Origin of the low energy resonance in the double photoionization of pyrene and coronene, and its absence in the double photoionization of corannulene

The low energy resonance in the double photoionization of the aromatic hydrocarbons pyrene (C$_{16}$H$_{10}$) and coronene (C$_{24}$H$_{12}$) is investigated theoretically using an approach based on the one-dimension Hubbard model for $\pi$-conjugated systems with nearest-neighbor interactions. The Independent Subsystem Approximation, where the perimeter and interior carbon atoms are treated as independent entities, is employed. Since no low energy resonances have been found in aromatic hydrocarbons where there are only perimeter carbon atoms, we attribute the low energy resonances in pyrene and coronene to the interior carbon atoms. However, corannulene (C$_{20}$H$_{10}$) having five interior carbon atoms does not exhibit a low-energy resonance in the experimental data. We attribute the absence of this resonance to the odd number of interior carbon atoms.