Pi-stacking

In chemistry, pi stacking (also called π–π stacking) refers to attractive, noncovalent interactions between aromatic rings, since they contain pi bonds. These interactions are important in nucleobase stacking within DNA and RNA molecules, protein folding, template-directed synthesis, materials science, and molecular recognition, although new research suggests that pi stacking may not be operative in some of these applications. Despite intense experimental and theoretical interest, there is no unified description of the factors that contribute to pi stacking interactions.

The benzene dimer is the prototypical system for the study of pi stacking, and is experimentally bound by 8–12 kJ/mol (2–3 kcal/mol) in the gas phase with a separation of 4.96 Å between the centers of mass for the T-shaped dimer. The small binding energy makes the benzene dimer difficult to study experimentally, and the dimer itself is only stable at low temperatures and is prone to cluster.

Other evidence for pi stacking comes from X-ray crystal structures. Perpendicular and offset parallel configurations can be observed in the crystal structures of many simple aromatic compounds. Similar offset parallel or perpendicular geometries were observed in a survey of high-resolution x-ray protein crystal structures in the Protein Data Bank. 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.

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. The two most stable conformations are the parallel displaced and T-shaped, which are essentially isoenergetic and represent energy minima. In contrast, the sandwich configuration maximizes overlap of the pi system, is least stable, and represents an energetic saddle point. This later finding is consistent with a relative rarity of this configuration in x-ray crystal data.

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. While benzene does not have a dipole moment, it has a strong quadrupole moment. The local C-H dipole means that there is positive charge on the atoms in the ring and a correspondingly negative charge representing an electron cloud above and below the ring. The quadrupole moment is reversed for hexafluorobenzene due to the electronegativity of fluorine. The benzene dimer in the sandwich configuration is stabilized by London dispersion forces but destabilized by repulsive quadrupole/quadrupole interactions. By offsetting one of the benzene rings, the parallel displaced configuration reduces these repulsive interactions and is stabilized. The T-shaped configuration enjoys favorable quadrupole/quadrupole interactions, as the positive quadrupole of one benzene ring interacts with the negative quadrupole of the other. The benzene rings are furthest apart in this configuration, so the favorable quadrupole/quadrupole interactions evidently compensate for diminished dispersion forces.

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