An Overview of Strengths and Directionalities of Noncovalent Interactions: σ-Holes and π-Holes

Quantum mechanics, through the Hellmann–Feynman theorem and the Schrödinger equation, show that noncovalent interactions are classically Coulombic in nature, which includes polarization as well as electrostatics. In the great majority of these interactions, the positive electrostatic potentials result from regions of low electronic density. These regions are of two types, designated as σ-holes and π-holes. They differ in directionality; in general, σ-holes are along the extensions of covalent bonds to atoms (or occasionally between such extensions), while π-holes are perpendicular to planar portions of molecules. The magnitudes and locations of the most positive electrostatic potentials associated with σ-holes and π-holes are often approximate guides to the strengths and directions of interactions with negative sites but should be used cautiously for this purpose since polarization is not being taken into account. Since these maximum positive potentials may not be in the immediate proximities of atoms, interatomic close contacts are not always reliable indicators of noncovalent interactions. This is demonstrated for some heterocyclic rings and cyclic polyketones. We briefly mention some problems associated with using Periodic Table Groups to label interactions resulting from σ-holes and π-holes; for example, the labels do not distinguish between these two possibilities with differing directionalities.