Pi-stacking

What is more commonly observed (see figure to the right) is either a staggered stacking (parallel displaced) or pi-teeing (perpendicular T-shaped) interaction both of which are electrostatic attractive[2][3] For example, the most commonly observed interactions between aromatic rings of amino acid residues in proteins is a staggered stacked followed by a perpendicular orientation.

An alternative explanation for the preference for staggered stacking is due to the balance between van der Waals interactions (attractive dispersion plus Pauli repulsion).

[7] Analysis of the aromatic amino acids phenylalanine, tyrosine, histidine, and tryptophan indicates that dimers of these side chains have many possible stabilizing interactions at distances larger than the average van der Waals radii.

[4] The preferred geometries of the benzene dimer have been modeled at a high level of theory with MP2-R12/A computations and very large counterpoise-corrected aug-cc-PVTZ basis sets.

[citation needed] The relative binding energies of these three geometric configurations of the benzene dimer can be explained by a balance of quadrupole/quadrupole and London dispersion forces.

[10] They used a simple mathematical model based on sigma and pi atomic charges, relative orientations, and van der Waals interactions to qualitatively determine that electrostatics are dominant in substituent effects.

According to their model, electron-withdrawing groups reduce the negative quadrupole of the aromatic ring and thereby favor parallel displaced and sandwich conformations.

Based on this model, the authors proposed a set of rules governing pi stacking interactions which prevailed until more sophisticated computations were applied.

[11] In these compounds the aryl groups "face-off" in a stacked geometry due to steric crowding, and the barrier to epimerization was measured by nuclear magnetic resonance spectroscopy.

The interpretation of this result was that these groups reduced the electron density of the aromatic rings, allowing more favorable sandwich pi stacking interactions and thus a higher barrier.

[citation needed] Hunter et al. applied a more sophisticated chemical double mutant cycle with a hydrogen-bonded "zipper" to the issue of substituent effects in pi stacking interactions.

Correspondingly, this trend was exactly inverted for interactions with pentafluorophenylbenzene, which has a quadrupole moment equal in magnitude but opposite in sign as that of benzene.

However, the stacking interactions measured using the double mutant method were surprisingly small, and the authors note that the values may not be transferable to other systems.

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.

Finally, Sherill 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.

Remarkably, this crude model resulted in the same trend in relative interaction energies, and correlated strongly with the values calculated for Ph–X.

However, several groups have provided contrary evidence, calling into question whether pi stacking is a unique phenomenon or whether it extends to other neutral, closed-shell molecules.

In an experiment not dissimilar from others mentioned above, Paliwal and coauthors constructed a molecular torsion balance from an aryl ester with two conformational states.

The NMR chemical shifts of the two conformations were distinct and could be used to determine the ratio of the two states, which was interpreted as a measure of intramolecular forces.

Other evidence for non-aromatic pi stacking interactions results include critical studies in theoretical chemistry, explaining the underlying mechanisms of empirical observations.

Grimme reported that the interaction energies of smaller dimers consisting of one or two rings are very similar for both aromatic and saturated compounds.

Indeed, large aromatic dimers are only stabilized relative to their saturated counterparts in a sandwich geometry, while their energies are similar in a T-shaped interaction.

Stoddart and co-workers developed a series of systems utilizing the strong π–π interactions between electron-rich benzene derivatives and electron-poor pyridinium rings.

The π–π interaction between A and B directed the formation of an interlocked template intermediate that was further cyclized by substitution reaction with compound C to generate the [2]catenane product.