Symmetry and Stability of Nanotubes Based on Titanium Dioxide

摘要

The process of rolling a monolayer of bulk crystal with biperiodical planar lattice to the nanotube was analyzed. It was shown by an example of the carbon nanotubes how the tube symmetry can be revealed through the analysis of symmetry of graphene layers (the layer group with a hexagonal planar lattice) and its changes at the rolling to form the tube. The developed approach can be used to analyze the symmetry of any nanotube. A computer program we developed is discussed that allows to determine the nanotube symmetry using the data on the symmetry and coordinates of the atoms in the nanolayer and get the coordinates of the atoms in the unit cell of the nanotube which can be used for the further quantum-chemical calculations. The method and results of ab initio calculations of the titanium dioxide monolayer stability in the LCAO basis optimized for the bulk crystal, using the hybrid exchange-correlation potential PBEO are presented. Symmetry properties of nanotubes obtained by rolling the three- and six-plane monolayers (101) and (001) of anatase are discussed. Atomic and electronic structure of TiO2 nanotubes found by geometry optimization is analyzed. It is shown that titanium dioxide nanotubes based on the three-plane monolayers with hexagonal and square lattice are approximately of the same stability. The data on the stability of nanotubes are essential for the synthesis of new nanomaterials based on titanium dioxide.