The interactions within two models for graphene, coronene and hexabenzocoronene (HBC), and (H3C(CH2)(5))(6)-HBC, a synthesizable model for asphaltenes, were studied using density functional theory (DFT) with dispersion corrections. The corrections were implemented using carbon atom-centered effective core-type potentials that were designed to correct the erroneous long-range behavior of several DFT methods. The potentials can be used with any computational chemistry program package that can handle standard effective core potential input, without the need for software modification. Testing on a set of common noncovalently bonded dimers shows that the potentials improve calculated binding energies by factors of 2-3 over those obtained without the potentials. Binding energies are predicted to within ca. 15%, and monomer separations to within ca. 0.1 angstrom, of high-level wave function data. The application of the present approach predicts binding energies and structures of the coronene dimer that are in excellent agreement with the results of other DFT methods in which dispersion is taken into account. Dimers of HBC show extensive binding in pi-stacking arrangements, with the largest binding energy, 44.8 kcal/mol, obtained for a parallel-displaced structure. This structure is inline with the published crystal structure. Conformations in which the monomers are perpendicular to one another are much more weakly bound and have binding energies less than 10 kcal/mol. For dimers of (H3C(CH2)(5))(6)-HBC, which contain 336 atoms, we find that a slipped-parallel structure with C-s symmetry has a binding energy of 52.4 kcal/mol, 8.9 kcal/mol lower than that of a bowl-like, C-6v-symmetric structure.