From anatase (1 0 1) surface to TiO2 nanotubes: Rolling procedure and first principles LCAO calculations

A simple procedure of 1D nanotubes (NT) construction based on the supercell of 2D (1 0 1) slab rolling and subsequent cylindrical coordinate system introduction is suggested. This procedure is applicable for any of five 2D lattices as well as both single- and multi-wall nanotubes provided that the chirality and translation vectors orthogonality condition is satisfied. The procedure suggested is applied to the centered rectangular 2D lattice, formed by (1 0 1) sheet of the bulk anatase. It is shown that (n, 0) and (0, m) nanotubes can be constructed by rolling an anatase (1 0 1) sheet along the [1¯01] and [0 1 0] directions respectively. The orthogonal to chirality vector translation vector does not exist for n ≠ m ≠ 0 general case. The first principles LCAO calculations of (n, 0) and (0, m) NT's are made with hybrid HF/KS (PBE0) exchange-correlation functional for systems containing up to 180 atoms (n = 6, 9, 12, 15; m = 3−6). It is demonstrated that the energy band gap increases (from 4.7 to 5.4 eV) when the NT radius changes from 3.61 to 9.92 Å. The strain energy is larger for (n, 0) than for (0, m) nanotubes of a similar radius. The changes of the unit cell periodicity and radius of titania nanotubes after the structure optimization are negligible, however the atomic relaxations are noticeable.