In this work, we characterize the nonvalence correlation-bound anion states of several polycyclic aromatic hydrocarbon (PAH) molecules. Unlike the analogous image potential states of graphene that localize the charge density of the excess electron above and below the plane of the sheet, we find that for PAHs, much of the charge distribution of the excess electron is localized around the periphery of the molecule. This is a consequence of the electrostatic interaction of the electron with the polar CH groups. By replacing the H atoms by F atoms or the CH groups by N atoms, the charge density of the excess electron shifts from the periphery to above and below the plane of the ring systems.