We analyze the influence of different groups on the intermolecular energy of aromatic homodimers and on the interaction between a single aromatic molecule and a graphene surface. The analysis is performed for benzene, phenol, catechol, and dopamine. For calculating the energies, we employ density functional theory within the local density approximation (LDA-DFT). Our results show that the lowest intermolecular energies between the aromatic molecules are related to the T-shaped configurations. This lower energy results from the quadrupole interaction. In the case of the interaction between the graphene sheet and the aromatic molecules, the lowest energy configuration is the face to face. The adsorption energy of a molecule on a graphene surface involves π - π interactions that explain the face to face arrangement. These results provide insight into the manner by which substituents can be utilized in crystal engineering, supramolecular chemistry, bioinspired materials, formation of various molecular clusters, parameterization of force fields suitable for classical simulations, and design of novel sensing, drug delivery, and filters based on graphene.