Calculation of magic-angle spinning nuclear magnetic resonance spectra of paramagnetic solids

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Abstract
This study provides the first quantitative interpretation of the intensity pattern of spinning sidebands observed in the magic‐angle spinning (MAS) NMR spectra of paramagnetic solids. The 200 MHz 1H MAS‐NMR spectrum of copper chloride dihydrate and its deuterated analog are reported. The inhomogeneous interactions predominantly responsible for the sidebands are the magnetic dipolar couplings between the nucleus and the thermally‐averaged magnetic moments due to the unpaired electrons on copper atoms. It is demonstrated that even in the presence of many such couplings to a given nucleus, a g anisotropy of the unpaired electron, and a chemical shift anisotropy of the nucleus, the net inhomogeneous interaction responsible for the sideband intensities is formally equivalent to a chemical shift tensor. However, inhomogeneous dipolar couplings to other nuclei give rise to subspectra corresponding to individual spin states of the other nucleus; the resultant composite spectrum no longer resembles that arising from a chemical shift tensor. The 1H MAS‐NMR spectrum calculated using the known structure of copper chloride dihydrate correctly predicts the overall spectral width and sideband intensity pattern experimentally observed for the deuterated compound, and indicates that the unpaired electron density on the copper atom is partially delocalized (∼15%) onto the neighboring chlorine atoms. Two comparable sources of line broadening in deuterated copper chloride dihydrate are demonstrated to be the magnetic susceptibility anisotropy and T2 relaxation. The isotropic proton chemical shift is shown to be influenced by a small pseudocontact shift (∼10 ppm upfield) and a larger Fermi contact shift (∼76 ppm downfield).