Abstract
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.
Highlights
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
A π-hole is a region of lower electronic density, but it is above and below a planar portion of a molecule. These regions of lower electronic density, which reflect the anisotropies of covalently-bonded atoms [6,7,8,9,10,11], often give rise to positive electrostatic potentials
Since molecular electrostatic potentials have played an important part in elucidating the natures of interactions due to σ-holes and π-holes, we will briefly review this property
Summary
Since molecular electrostatic potentials have played an important part in elucidating the natures of interactions due to σ-holes and π-holes, we will briefly review this property. In the context of noncovalent interactions, V(r) is typically computed on the molecular surface defined, following Bader et al [29], by the 0.001 au contour of the electronic density The potential on this surface is designated as VS (r) and its most positive and negative values (of which there may be several) as VS,max and VS,min. It must be stressed that, as shown in Equation (1), the molecular electrostatic potential reflects the positive contributions of the nuclei as well as the negative ones of the electrons. The assumption is sometimes made that “electron-rich” regions will have negative V(r) and “electron-poor” ones will have positive V(r) This is not necessarily the case; the electrostatic potential does not follow the electronic density [30,31,32,33,34].
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