Simple, near-universal relationships between bond lengths, strengths, and anharmonicities

Harmonic bond force constants and bond lengths are shown to generally obey the simple relationships, ke=ζ2Re−3 (hydrides) and ke=10ζ1/2Re−4 (all other bond types), where ζ is the reduced nuclear charge and Re is the equilibrium bond length. Equally simple power-law relationships are found for higher-order bond force constants. Although not spectroscopically accurate, these models are nonetheless of significant heuristic value for identifying strongly multireference states of diatomic molecules (including electronically coupled excited states ill-suited for inclusion in laser-cooling schemes), rationalizing the observed trends in vibrational frequencies for diatomics and/or local mode oscillators within molecules or complexes and estimating and/or validating covalent bonding parameters within molecular mechanics force fields. Particular advantages of our approach over other bond length-strength scaling relationships proposed in the literature include its simplicity and generality and its appropriate asymptotic behavior. Notably, the relationships derived in this work can be used to predict harmonic and higher-order force constant bonds between any pair of atoms in the Periodic Table (including transition metals and lanthanides) without requiring row- or column-dependent parameterization, to accuracies commensurate with conventional force field transferability errors. We therefore anticipate that they will expedite force field development for metal-containing complexes and materials, which are structurally well-characterized but challenging to parameterize ab initio.