Reinterpreting π-Stacking

Abstract

The nature of pi-pi interactions has long been debated. The term "pi-stacking" is considered by some to be a misnomer, in part because overlapping pi-electron densities are thought to incur steric repulsion, and the physical origins of the widely-encountered "slip-stacked" motif have variously been attributed to either sterics or electrostatics, in competition with dispersion. Here, we use quantum-mechanical energy decomposition analysis to investigate pi-pi interactions in supramolecular complexes of polycyclic aromatic hydrocarbons, ranging in size up to realistic models of graphene, and for comparison we perform the same analysis on stacked complexes of polycyclic <i>saturated</i> hydrocarbons, which are cyclohexane-based analogues of graphane. Our results help to explain the short-range structure of liquid hydrocarbons that is inferred from neutron scattering, trends in melting-point data, the interlayer separation of graphene sheets, and finally band gaps and observation of molecular plasmons in graphene nanoribbons. Analysis of intermolecular forces demonstrates that aromatic pi-pi interactions constitute a unique and fundamentally quantum-mechanical form of non-bonded interaction. Not only do stacked pi-pi architectures enhance dispersion, but quadrupolar electrostatic interactions that may be repulsive at long range are rendered attractive at the intermolecular distances that characterize pi-stacking, as a result of charge penetration effects. The planar geometries of aromatic sp<sup>2</sup> carbon networks lead to attractive interactions that are "served up on a molecular pizza peel", and adoption of slip-stacked geometries minimizes steric (rather than electrostatic) repulsion. The slip-stacked motif therefore emerges not as a defect induced by electrostatic repulsion but rather as a natural outcome of a conformation landscape that is dominated by van der Waals interactions (dispersion plus Pauli repulsion), and is therefore fundamentally quantum-mechanical in its origins. This reinterpretation of the forces responsible for pi-stacking has important implications for the manner in which non-bonded interactions are modeled using classical force fields, and for rationalizing the prevalence of the slip-stacked pi-pi motif in protein crystal structures.<br><br>