Graphene sheets are the building blocks of carbon nanotubes and a variety of functionalized nanomaterials. Methods to be used for computer-aided design of such materials or for the study of aromatic-aromatic interactions in biopolymers and other soft materials should be validated for smaller systems where reliable estimates of interaction energies are available. In this work, we first validated the M06-2X functional against the S22 database of noncovalent interaction energies of biological importance. We then applied the M06-2X functional to study aromatic-aromatic interactions in coronene dimers. We located six stationary points on the potential energy surface of coronene dimer, we calculated the potential energy curves for the sandwich, T-shaped, and parallel-displaced configurations of this prototype of aromatic-aromatic interactions, and we found that a parallel displaced configuration is the global minimum. The potential curves for the coronene dimers will aid the development of new force fields and potential energy functions that are computationally efficient and capable of modeling large graphene or aromatic clusters.