The Lewis model and beyond

The electron pair density, in conjunction with the definition of an atom in a molecule, enables one to determine the average number of electron pairs that are localized to each atom and the number that are formed between any given pair of atoms. Thus, it is through the pair density that the Lewis mo del of electronic structure finds physical expression. The pairing of elect rons is a consequence of the Pauli principle whose effect is made manifest through the creation of the Fermi hole. The density describing the spatial distribution of the Fermi hole for an electron of given spin determines how the density of that electron is spread out in space, excluding an equivale nt amount of same-spin density. The averaging of the Fermi density over sin gle atoms or pairs of atoms determines the corresponding contributions to t he total Fermi correlation. It is these terms that yield the focalization a nd delocalization indices that determine the intra- and interatomic distrib ution of electron pairs that enables one to compare the pairing predicted b y theory with that of a Lewis structure. The agreement is best at the Hartr ee-Fock lever, where the Fermi hole is the sole source of correlation betwe en the electrons. The introduction of the remaining correlation, the Coulom b correlation, disrupts the sharing of electron pairs between the atoms, an d its effect is therefore, most pronounced for shared interactions. For exa mple, Coulomb correlation reduces the number of shared pairs in N-2 from th e Hartree-Fock value of three to just above two. In ionic systems, the elec trons are strongly localized within each atomic basin and the effect of Cou lomb correlation on the atomic pairing is minimal, approaching zero over ea ch of the atomic basins, as it does for the total molecule.