Size evolution of characteristic acoustic oscillations of fullerenes and its connection to continuum elasticity theory

We performed a theoretical investigation, based on density functional theory, on the vibrational properties of fullerenes and its dependence with size ( 20→ 720 atoms). Characteristic acoustic oscillations like the breathing (BM) and quadrupolar (QM) modes were located using the calculated vibrational density of states. In particular, it was obtained that the acoustic gap (lowest frequency value) corresponds to the QM five-fold degenerate frequency, as expected in cage-like quasi-spherical nanostructures. The main finding indicates a linear dependence for the vibrational periods of the BM and QM with the fullerenes size. The results obtained for the BM are consistent with a continuum elastic theory approach to describe the acoustic oscillations of a cage-like structure. Moreover, this behavior is also similar to that one found in metal nanoparticles with size in the range of 0.5–4 nm, indicating that the covalent nature of the bonding in fullerenes does not induce anomalous effects in their acoustic oscillations. Graphic Abstract) .