  quasi-one-dimensional (1D) titania nanostructures - single-walled nanotubes
formed by rolling [101] planes of TiO$_2$ (anatase phase) are modeled and their
electronic properties and bond orders indices are studied using the
tight-binding band theory. We show that all zigzag (n,0)- and armchair
(n,n)-like nanotubes are uniformly semiconducting, and the band gap trends to
vanish as the tube diameters decrease. It was established that the zigzag (n,0)
nanotubes configurations are more likely to form when the diameters are larger
1 nm. The Ti-O covalent bonds were found to be the strongest interactions in
TiO$_2$ tubes, whereas Ti-Ti bonds proved to be much weaker.
