Knowledge Bank

The qualitative appearance of the fullerene absorption spectra is typical of many catacondensed hydrocarbons that, in the Platt notation, exhibit a forbidden, long-wavelength $L\leftarrow$A transition followed by allowed $B\leftarrow A$ transitions. These features may be explained by simple angular momentum selection rules using a particle-on-a-sphere” model of the fullerenes. This model gives the first allowed transition of $C_{60}$ at 342nm, close to the experimental value of 328nm. The other predictions of this simplistic representation are grossly inaccurate (e.g. electron pairing, orbital degeneracies). The model is improved by replacing the spherical potential with, for example, the icosahedral potential to better represent the $C_{60}$ carbon framework and computing the crystal field” splitting of the individual terms. The potential lifts the degeneracy of all levels with $l>2$ and leads to the energy level ordering that correctly predicts the orbital configuration for $C60$ and accounts for the three, intense bands observed in the ultraviolet as allowed, inter-term transitions. The predicted energy level ordering and degeneracies are comparable to those obtained from molecular orbital calculations using a ``bent” p-orbital basis. In the crystal-field model, the weak long-wavelength transition of $C60$ is an intra-term, parity forbidden excitation and the higher energy transitions correspond to allowed inter-term excitations. Term splitting arise from non-zero matrix elements of the crystal field between sub-levels of the same term or between terms in l and $l\pm 2$. This approach is easily generalized to treat the spectra of higher fullerenes by adding appropriate terms to the potential. The same potential may be employed to interpret the spectra of endohedral metal-fullerene complexes in which the potential acts to split the metal d- or f-orbital degeneracies.