Vibration spectra of fullerene family

This Letter considers a molecular mechanics approach for the vibration spectra analysis of fullerenes. Sixteen different fullerenes starting from C20 to C720 are considered. The universal force field potential is used for the molecular mechanics approach. An analytical expression based on the elastic shell theory is suggested to explain the variation of the natural frequencies across the whole family. It is shown that any given frequency across the fullerene family varies proportional to the inverse square root of their mass.

► We consider vibration spectra of fullerene family.
► Sixteen different fullerenes starting from C20 to C720 are considered.
► Molecular mechanics and new closed-form analytical expressions are proposed.
► Any given frequency across the fullerene family varies proportional to the inverse square root of their mass.