Clar Covers and Zhang-Zhang Polynomials of Zigzag and Armchair Carbon Nanotubes

We derive here compact formulas for the Zhang-Zhang (ZZ) polynomials of two classes of finite open-ended carbon nanotubes: zigzag nanotubes (n, 0) of length d and armchair nanotubes (n, n) of length d. For zigzag nanotubes, the underlying Clar cover theory is trivial; in contrast, for armchair nanotubes, the Clar theory is complex and abundant in results. The ZZ polynomial formulas have been obtained using the interface theory of benzenoids and the transfer matrix methodology.