TiS2 and ZrS2 single- and double-wall nanotubes: first-principles study.

Hybrid density functional theory has been applied for investigations of the electronic and atomic structure of bulk phases, nanolayers, and nanotubes based on titanium and zirconium disulfides. Calculations have been performed on the basis of the localized atomic functions by means of the CRYSTAL-2009 computer code. The full optimization of all atomic positions in the regarded systems has been made to study the atomic relaxation and to determine the most favorable structures. The different layered and isotropic bulk phases have been considered as the possible precursors of the nanotubes. Calculations on single-walled TiS2 and ZrS2 nanotubes confirmed that the nanotubes obtained by rolling up the hexagonal crystalline layers with octahedral 1T morphology are the most stable. The strain energy of TiS2 and ZrS2 nanotubes is small, does not depend on the tube chirality, and approximately obeys to D(-2) law (D is nanotube diameter) of the classical elasticity theory. It is greater than the strain energy of the similar TiO2 and ZrO2 nanotubes; however, the formation energy of the disulfide nanotubes is considerably less than the formation energy of the dioxide nanotubes. The distance and interaction energy between the single-wall components of the double-wall nanotubes is proved to be close to the distance and interaction energy between layers in the layered crystals. Analysis of the relaxed nanotube shape using radial coordinate of the metal atoms demonstrates a small but noticeable deviation from completely cylindrical cross-section of the external walls in the armchair-like double-wall nanotubes.