Theory of thermal effects in nuclear magnetic resonance spectra of metal hydrides undergoing quantum mechanical exchange

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Abstract
Thermal effects in nuclear magnetic resonance spectra of transition metal hydrides exhibiting resolved quantum mechanical exchange splittings are consistently explained. Interactions of the relevant spatial degrees of freedom of the hydride protons with a quantum mechanical thermal bath are described in terms of Wangsness–Bloch–Redfield (WBR) theory. Upon elimination of the vibrational modes which relax too quickly to be observed on the NMR time scale, the WBR equation for the remaining, slowly relaxing modes (exchange modes) is shown to be equivalent to the Alexander–Binsch equation for classically exchanging nuclei, where the standard spin–spin coupling term is replaced by (or augmented with) quantum exchange term. Numerical calculations were performed for a one‐dimensional model of the relevant spatial motions, where the vibrational relaxation effects were described in terms of two adjustable parameters only. The assumed motion includes correlated rotation of a pair of the hydride protons, where the interproton distance may vary with the rotation angle. These calculations confirm that the present approach affords a consistent theoretical reproduction of the effects observed experimentally, i.e., an increase of the effective splitting with increasing temperature, with a gradual emergence of stochastic exchange that ultimately leads to motionally narrowed NMR spectrum lacking any fine structure.