The preferred geometries of the benzene dimer have been modeled at a high level of theory with MP2-R12/A computations and very large counterpoise-corrected aug-cc-PVTZ basis sets. The two most stable conformations are the parallel displaced and T-shaped, which are essentially isoenergetic. In contrast, the sandwich configuration maximizes overlap of the pi system, which destabilizes the interaction. The sandwich configuration represents an energetic saddle point, which is consistent with the relative rarity of this configuration in x-ray crystal data.
The relative binding energies of these three geometric configurations of the benzene dimer can be explained by a balance of quadrupole/quadrupole and London dispersion forces. While benzene does not have a dipole moment, it has a strong quadrupole moment. The local C–H dipole means that there is positive charge on the atoms in the ring and a correspondingly negative charge representing an electron cloud above and below the ring. The quadrupole moment is reversed for hexafluorobenzene due to the electronegativity of fluorine. The benzene dimer in the sandwich configuration is stabilized by London dispersion forces but destabilized by repulsive quadrupole/quadrupole interactions. By offsetting one of the benzene rings, the parallel displaced configuration reduces these repulsive interactions and is stabilized. The large polarizability of aromatic rings lead to dispersive interactions as major contribution to stacking effects. These play a major role for interactions of nucleobases e.g. in DNA.  The T-shaped configuration enjoys favorable quadrupole/quadrupole interactions, as the positive quadrupole of one benzene ring interacts with the negative quadrupole of the other. The benzene rings are furthest apart in this configuration, so the favorable quadrupole/quadrupole interactions evidently compensate for diminished dispersion forces.