Incommensurate oscillations of excitation gaps

Oligoacenes are basic compounds of hydrogen and carbon, which look like linearly fused hexagonal rings:
(a) Examples of oligoacenes: benzene (N=1), anthracene (N=3) and hexacene (N=6).
(b) Dependence of the excitation gap as a function of the number of rings N. There is a non-trivial period of 11 rings.
(c) Emergence of the gap oscillations: Energies of molecular states form a web pattern, the lines are related to the band-structure.