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.