We have generated models of nanotubes by selecting atoms from the unit cells of TiO2 crystals (rutile
and anatase) in specific planes, i.e., the plane (101) for anatse and the plane (110) for rutile. Using a programming
language created in shell bash we designed clusters of titanium dioxide nanotubes with different
lengths and diameters. The structures generated were submitted to quantum mechanical calculations using the
semi-empirical PM7 method, HF and DFT methods with the 6-31g and 6-311G basis sets. The clusters were
optimized and the one with the most stable structures were those with the largest diameters. The best models,
i.e. the most stable structures, were the anatase nanotube of molecular formula [[(TiO2)4]20]3 and the rutile
nanotube with molecular formula [[(TiO2)2]13]3. Comparing the relative free energies of the structures with the
same number of atoms we concluded that the anatase nanotubes had a greater stability in comparison with the
rutile nanotubes. Calculations of the DFT energy gaps yields values between 2.0 and 2.5 eV, characteristic of
semiconductors and in agreement with experiment.
Keywords: DFT, HF, graphene, nanotubes, PM7, TiO2.
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