  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.
