Potential energy surface for the benzene dimer and perturbational analysis of π-π interactions

We present a complete 6-dimensional potential energy surface for the benzene dimer obtained using symmetry-adapted perturbation theory (SAPT) of intermolecular interactions based on Kohn-Sham's description of monomers. Ab initio calculations were performed for 491 dimer geometries in a triple-zeta-quality basis set supplemented by bond functions. An accurate analytic fit to the ab initio results has been developed and low-energy stationary points on the potential energy surface have been found. We have determined that there are three minima on the surface. Two of them, the tilted T-shape and the parallel-displaced, are nearly isoenergetic with interaction energies of -2.77 and -2.74 kcal/mol, respectively. The third minimum, a twisted edge-to-edge conformation, is significantly less attractive, with the interaction energy equal to -1.82 kcal/mol. Both the T-shape and sandwich geometries, sometimes assumed to be minima, are shown to be only saddle points. The potential energy surface is extremely flat between the two lowest minima, the barrier being only 0.10 kcal/mol above the global minimum. The second-virial coefficient obtained with the new potential agrees well with experimental results over a wide range of temperatures. The SAPT approach rigorously decomposes the interaction energy into physical components. The relative importance of these components has been analyzed.