Beyond the Benzene Dimer: An Investigation of the Additivity of π−π Interactions

The benzene dimer is the simplest prototype of π−π interactions and has been used to understand the
fundamental physics of these interactions as they are observed in more complex systems. In biological systems,
however, aromatic rings are rarely found in isolated pairs; thus, it is important to understand whether aromatic
pairs remain a good model of π−π interactions in clusters. In this study, ab initio methods are used to compute
the binding energies of several benzene trimers and tetramers, most of them in 1D stacked configurations.
The two-body terms change only slightly relative to the dimer, and except for the cyclic trimer, the three-
and four-body terms are negligible. This indicates that aromatic clusters do not feature any large nonadditive
effects in their binding energies, and polarization effects in benzene clusters do not greatly change the binding
that would be anticipated from unperturbed benzene−benzene interactions, at least for the 1D stacked systems
considered. Three-body effects are larger for the cyclic trimer, but for all systems considered, the computed
binding energies are within 10% of what would be estimated from benzene dimer energies at the same
geometries.