The electron pair

Eighty years have elapsed since Lewis introduced the concept of an electron pair into chemistry where it has continued to play a dominant role to this day. The pairing of electrons is a consequence of the Pauli exclusion principle and is the result of the localization of one electron of each spin to a given region of space. It is the purpose of this paper to demonstrate that all manifestations of the spatial localization of an electron of a given spin are a result of corresponding localizations of its Fermi hole. The density of the Fermi hole determines how the charge of a given electron is spread out in the space occupied by a second same-spin electron, thereby excluding an amount of same-spin density equivalent to one electronic charge. The Fermi hole is an electron's doppelganger-it goes where the electron goes and vice versa: if the hole is localized, so is the electron. The topologies of two fields have been shown to provide information about the spatial localization of electronic charge: the negative of the Laplacian of the electron density, referred to here as L(r), and the electron localization function ELF or eta(r). The measure provided by L(r) is empirical. It is based upon the remarkable correspondence exhibited by its topology with the number and arrangement of the localized electron domains assumed in the VSEPR model of molecular geometry. eta(r) is based upon the local behavior of the same-spin probability, and it is shown that the picture of electron localization that its topology provides is a consequence of a corresponding localization of the Fermi hole density. This paper provides a complete determination and comparison of the topologies of L(r) and eta(r) for molecules covering a wide spectrum of atomic interactions. The structures of the two fields are summarized and compared in terms of the characteristic polyhedra that their critical points define fur a central atom interacting with a set of ligands. In general, the two fields an found to be homeomorphic in terms of the number and arrangement of electron localization domains that they define. The complementary information provided by the similarities in and differences between these two fields extends our understanding of the origin of electron pairing and its physical consequences.