Valence-Length Correlations for Chemical Bonds from Atomic Orbital Exponents

Abstract

Pauling’s empirical bond valence-length correlation has proven valuable because it offers a quick and convenient way of checking and evaluating molecular structures and determining oxidation states from measured bond lengths. In this study, a simplified quantum-mechanical approach was used to derive Pauling’s empirical bond valence-length relationship by considering overlap of hydrogen-like orbitals. An expression for the b “empirical” fitting parameter was derived in terms of atomic-orbital exponents. A new set of orbital exponents is presented using published atomic/covalent radii and a continuous function for the effective principal quantum. The b parameters calculated from the orbital exponents are consistent with bond valence-length data from crystallographic data. In general, atomic-orbital exponents may be used to determine bond valence- length relationships for any chemical bond regardless of state, oxidation number, or environment.