Ab initio study of the vibrational properties of single-walled silicon nanotubes

We investigate the vibrational properties of pentagonal and hexagonal single walled silicon nanotubes by using DFT and the frozen phonons method. The phononic band structure and the vibrational density of states are reported. The stability of each structure is discussed based on these results. We investigate the influence of isotopic substitutions upon the vibrational density of states for the two types of nanotubes. Finally, we show that the model of vibrational Hamiltonian in a diatomic chain can be used to give a qualitative description of the relation between the amount of isotopically substituted layers in the nanotube and their influence upon the vibrational density of states.