Bond length estimates for oxide crystals with a molecular power law expression

A molecular power law bond length regression expression, R(M–O) = 1.39(s/r)−0.22, defined in terms of the quotient, s/r, where s is the averaged Pauling bond strength for the bonded interaction comprising a given molecular coordination polyhedron and r is the periodic table row number for the M atom, serves to replicate the bulk of the 470 individual experimental M–O average bond lengths estimated with Shannon’s (Acta Crystallogr A 32(5):751–767, 1976) crystal radii for oxides to within 0.10 A. The success of the molecular expression is ascribed to a one-to-one deep-seated connection that obtains between the electron density accumulated between bonded pairs of atoms and the average Pauling bond strength. It also implies that the bonded interactions that constitute oxide crystals are governed in large part by local forces. Although the expression reproduces the bond lengths involving rare earth atoms typically to within ~0.05 A, it does not reproduce the lanthanide ionic radius contraction. It also fails to reproduce the experimental bond lengths for selected transition cations like Cu1+, Ag1+ and VILSFe2+ and for cations like IVK+, VIBa2+ and IIU6+.