Symmetry and models of single-wall BN and TiO2 nanotubes with hexagonal morphology

For ab initio simulations on hexagonal single-wall BN and TiO₂ nanotubes (SW NTs), we have applied the formalism of line symmetry groups describing one-periodic (1D) nanostructures with rotohelical symmetry. Both types of NTs can be formed by rolling up the stoichiometric nanosheets of either (i) a (0001) monolayer of BN hexagonal phase or (ii) a three-layer (111) slab of fluorite-type TiO₂ phase. Optimized parameters of the atomic and electronic structure of corresponding slabs and nanotubes have been calculated using hybrid LCAO method as implemented in CRYSTAL code. Their band gaps (Δε_gap) and strain energies (E_strain) have been analyzed as functions of NT diameter (D_NT). For hexagonal BN and TiO₂ nanotubes, certain qualitative similarities between the Δε_gap(D_NT) or E_strain(D _NT) functions exist despite the different chemical nature.