Quantum Chemistry Assisted Normal Coordinate Analysis

DFT calculations were performed on Mo dinitrogen, hydra-zido(2-) and hydrazidium complexes. The calculations are based on available X-ray crystal structures, simplifying the phosphine ligands by PH3 groups. Vibrational spectroscopic data were then evaluated with a quantum chemistry-assisted normal coordinate analysis (QCA-NCA) which involves calculation of the / matrix by DFT and subsequent fitting of important force constants to match selected experimentally observed frequencies, in particular v(NN), v(MN), and 8(MNN) (M = Mo, W). Furthermore time-dependent (TD-) DFT was employed to calculate electronic transitions, which were then compared to experimental UVATs absorption spectra (16). As a result, a close check of the quality of the quantum chemical calculations was obtained. This allowed us to employ these calculations as well as to understand the chemical reactivity of the intermediates of N2 fixation (cf. Section III). 

Based on the experimental frequencies and isotope shifts, a Quantum-Chemistry Assisted Normal Coordinate Analysis (QCA-NCA) has been performed. Details of the QCA-NCA procedure of I, including the f-matrix and the definition of the symmetry coordinates, have been described previously (12a). The NCA is based on model I (vide supra). Assignments of the experimentally observed vibrations and frequencies obtained with the QCA-NCA procedure are presented in Table II. The symbolic F-matrix for model I is shown in Scheme 3. Table III collects the force constants of the central N-N-M-N-N unit of I resulting from QCA-NCA. As evident from Table II, good agreement between measured and calculated frequencies is achieved, demonstrating the success of this method. 

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