Bond Length - Bond Valence Relationships for Carbon - Carbon and Carbon - Oxygen Bonds

In the present study, relationships are developed for determining bond orders (also referred to as bond valences or bond numbers) from published bond lengths for carbon-carbon (C-C) and carbon-oxygen (C-O) bonds. The relationships are based on Pauling’s empirical formula s = exp((Ro-R)/b)), where s is the bond order, R is the corresponding bond length, Ro is the unit valence bond length, and b is a fitting parameter. We use a recently derived relationship for the b parameter in terms of the bonding atoms’ published atomic orbital exponents. The resulting equations were checked against published x-ray diffraction (XRD) data for 176 carbon systems with 540 published C-C bond lengths, and 50 oxygen systems having 72 published C-O bond lengths. The C-C and C-O bond length-valence relationships are shown to have sufficient applicability and accuracy for use in any bonding environment, regardless of physical state or oxidation number.