Vibrational analysis of the fullerene family using Tersoff potential

Using Tersoff bond order potential, a vibrational analysis of the spherical fullerene family, namely C60, C80, C180, C240, C260, C320, C500, and C720 was performed. To evaluate the validity of our results, we have compared our simulation results with available experimental data and also with DFT B3LYP/6-31G(d) calculations. In general, molecular stiffness tends to decrease with increasing size, but its variation is limited in cases where mostly the tension-compression interaction sites are active such as the breathing mode. Furthermore, the bond length of each molecule is derived and compared with experimental and theoretical values calculated for graphene. Finally, vibrational frequencies are plotted in a histogram to reveal the common frequency gap and concentration points of the frequency distribution.