A Hybrid Density Functional Study of Armchair Si and Ge Nanotubes
  First principles calculations based on hybrid density functional theory have been used to study the electronic and geometric properties of armchair silicon and germanium nanotubes ranging from A (3, 3) through A (9, 9). The approach used is the finite cluster approach with hydrogen termination to simulate the effects of longer tubes. A detailed comparison of the structures and stabilities of Si and Ge nanotubes has been performed and the dependence of the HOMO- LUMO or band gaps on the tube diameters has been investigated. Silicon nanotubes appear to be less-puckered and more stable compared to germanium nanotubes. The largest silicon nanotube studied has a cohesive energy of 3.138eV/atom to be compared with the cohesive energy of 2.770eV/atom for the corresponding germanium nanotube. Contrary to some published results in the literature, silicon nanotubes do not appear to be metallic for the cases studied in the armchair configuration. 
Prachi Pradhan and Asok Ray