In this work, we present the calculated analytical form of the intermolecular pair interaction potential in a vacuum between asphaltene-asphaltene (U-AA), asphaltene-resin (U-AR), and resin-resin (U-RR) systems using two methods: density functional theory (DFT) and compass-classical force field. The binding energy was obtained by varying the minimum atomic distance (contact distance) between the interacting species and their relative angle; that is, by taking into account all possible interactions between the species (T-shape, face-to-face, edge-to-edge, and random configurations). For the asphaltene molecule, we used the proposed Groenzin-Mullins structure (Energy Fuels 2000, 14, 677), and for the resin molecule, we used 6-methyl-dibenzothiophene (Energy Fuels 1999, 13, 278). The binding energy between the interacting species was obtained using compass-classical force field, DFT with the Harris functional (DFT-Harris), and DFT with the self-consistent GGA Perdew-Wang 91 functional (DFT-SC). The potential curves were obtained by fitting an algebraic expression to the energy versus contact distance data. The DFT calculations allow the correlation between the electronic clouds in the molecules to be taken into account; it is not possible to account for this with classical force-field alculations. The DFT intermolecular dimer interaction potentials between species alpha and beta, where alpha and beta correspond to asphaltene or resin species, Up, are compared with the classical force-field results. To validate the quantum and classical calculations, we applied the same methodology for the benzene-benzene and coronene-coronene dimers. Our results are compared with experimental and theoretical data reported. We found that the DTF-SC method gives a reliable result for the binding energy and a good description of the potential curve shape. For the asphaltene-asphaltene, asphaltene-resin and resin-resin dimers, we found that the preferred configuration corresponds to the face-to-face orientation. We found that the binding energies for the asphaltene-asphaltene, asphaltene-resin, and resin-resin dimers are similar to 12-15, similar to 12-14, and similar to 4-7.5 kcal/mol, respectively.