Titania nanotubes modeled from 3- and 6-layered (1 0 1) anatase sheets: Line group symmetry and comparative ab initio LCAO calculations

Abstract

The formalism of line groups for one-periodic (1D) nanostructures with rotohelical symmetry has been applied for construction of TiO 2 nanotubes (NTs). They are formed by rolling up the stoichiometric two-periodic (2D) sheets cut from the energetically stable (1 0 1) anatase surface, which contains either six (O–Ti–O_O–Ti–O) or three (O–Ti–O) layers. After optimization of geometry the former keeps the centered rectangular symmetry of initial slab while the latter is spontaneously reconstructed to the hexagonal fluorite-type (1 1 1) sheet. We have considered the four sets of TiO 2 NTs with optimized 6- and 3-layered structures, which possess the two pairs of either anatase (− n, n) and ( n, n) or fluorite ( n, n) and ( n,0) chiralities, respectively. To analyze their structural and electronic properties, we have performed ab initio LCAO calculations on titania slabs and nanotubes using the hybrid Hartree-Fock/Kohn-Sham exchange-correlation functional PBE0. Both band gaps and strain energies of these nanotubes have been computed as functions of NT diameter consequently changed from 0.5 nm to 4.0 nm with number of atoms per nanotube unit cell increased from 30 up to 288. A ratio of the calculated strain energies between the 3- and 6-layered titania NTs achieves 2–3 for nanotubes with diameters ≤1.0 nm and remains noticeable for those with diameters ≤2.0 nm, i.e., the latter are more stable energetically. When diameters of nanotubes increase up to 4.0 nm these strain energies substantially decrease and approach each other. At the same time, the strain energy of 6-layered NTs with (− n, n) chirality is smaller than that for ( n, n) NTs of a similar diameter, while in 3-layered nanotubes of similar diameters, the difference in strain energies for fluorite-type ( n, n) and ( n,0) chiralities is rather negligible. The band gaps of 6-layered titania nanotubes are found to be noticeably larger as compared to 3-layered NTs with the same diameter. When these diameters markedly increase, their band gaps asymptotically approach to those for the corresponding 2D slabs. As to other nanotube properties, the O(2 p)–Ti(3 d) bond hybridization is more pronounced at the projected densities of states (PDOS) calculated for equilibrium 6-layered TiO 2 NT structures, i.e., they are more stable chemically.