First-principles calculations of single-walled nanotubes in sulfides MS₂ (M = Ti, Zr)

Hybrid density functional theory has been applied for investigations of the electronic and atomic structure of nanotubes based on titanium and zirconium disulfides. The full optimization of all atomic positions in the considered systems has been performed to study the atomic relaxation and to determine the most favorable nanostructures. Our calculations on single-wall TiS₂ and ZrS₂ nanotubes confirmed that the nanotubes obtained by rolling of the hexagonal layers of 1T crystalline polymorphs with the octahedral morphology (and with the layer group P 3-bar m1) are the most stable. However, it is also possible to obtain the relatively stable nanotubes with lepidocrocite morphology by rolling up layers of the metastable tetragonal or orthorhombic phases. The strain energy of TiS₂ is almost the same as that of ZrS₂ but it is greater than the strain energy of TiO₂ and ZrO₂ nanotubes. However, the formation energy of the sulfide nanotubes is considerably less than the formation energy of the oxide nanotubes. (paper)