PAULING BOND STRENGTH, BOND LENGTH AND ELECTRON DENSITY DISTRIBUTION

Bond lengths determined for oxide molecules and crystals, R(M-O), are related to the normalized Pauling bond strengths, s/r, by the power law regression expression R(M-O) = 1.42(s/r)^-0.21 where r is the row number of the M atom. Bond lengths determined for crystals at ambient conditions and at pressures as great at 80 GPa are related to ρ(r_c)/r where ρ(r_c) is the value of the electron density between M-O bonded pairs by the expression R(M-O) = 1.41(ρ(r_c)/r)^-0.21. When the two power law expressions are recast in terms of s and ρ(r_c), respectively, the expressions s = r(1.42/R(M-O))^4.76 and ρ(r_c) = r(1.41/R(M-O))^4.76 result, revealing that s ≈ ρ(r_c). The agreement overall between average value of ρ(r_c) and s is typically less than 0.1 for the bulk of the M atoms of the periodic table with more than 94% of the variation in the bond strength of a M-O bonded interaction being explained in terms of a linear dependence on the electron density. It is remarkable to us that the regression line is statistically identical with a one-to-one correlation between ρ(r_c) and s for the bonded interactions for a large number of coordinated polyhedra, a testament of Pauling's genius in choosing a simple empirical parameter like the electrostatic bond strength as a gauge of the strength of a bonded interaction. Given that the strength of a M-O bonded interaction is a direct measure of the electron density accumulated between a pair of bonded atoms and that the atoms in a crystal are largely neutral, then the strength of a bonded interaction can be defined as the quotient of the number of valence electrons of an M atom involved in the bonded interactions and the number of bonded interactions that it makes with its coordinating O atoms. This definition is consistent with Pauling’s model of resonating bonded interactions where the valence of the metal atom tends to be divided equally among the bonded interactions reaching the coordinating oxygen atoms, a rule that is equivalent to the electrostatic rule in that it satisfies the valences of the nonmetal atoms. Given the connection between the accumulation of the electron density between a bonded pair of atoms, the strength of the interaction and the bond length of the bonded pair, it makes little difference whether a bonded interaction is considered to be either electrostatic or covalent.