Clar valence bond representation of pi-bonding in carbon nanotubes

The application of the Clar aromatic sextet valence bond (VB) model to extended, defect-free single-walled carbon nanotubes (CNTs) with roll-up vectors (m, n) provides a real space model of their electronic structure. If m - n = 3k, where k is an integer, then all pi-electrons can be represented by aromatic sextets, and the CNT is fully benzenoid; the converse is also true. Since m - n = 3k is known to be a necessary criterion for conductivity in CNTs, only fully benzenoid CNTs are metallic, and only potentially metallic CNTs are fully benzenoid. This behavior contrasts with that of planar polycyclic aromatic hydrocarbons, in which the fully benzenoid structures are known to have large HOMO-LUMO gaps. For CNTs that are not fully benzenoid, e.g., m - n = 3k + l, where l = 1 or 2 and k is an integer, a seam of double bonds wraps about an otherwise benzenoid CNT at the chiral angle - 60 degrees or the chiral angle, respectively. Nucleus-independent chemical shift calculations on hydrogen-terminated CNT segments support this, and show that the magnetic manifestation of aromatic sextets is not due to electron correlation. The resonance hybrid of the Clar VB structures corresponds to patterns occasionally observed in scanning tunneling microscopy images of CNTs.