Estimate of HubbardUforC60by use of optical absorption

We consider the optical absorption of ${\mathrm{C}}_{60}$ within a simple tight-binding model. To obtain a reasonable agreement with experiment a sizable Hubbard U must be included. We estimate U to be in the range from one-half to the full ‘‘bandwidth’’ where the bandwidth is roughly 13 eV. In our picture the two lowest-energy large-absorption peaks are due to single-particle transitions: ${\mathit{H}}_{\mathit{u}}$ goes to ${\mathit{T}}_{1\mathit{g}}$ and ${\mathit{H}}_{\mathit{g}}$ goes to ${\mathit{T}}_{1\mathit{u}}$, respectively. The weak absorption from 3.0 to 1.9 eV is attributed to the dipole-forbidden transition: ${\mathit{H}}_{\mathit{u}}$ goes to ${\mathit{T}}_{1\mathit{u}}$ ‘‘split’’ by electron-electron repulsion.