From anatase (1 0 1) surface to TiO 2 nanotubes: Rolling procedure and first principles LCAO calculations

Abstract

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 ¯ 0 1 ] 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.