Density functional tight-binding studies of carbon nanotube structures

A density functional tight-binding self-consistent charge approach has been used to study the structures and elastic properties of nine model carbon nanotubes of different helicities and diameters between 5.5 and 10.8 A. The systems contain from 112 to 268 atoms and were optimized under periodic boundary conditions in the axial direction. Both the carbon networks and the overall tube dimensions were optimized. Most of the C-C bond lengths are slightly lengthened relative to graphene (two-dimensional graphite); the others remain essentially the same or are shorter. There is overall a longitudinal compression of the tube. The strain energy per atom, relative to graphene, varies inversely with the square of the tube radius. The Young's moduli decrease with increasing radius but do not depend upon chirality. The Poisson ratios are nearly constant. The consequences of removing an electron from each system were also investigated. In most instances, the tube dimensions were little affected; in only a few cases is there a change in length or radius (positive or negative) as large as 0.10%. The Young's moduli remain the same as for the neutral systems, but the Poisson ratios tend to increase for metals and semimetals and to decrease for semiconductors.