The Lewis Model and Beyond

Abstract

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 model of electronic structure finds physical expression. The pairing of electrons 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 equivalent amount of same-spin density. The averaging of the Fermi density over single atoms or pairs of atoms determines the corresponding contributions to the total Fermi correlation. It is these terms that yield the localization and delocalization indices that determine the intra- and interatomic distribution of electron pairs that enables one to compare the pairing predicted by theory with that of a Lewis structure. The agreement is best at the Hartree−Fock level, where the Fermi hole is the sole source of correlation between the electrons. The introduction of the remaining correlation, the Coulomb correlation, disrupts the sharing of electron pairs between the atoms, and its effect is therefore, most pronounced for shared interactions. For example, Coulomb correlation reduces the number of shared pairs in N2 from the Hartree−Fock value of three to just above two. In ionic systems, the electrons are strongly localized within each atomic basin and the effect of Coulomb correlation on the atomic pairing is minimal, approaching zero over each of the atomic basins, as it does for the total molecule.

Bond order and valence indices: A personal account

“…The bond order index has been introduced in the AIM theory by Ángyán et al 39 Somewhat later, Fradera et al 40 introduced a "delocalization index" which in the single determinant case is identical with the index of Ángyán et al, 39 and most authors who are using it for the the Hartree-Fock or DFT cases are not aware of the original paper. 39 The delocalization index of Fradera et al 40 is defined in such a way that for the explicitly correlated case it involves the use of the total ρ xc ( r 1 , r 2 ) in eq. (68) mentioned earlier, which, as already noted, I cannot recommend.…”

Restoring orbital thinking from real space descriptions: bonding in classical and non-classical transition metal carbonyls

“…26 Effective one-electron functions may be defined by diagonalizing the DAFH on the basis of occupied orbitals. 15,16 In this way, G O (r) = P i=1 n i |f i (r)| 2 , the f i 's being one-electron functions or domain natural orbitals (DNOs), and the n's a set of occupation numbers that reconstruct by summation N O .…”

Electron pairing and chemical bonds: Pair localization in ELF domains from the analysis of domain averaged Fermi holes

“…Because of immense debt which chemistry owes to the classical model of molecule as composed of directionally oriented and well localized chemical bonds, it is not surprising that a lot of effort was and still is devoted to its reconciliation with the quantum mechanical description in terms of delocalized wave functions. [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] One of the promising procedures which indeed seem to provide the desired link between the classical and quantum chemical description of chemical bonding is the approach based on the so-called electron localization function (ELF). [19][20][21][22] This function allows the unique partitioning of the molecule into disjunct domains, which indeed are reminiscent of classical chemical bonds.…”