Stacking (chemistry) - Substituent Effects - Direct Interaction Model

Direct Interaction Model

The Hunter-Sanders model has been criticized by numerous research groups offering contradictory experimental and computational evidence of pi stacking interactions that are not governed primarily by electrostatic effects.

The clearest experimental evidence against electrostatic substituent effects was reported by Rashkin and Waters. They used meta- and para-substituted N-benzyl-2-(2-fluorophenyl)-pyridinium bromides, which stack in a parallel displaced conformation, as a model system for pi stacking interactions. In their system, a methylene linker prohibits favorable T-shaped interactions. As in previous models, the relative strength of pi stacking interactions was measured by NMR as the rate of rotation about the biaryl bond, as pi stacking interactions are disrupted in the transition state. Para-substituted rings had small rotational barriers which increased with increasingly electron-withdrawing groups, consistent with prior findings. However, meta-substituted rings had much larger barriers of rotation despite having nearly identical electron densities in the aromatic ring. The authors explain this discrepancy as direct interaction of the edge of hydrogen atoms of one ring with the electronegative substituents on the other ring. This claim is supported by chemical shift data of the proton in question.

Much of the detailed analyses of the relative contributions of factors in pi stacking have been borne out by computation. Sherill and Sinnokrot reported a surprising finding using high-level theory that all substituted benzene dimers have more favorable binding interactions than a benzene dimer in the sandwich configuration. Later computational work from the Sherill group revealed that the substituent effects for the sandwich configuration are additive, which points to a strong influence of dispersion forces and direct interactions between substituents. It was noted that interactions between substituted benzenes in the T-shaped configuration were more complex. Finally, Sherril and Sinnokrot argue in their review article that any semblance of a trend based on electron donating or withdrawing substituents can be explained by exchange-repulsion and dispersion terms.

Houk and Wheeler also provide compelling computational evidence for the importance of direct interaction in pi stacking. In their analysis of substituted benzene dimers in a sandwich conformation, they were able to recapitulate their findings using an exceedingly simple model where the substituted benzene, Ph-X, was replaced by H-X. Remarkably, this crude model resulted in the same trend in relative interaction energies, and correlated strongly with the values calculated for Ph-X. This finding suggests that substituent effects in the benzene dimer are due to direct interaction of the substituent with the aromatic ring, and that the pi system of the substituted benzene is not involved. This latter point is expanded upon below.

In summary, it would seem that the relative contributions of electrostatics, dispersion, and direct interactions to the substituent effects seen in pi stacking interactions are highly dependent on geometry and experimental design. The lack of consensus on the matter may simply reflect the complexity of the issue.