Force-constant model of a fullerene based on a first-principles method and bond-population analysis: Applications to ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$

We propose a method based on first-principles molecular-orbital (MO) calculations and a force-constant model with Mulliken’s bond-population analysis to calculate vibrational properties of fullerenes. In this force-constant model, the parameters are determined by first-principles MO calculations based on the nonlocal-density-functional formalism. This method may be successfully applied to any higher fullerenes, because the number of force constants is extremely reduced by using the bond-population analysis. The calculated vibrational frequencies for ${\mathrm{C}}_{60}$ agree well with experimental ones. Also, we calculate the vibrational frequencies of ${\mathrm{C}}_{70}$ and reveal that three types of covalent bonds exist, double bonds, single bonds, and 1.5 bonds. We give a reasonable explanation to this remarkable feature of ${\mathrm{C}}_{70}$.