A quantum-mechanical LCAO approach was used to derive Pauling’s popular empirical bond valencelength relationship s = exp((R₀-R)/b), where s is the bond order or bond valence associated with bond length R, and R₀ and b are fitting parameters. An expression for the b “empirical” fitting parameter is derived in terms of atomic orbital exponents. The b parameters calculated from the atomic orbital exponents are consistent with optimized b parameters. In general, atomic orbital exponents may be used to determine bond valence-length relationships for any chemical bond regardless of valence state, oxidation number, physical or chemical environment. In this study, almost two-thousand carbon-carbon and carbon-hydrogen bond lengths were evaluated from over 40 compounds to yield reliable bond valence – bond length relationships for C-C and C-H bonds. The atomic orbital exponent for carbon was found to be ζC = 1.651. Unit valence bond lengths (R₀ where s = 1) were found to be 1.493 Å for the carbon-carbon bond and 1.061 Å for the carbon-hydrogen bond.
Hardcastle, F. D.
"A General Valence-Length Correlation for Determining Bond Orders: Application to Carbon-Carbon and Carbon-Hydrogen Chemical Bonds,"
Journal of the Arkansas Academy of Science: Vol. 70
, Article 17.
Available at: http://scholarworks.uark.edu/jaas/vol70/iss1/17