Properties of Carbon Nanotubes: An ab initio Study Using Large Gaussian Basis Sets and Various DFT Functionals

The structural, electronic, dielectric, and elastic properties of zigzag and armchair single-walled carbon nanotubes are investigated at different DFT levels (LDA, GGA, hybrids) with Gaussian type basis sets of increasing size (from 3-21G to 6-1111G(2d,f)). The longitudinal and transverse polarizabilities are evaluated by using the Coupled Perturbed Hartree--Fock and Kohn--Sham computational schemes, which take into account the orbital relaxation through a self-consistent scheme. It is shown that the difference between the frequently adopted SOS (sum over states, uncoupled) and the fully coupled results is far from being negligible and varies as a function of the tensor component and the adopted functional. Helical symmetry is fully exploited. This allows simulation of tubes larger (up to 140 atoms in the unit cell) than in previous studies by using extended basis sets and severe computational conditions. All the 12 functionals considered here provide similar results for the structural and the elastic properties and for the relative stability among nanotubes and with respect to graphene. On the contrary, the stability with respect to diamond, which has a quite different density than that of nanotubes, sensitively depends on the adopted functional. The band gap and the longitudinal polarizability are strongly dependent on the level of approximation: hybrid functionals provide the least deviation from experimental data. In general, data obtained for (n, n), (3n, 0), (3n + 1, 0), and (3n + 2, 0) rolling directions approach the slab limit for large radii following four distinct trends.