Periodic n-dependence in the lowest excitation energies of the tube-like fullerenes C60 + 10n

A periodic n-dependence has been found in the lowest excitation energies of the tube-like fullerenes C60 + 10n (n=1,2,…), each consisting of a pair of the bisected caps of C60 and a single-wall cylinder. By inspection of the periodicity, the tube-like fullerenes are classified into three series of C70 + 30m, C80 + 30m and C90 + 30m (m=0,1,2,…). The analysis with the Pauling bond order indicates the formation of a pseudo π-conjugation on each layer of the cyclo-pentaphenylene structure with 30 C-atoms in the central cylindrical parts of the tube-like fullerenes.