On the forbidden graphene’s ZO (out-of-plane optic) phononic band-analog vibrational modes in fullerenes

Abstract

The vibrational properties of fullerenes are incompletely understood, particularly with respect to the effect of molecular size. Here the vibrational density of states of fullerenes is shown by density functional theory to converge smoothly to that of graphene, hindered only by the presence of frequency compressed radial optic vibrations due to the pentagonal faces in the fullerene family.