Parallel displaced and sandwich configurations of hexafluorobenzene-substituted benzene dimers are studied by ab initio molecular orbital methods up to the MP2(full)/aug-cc-pVDZ level of theory to reveal how substituents influence pi-pi interactions. Two minimum energy configurations are found, one with the substituent group away from the pi-face of the hexafluorobenzene ring (2a-f) and the other with the substituent group on top of the pi-face of the hexafluorobenzene (3a-f). Higher binding energies are predicted for dimers with the substituent on the pi-face (3a-f). All sandwich dimers (4a-e) are found to be saddle points on the potential energy surfaces. A parallel-displaced minimum energy configuration is also predicted for the parent complex, C6F6-C6H6, which is in contrast to predictions based on quadrupole moments of benzene and hexafuorobenzene. The preference for the parallel displaced, rather than the sandwich configuration, is rationalized based on the smaller interplanar distance in the former. The closeness of contact in the parallel-displaced dimers leads to greater binding energies. The shape of the electron density isosurface of the monomers is suggested to provide a guide for the prediction of how arenes stack with one another. A large difference in binding energy between the C6F6 complex of aniline (3e) and N,N-dimethylaniline (3f) is calculated, and charge-transfer interactions are suggested to play a role in the latter.