Symmetry analysis of relative motions in a double-wall carbon nanotube

The binding energy of a double-wall carbon nanotube (DWNT) is theoretically studied as a function of the relative longitudinal shift and relative rotation of the component single-wall carbon nanotubes (SWNTs). It is shown that the binding energy is an oscillating function of the relative shift and rotation, with the oscillation period depending on the relations between symmetry elements of the SWNTs. The results of numerical calculations of the binding energy of DWNTs, performed in the approximation of weak van der Waals interlayer interaction, are presented.