The Lennard-Jones Function: A Quantitative Description of the Spatial Correlation of Electrons As Determined by the Exclusion Principle

Abstract

Lennard-Jones was among the earliest to stress the dominant role played by the exclusion principle in chemistry and was the first to exploit the properties of the same-spin pair density to demonstrate the most probable spatial distribution of a given number of electron pairs. This paper demonstrates that a related distribution function, the conditional probability for same-spin electrons, is so successful in recovering the geometrical models associated with differing numbers of electron pairs, as suggested by the work of Lennard-Jones and subsequently adopted as the basis for the VSEPR model, that we propose that it be called the Lennard-Jones function, or LJF. The maxima in LJF show where the density of the other electrons is most likely to be found, relative to a fixed position of a same-spin reference electron. The digonal, trigonal, tetrahedral, bipyramidal, and octahedral patterns of maxima obtained in such displays demonstrate that these are the most probable arrangements for corresponding numbers of electron pairs. LJF provides a quantitative measure of the extent of exclusion of the density of one electron from that of another of the same spin. There is a remarkable similarity in the patterns of spatial pairing exhibited by LJF and L(r) = −∇2ρ(r), and the manner in which the two-electron correlation contained in LJF is transmitted to the density and hence to L(r) is accounted for.