We investigate the linear behavior in the 2+ ion concentration observed in the double photoionization of a variety of aromatic molecules. We show it arises when the photoelectrons are emitted simultaneously. Neglecting the momentum of the incoming photon and the momentum transferred to the molecule, it follows that the momenta of the individual photoelectrons are oppositely directed and equal in magnitude. Under steady-state conditions, the ion concentration is proportional to the rate at which the ions are created which, in turn, varies as the product of the densities of states of the individual electrons. The latter vary as the square root of the kinetic energy, leading to overall linear behavior. The origin of the linear behavior in pyrrole and related molecules is attributed to the presence of atoms that destroy the periodicity of a hypothetical carbon loop. In contrast, the resonant behavior observed in pyridine and related molecules, where a fraction of the CH pairs is replaced by N atoms, is associated with electron transfer between the nitrogen atoms and carbon atoms that preserves the periodicity of the closed loop.
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