Origins of linewidth in $H1$ magic-angle spinning NMR

A detailed study of the factors determining the linewidth (and hence resolution) in $H1$ solid-state magic-angle spinning NMR is described. Although it has been known from the early days of magic-angle spinning (MAS) that resolution of spectra from abundant nuclear spins, such as $H1$⁠, increases approximately linearly with increasing sample rotation rate, the difficulty of describing the dynamics of extended networks of coupled spins has made it difficult to predict a priori the resolution expected for a given sample. Using recently developed, highly efficient methods of numerical simulation, together with experimental measurements on a variety of test systems, we propose a comprehensive picture of $H1$ resolution under MAS. The “homogeneous” component of the linewidth is shown to depend primarily on the ratio between an effective local coupling strength and the spin rate, modified by geometrical factors which loosely correspond to the “dimensionality” of the coupling network. The remaining “inhomogeneous” component of the natural linewidth is confirmed to have the same properties as in dilute-spin NMR. Variations in the NMR frequency due to chemical shift effects are shown to have minimal impact on $H1$ resolution. The implications of these results for solid-state NMR experiments involving $H1$ and other abundant-spin nuclei are discussed.