Polarizabilities, charge states, and vibrational modes of isolated fullerene molecules

We have used our local-orbital cluster codes to perform detailed density-functional-based calculations on isolated ${\mathrm{C}}_{60}$ molecules. We present first- and second-electron affinities, which include all effects due to spin polarization and charge-induced geometrical relaxation. The effects due to the generalized gradient approximation are reported as well. The two ${\mathit{A}}_{\mathit{g}}$ and single ${\mathit{A}}_{\mathit{u}}$ vibrational modes are presented and frequency shifts due to charging are estimated. By placing the fullerene molecules in a static electric field of variable strength, the molecular static polarizabilities are obtained. In comparison to isolated carbon atoms, we find enhancements in the linear polarizabilities due to the delocalized electrons at the Fermi level, but do not observe any large nonlinear static contributions. By including effects due to charge transfer, on-site geometric relaxation, and fullerene polarization, we introduce a simple potential that accounts for long-range interactions and predict Hubbard parameters as a function of alkali-dopant concentration.