Determination of the Cu(III)-OH Bond Distance by Resonance Raman Spectroscopy Using a Normalized Version of Badger's Rule

The stretching frequency, ν(Cu-O), of the [CuOH]²⁺ core in the complexes LCuOH (L = N,N′-bis(2,6-diisopropyl-4-R-phenyl)pyridine-2,6-dicarboxamide, R = H or NO₂, or N,N′-bis(2,6-diisopropylphenyl)-1-methylpiperidine-2,6-dicarboxamide) was determined to be ∼630 cm^-1 by resonance Raman spectroscopy and verified by isotopic labeling. In efforts to use Badger's rule to estimate the bond distance corresponding to ν(Cu-O), a modified version of the rule was developed through use of stretching frequencies normalized by dividing by the appropriate reduced masses. The modified version was found to yield excellent fits of normalized frequencies to bond distances for >250 data points from theory and experiment for a variety of M-X and X-X bond distances in the range ∼1.1-2.2 Å (root mean squared errors for the predicted bond distances of 0.03 Å). Using the resulting general equation, the Cu-O bond distance was predicted to be ∼1.80 Å for the reactive [CuOH]²⁺ core. Limitations of the equation and its use in predictions of distances in a variety of moieties for which structural information is not available were explored.