Abstract:The formalism of line symmetry groups for one-periodic (1D) nanostructures with rotohelical symmetry has been applied for symmetry analysis of single-walled titania nanotubes (SW TiO 2 NTs) formed by rolling up the stoichiometric two-periodic (2D) slabs of anatase structure. Either six-or twelve-layer (101) slabs have been cut from TiO 2 crystal in a stable anatase phase. After structural optimization, the latter keeps the centered rectangular symmetry of initial slab slightly compressed along a direction coincided with large sides of elemental rectangles. We have considered two sets of SW TiO 2 NTs with optimized six-and twelve-layer structures, which possess chiralities (− ) and ( ) of anatase nanotubes. To analyze the structural and electronic properties of titania slabs and nanotubes, we have performed their ab initio LCAO calculations, using the hybrid Hartree-Fock/Kohn-Sham exchange-correlation functional PBE0. The band gaps (∆ε ) and strain energies (E ) of six-layer nanotubes have been computed and analyzed as functions of NT diameter (D NT ). As to models of 12-layer SW TiO 2 NTs of both chiralities, their optimization results in structural exfoliation, , the multi-walled structure should be rather formed in nanotubes with such a number of atomic layers.