Stability of tubulenes

Tubulenes are defined as capped nanotubes built up from two generalized hemifullerene caps and a distancing nanotube portion tessellated by hexagons. Spectral regularities appearing in families of tubulenes are summarized in rules for their pi-electronic structure, in the Huckel model. The new cylinder rules are: (i) the "t-armchair" cylinder rule TACR, which states the periodicity of closed shells in tubulenes of general structural formula C-8k,C-k-A[2k,C-n]-[5,C-6,C-7] at nuclearity N = 8k + 2k(4 + 3m); m = 0, 1, 2,...; (ii) the "tn-armchair" cylinder rule TNACR, which involves closed shells (with nonbonding LUMO) in tubulenes with structural formula C-8k,C-k-A[2k,C-n]-[5,C-6,C-7], at N = 8k + 2k(11 + 3m); m = 0, 1, 2,... and (iii) the "zigzag" cylinder rule ZCR, which predicts closed shell tubulenes of general structural formula C-13k,C-k-Z[3k,C-n]-[6] at nuclearity N = 13k + 3k.n; k = 4m + 2 or k = 4m; m = 1,2,... n = 1,2,.... Appropriate modification of the cylinder cap can shift the HOMO orbital to the non-bonding or antibonding eigenvalues of the adjacency matrix. Semiempirical calculations support the Huckel spectral data.