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.

中文翻译：

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使用 Badger 规则的归一化版本通过共振拉曼光谱测定 Cu(III)-OH 键距

配合物 LCuOH (L = N,N'-双(2,6-二异丙基-4-R-苯基)吡啶-2,6 中 [CuOH]2+ 核心的拉伸频率 ν(Cu-O) -二甲酰胺，R = H或NO2，或N,N'-双(2,6-二异丙基苯基)-1-甲基哌啶-2,6-二甲酰胺)通过共振拉曼光谱测定为～630 cm-1，并通过以下方法验证同位素标记。在使用 Badger 规则来估计与 ν(Cu-O) 相对应的键距的过程中，通过使用通过除以适当的约化质量而归一化的拉伸频率开发了该规则的修改版本。我们发现，对于 1.1-2.2 Å 范围内的各种 MX 和 XX 键距（预测键的均方根误差），经理论和实验得出的修改后的版本可以对大于 250 个数据点的归一化频率与键距产生出色的拟合0.03 Å 的距离）。使用所得的一般方程，反应性 [CuOH]2+ 核的 Cu-O 键距预计为 ∼1.80 Å。探讨了该方程的局限性及其在预测无法获得结构信息的各种部分的距离中的用途。