Pauling determined an empirical logarithmic dependence of bond order (bond valence), s, to bond length, R, s = exp(R0 – R/ b), where R0 is unit bond length and b is a fitting parameter. Recently, an expression was derived for relating the b fitting parameter to theoretically derived atomic orbital exponents. With a method to calculate b, both R0 and atomic orbital exponents can be experimentally determined through optimized fitting for Cr-O, Cr-S, Mo-O, and Mo-S. In the present study, bond length – valence relationships are found for Cr-O, Cr-S, Mo-O, and Mo-S chemical bonds using published crystallographic data. In addition, atomic orbital exponents were found for chromium and molybdenum: zCr = 1.247 and zMo = 1.381. Finally, bond lengths of unit bond valence, or true single bonds, were found using the bond valence model: Ro(Cr-O) = 1.770 Å, Ro(Cr-S) = 2.159 Å, Ro(Mo-O) = 1.893 Å, and Ro(Mo-S) = 2.264 Å.
Labrecque, J. and Hardcastle, F. D.
"Bond Length and Bond Valence Relationships for Chromium Oxides, Chromium Sulfides, Molybdenum Oxides, and Molybdenum Sulfides,"
Journal of the Arkansas Academy of Science: Vol. 71
, Article 14.
Available at: http://scholarworks.uark.edu/jaas/vol71/iss1/14