Symmetry and Models of Single-Wall BN and TiO2 Nanotubes with Hexagonal Morphology

For ab initio simulations on hexagonal single-wall BN and TiO 2 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 TiO 2 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 TiO 2 nanotubes, certain qualitative similarities between the Δε gap ( D NT ) or E strain ( D NT ) functions exist despite the different chemical nature.