Bond valence – bond length empirical correlations are of great interest in chemistry, biology, geology and materials science because they offer a quick and convenient way of checking and evaluating molecular structures. Linus Pauling’s relationship is the most commonly used, but is a two-parameter fit where R0 and b must be optimized. In this study, a simplified quantum-mechanical approach was used to derive Pauling’s empirical bond valence – bond length relationship. A covalency factor was also introduced to account for the difference in “softness” between cation and anion (resulting in increased orbital overlap). An expression for the b parameter was determined that yields values that are in agreement with experimental data. The derived relationship for the b parameter allows an independent determination of b using orbital exponents and electronegativity values for the cation and anion.
Hardcastle, F. D. and Laffoon, S.
"Theoretical Justification for Bond Valence -- Bond Length Empirical Correlations,"
Journal of the Arkansas Academy of Science: Vol. 66, Article 18.
Available at: https://scholarworks.uark.edu/jaas/vol66/iss1/18