Once more into the benzene dimer (see these previous posts: “Benzene dimer again“, “Benzene dimer“, “π-π stacking (part 2)“, “π-π stacking“)! Sherrill has published a detailed and impressive benchmark study of the benzene dimer in its three most important configurations: the D_6h stacked arrangement (1), the T-shaped arrangement (2) and the parallel displaced arrangement (3). ¹

First, they performed a careful extrapolation study to obtain accurate binding energies based on CCSD(T) with large basis sets. Then they compared the potential energy curves of the three configurations of benzene dimer obtained with this accurate method with those obtained with less computationally expensive methods. These alternates include RI-MP2, SCS-MP2 and a variety of different density functional. Their results are summarized in Table 1. The upshot is that the SCS-MP2 results are very similar to the much more expensive CCDS(T) values. And while the errors are a bit larger with the DFT methods, their performance is really quite good, especially given their dramatically lower costs. (Note that the “-D” indicates inclusion of Grimme’s dispersion correction term.) Particularly worth mentioning is the very fine performance of the MO6-2X functional.

Table 1. Binding energies (kcal mol^-1) of the three benzene dimers with different computational methods.

Method	1	2	3
CCSD(T)	-1.65	-2.69	-2.67
SCS-MP2	-1.87	-2.47	-2.87
MO6-2X	-0.95	-2,42	-2.54
B3LYP-D	-1.20	-3.03	-2.51
PBE-D	-1.51	-3.02	-2.63

References

(1) Sherrill, C. D.; Takatani, T.; Hohenstein, E. G., "An Assessment of Theoretical Methods for Nonbonded Interactions: Comparison to Complete Basis Set Limit Coupled-Cluster Potential Energy Curves for the Benzene Dimer, the Methane Dimer, Benzene-Methane, and Benzene-H₂S" J. Phys. Chem. A 2009, ASAP, DOI: 10.1021/jp9034375