table . Case C: Plakhutin et al. (Ref. 12) (${\delta }_1=-29$, ${\delta }_2=-3\mathrm{meV}$); Case D: Wierzbowska et al. (Ref. 13) (${\delta }_1=6.9$, ${\delta }_2=12.4\mathrm{meV}$); Case E: Wierzbowska et al. (Ref. 13) (alternative interpretation, ${\delta }_1=-6.9$, ${\delta }_2=5.5\mathrm{meV}$); Case F: Lüders et al. (Ref. 4) (${\delta }_1=0$, ${\delta }_2=48\mathrm{meV}$). The dashed vertical line represents the value $V^{\prime }=1.52$ appropriate to the $h_g\left(1\right)$ mode of vibration of ${\mathrm{C}}_{60}$.