Manifestation of aromaticity and its effects on the electronic structure of finite single-wall carbon nanotubes

Finite single-wall carbon nanotubes (p,q), characterized by p=n+l+1, q=n−l, 0⩽l⩽n, and n=1,2,…, consisting of even nanotube (NT) sections may be viewed as a chain of aromatic `moleculesʹ with each `molecular-unitʹ consisting of two NT sections of 4n+2 sp2-bonded carbon atoms. Such (group II) NTs, have large energy gaps for short tubes, whereas for tubes of intermediate lengths, the energy gap decreases monotonically as a function of NT length. The energy gap behaviors are totally different from the previously studied group I NTs with p=n+l and q=n−l, which exhibited oscillatory characteristics.