Comments on Structural Types of Toroidal Carbon Nanotubes

摘要

We clarify the relationships between the eight structural types of toroidal carbon nanotubes (TCNTs), which can be identified as the eight corners of a cube of structural transformation. The four families with D_(nh) symmetry can be related by rim rotations, and the same is true for those with D_(nd) symmetries. These two sets are then connected by horizontal shifts, thereby completing the cube. Moreover, we further point out that there are five more highly symmetric D_(nh) structural types that can be derived from performing the generalized Stone-Wales transformation on TCNTs with D_(nh) structural types.