We present theoretical absolute charge exchange cross sections for multiply charged cations interacting with the Polycyclic Aromatic Hydrocarbon (PAH) molecules pyrene C(14)H(10), coronene C(24)H(12), or circumcoronene C(54)H(18). These planar, nearly circular, PAHs are modelled as conducting, infinitely thin, and perfectly circular discs, which are randomly oriented with respect to straight line ion trajectories. We present the analytical solution for the potential energy surface experienced by an electron in the field of such a charged disc and a point-charge at an arbitrary position. The location and height of the corresponding potential energy barrier from this simple model are in close agreement with those from much more computationally demanding Density Functional Theory (DFT) calculations in a number of test cases. The model results compare favourably with available experimental data on single- and multiple electron transfer reactions and we demonstrate that it is important to include the orientation dependent polarizabilities of the molecules (model discs) in particular for the larger PAHs. PAH ionization energy sequences from DFT are tabulated and used as model inputs. Absolute cross sections for the ionization of PAH molecules, and PAH ionization energies such as the ones presented here may be useful when considering the roles of PAHs and their ions in, e.g., interstellar chemistry, stellar atmospheres, and in related photoabsorption and photoemission spectroscopies.