Electron Delocalization and the Fermi Hole

Abstract

The delocalization of electrons is controlled by the Pauli exclusion principle through a corresponding delocalization of the density of the Fermi hole for electrons of given spin. It is proposed that the spatial distribution of the Fermi-hole density be used to provide a common, quantitative basis for the concept of electron delocalization, as it is used throughout chemistry. To this end, the following correspondences are made: The atomic patterns of delocalization of the Fermi hole recover the resonance structures corresponding to different possible spin-pairings and their relative importance, in terms of both energy and reactivity. The π-electron density of benzene distorted into a Kekulé-like structure is shown to be less delocalized than in the symmetrical structure. The effects of a hetero ring atom and of substituents on the delocalization of the π-electrons in benzene are quantified. To illustrate the range of phenomena that are determined by the delocalization of the Fermi-hole, it is shown that the measure of the extent of delocalization of the spin density from one hydrogen to another vicinal to it correlates with the variation in their spin−spin coupling with torsion angle, as predicted by the Karplus equation.