Hobza1 has published a very high-level computational study of the benzene dimer as a benchmark for this model of π-π stacking – a topic I have touched upon a number of times in this blog (post 1, post 2) . There are four local energy minima, shown in Figure 1. The most stable dimer is the tilted T-structure (TT), a structure often overlooked. Its complexation energy, computed at CCSD(T)/CBS, is 2.78 kcal mol-1. Only slightly higher in energy is the parallel displaced structure (PD), with a stabilization energy of 2.70 kcal mol-1. The T structure (T) is essentially isoenergetic with the PD one. The perfectly stacked structure (S) is much less stable, with a dimerization energy of 1.64 kcal mol-1. The DTF-D method, using the BLYP functional with dispersion parameters optimized for the benzene dimer provide energies within 0.2 kcal mol-1 of the computationally much more expensive benchmark values. As a word of caution though: use of more general dispersion parameters gives energies far worse and predicts the wrong energy order of the dimers.

TT
2.78
2.93
2.33

PD
2.70
2.88
2.57

T
2.69
2.80
2.03

S
1.64
1.84
1.45

Figure 1. Structures of the benzene dimer with stabilization energy (kcal mol-1) computed at CCSD(T)/CBS (bold), DFT-D/BLYP with optimized parameters (italics), and DFT-D/BLYP with general parameters (plain).1

References

(1) Pitonak, M.; Neogrady, P.; Rexac, J.; Jurecka, P.; Urban, M.; Hobza, P., "Benzene Dimer: High-Level Wave Function and Density Functional Theory Calculations," J. Chem. Theory Comput., 2008, 4, 1829-1834, DOI: 10.1021/ct800229h.