Title: Pauling bond strength, bond length and electron density distribution

A power law regression equation, = 1.46(<ρ(rc)>/r)-0.19, connecting the average experimental bond lengths, , with the average accumulation of the electron density at the bond critical point, <ρ(rc)>, between bonded metal M and oxygen atoms, determined at ambient conditions for oxide crystals, where r is the row number of the M atom, is similar to the regression equation R(M-O) = 1.39(ρ(rc)/r)-0.21 determined for three perovskite crystals for pressures as high as 80 GPa. The two equations are also comparable with those, = 1.43(/r)-0.21, determined for a large number of oxide crystals at ambient conditions and = 1.39(/r)-0.22, determined for geometry optimized hydroxyacid molecules, that connect the bond lengths to the average Pauling electrostatic bond strength, , for the M-O bonded interactions. On the basis of the correspondence between the two sets of equations connecting ρ(rc) and the Pauling bond strength s with bond length, it appears that Pauling’s simple definition of bond strength closely mimics the accumulation of the electron density between bonded pairs of atoms. The similarity of the expressions for the crystals and molecules is compelling evidence that the M-O bonded interactions for the crystals and molecules 2 containing the same bonded interactions are comparable. Similar expressions, connectingmore » bond lengths and bond strength, have also been found to hold for fluoride, nitride and sulfide molecules and crystals. The Brown-Shannon bond valence, σ, power law expression σ = [R1/(R(M-O)]N that has found wide use in crystal chemistry, is shown to be connected to a more universal expression determined for oxides and the perovskites, <ρ(rc)> = r[(1.41)/]4.76, demonstrating that the bond valence for a bonded interaction is likewise closely connected to the accumulation of the electron density between the bonded atoms. Unlike the Brown-Shannon expression, it is universal in that it holds for the M-O bonded interactions for a relatively wide range of M atoms of the periodic table. The power law equation determined for the oxide crystals at ambient conditions is similar to the power law expression <ρ(rc)> = r[1.46/]5.26 determined for the perovskites at pressures as high as 80 GPa, indicating that the intrinsic connection between R(M-O) and ρ(rc) that holds at ambient conditions also holds, to a first approximation, at high pressures.« less