An early model for the role of substituents in pi stacking interactions was proposed by Hunter and Sanders.

• Hunter CA, Sanders JK (1990). “The nature of π–π Interactions”. J. Am. Chem. Soc. 112 (14): 5525–5534. doi:10.1021/ja00170a016.

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. Contrastingly, electron donating groups increase the negative quadrupole, which may increase the interaction strength in a T-shaped configuration with the proper geometry. Based on this model, the authors proposed a set of rules governing pi stacking interactions which prevailed until more sophisticated computations were applied.

Experimental evidence for the Hunter–Sanders model was provided by Siegel et al. using a series of substituted syn- and anti-1,8-di-o-tolylnaphthalenes.

• Cozzi F, Cinquini M, Annuziata R, Siegel JS (1993). “Dominance of polar/.pi. Over charge-transfer effects in stacked phenyl interactions”. J. Am. Chem. Soc. 115 (12): 5330–5331. doi:10.1021/ja00065a069.

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 authors reported that aryl rings with electron-withdrawing substituents had higher barriers to rotation. 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. In other words, the electron-withdrawing groups resulted in “less unfavorable” electrostatic interactions in the ground state.

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.

• Cockroft SL, Hunter CA, Lawson KR, Perkins J, Urch CJ (June 2005). “Electrostatic control of aromatic stacking interactions”. Journal of the American Chemical Society. 127 (24): 8594–8595. doi:10.1021/ja050880n. PMID 15954755.

This technique has been used to study a multitude of noncovalent interactions. The single mutation, in this case changing a substituent on an aromatic ring, results in secondary effects such as a change in hydrogen bond strength. The double mutation quantifies these secondary interactions, such that even a weak interaction of interest can be dissected from the array. Their results indicate that more electron-withdrawing substituents have less repulsive 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.

• Battaglia MR, Buckingham AD, Williams JH (1981). “The electric quadrupole moments of benzene and hexafluorobenzene”. Chem. Phys. Lett. 78 (3): 421–423. Bibcode:1981CPL….78..421B. doi:10.1016/0009-2614(81)85228-1

The findings provide direct evidence for the Hunter–Sanders model. 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.

In a follow-up study, Hunter et al. verified to a first approximation that the interaction energies of the interacting aromatic rings in a double mutant cycle are dominated by electrostatic effects.

• Cockroft SL, Perkins J, Zonta C, Adams H, Spey SE, Low CM, et al. (April 2007). “Substituent effects on aromatic stacking interactions”. Organic & Biomolecular Chemistry. 5 (7): 1062–1080. doi:10.1039/b617576g. PMID 17377660. S2CID 37409177.

However, the authors note that direct interactions with the ring substituents, discussed below, also make important contributions. Indeed, the interplay of these two factors may result in the complicated substituent- and geometry-dependent behavior of pi stacking interactions.