The π-hole revisited

It follows from the Schrodinger equation that the forces operating within molecules and molecular complexes are Coulombic, which necessarily entails both electrostatics and polarization. A common and important class of molecular complexes is due to pi-holes. These are molecular regions of low electronic density that are perpendicular to planar portions of the molecular frameworks. pi-Holes often have positive electrostatic potentials associated with them, which result in mutually polarizing attractive forces with negative sites such as lone pairs, pi electrons or anions. In many molecules, pi-holes correspond to a flattening of the electronic density surface but in benzene derivatives and in polyazines the pi-holes are craters above and below the rings. The interaction energies of pi-hole complexes can be expressed quite well in terms of regression relationships that account for both the electrostatics and the polarization. There is a marked gradation in the interaction energies, from quite weak (about -2 kcal mol(-1)) to relatively strong (about -40 kcal mol(-1)). Gradations are also evident in the ratios of the intermolecular separations to the sums of the respective van der Waals radii and in the gradual transition of the pi-hole atoms from trigonal to quasi-tetrahedral configurations. These trends are consistent with the concept that chemical interactions form a continuum, from very weak to very strong.

Automated summary

It is found that within molecules, π-holes typically display positive electrostatic potentials and polarizing attractive forces with negative sites, resulting from low electronic density regions perpendicular to planar portions of molecular frameworks. Interaction energies of π-hole complexes can be well expressed in terms of regression relationships involving both electrostatics and polarization, exhibiting a range from weak to strong forces. Trend also shows gradual changes in intermolecular separations, van der Waals radii, and configurations of π-hole atoms, indicating a continuum of chemical interactions from weak to strong.