Resonance structures and aromaticity in capped carbon nanotubes

The shape of a single-walled carbon nanotube's cylinder is described by its chiral indices, (n,m), and important properties of the nanotube are determined by this pair of values. In particular, a nanotube is metallic or quasi-metallic when n-m is a multiple of 3, and is otherwise a semiconductor. This paper characterizes the conjugated π-systems that can form on capped nanotubes in each case. When n-m is a multiple of 3, there is a fully conjugated π-system running along the nanotube's cylinder such that two-thirds of the hexagons are benzene rings and one-third are in a resonant set. In contrast, when n-m is not a multiple of 3, the pattern is broken along the length of the cylinder by two fracture lines. Surprisingly, and contrary to conventional thinking, these results are completely independent of the nanotube caps. The results are related to a similar characterization for open nanotubes by Ormsby and King, although in that case only a single fracture line is necessary. This new work is backed by the authors’ previous results on the Clar numbers of fullerenes in general. It also provides new predictions for nanotubes and introduces the concept of the aromaticity ratio.