Two-dimensional nuclear magnetic resonance in rotating solids: An analysis of line shapes in chemical shift-dipolar spectra

Magic angle sample spinning is combined with two-dimensional NMR methods to obtain high resolution chemical shift-dipolar spectra. Because both interactions are inhomogeneous, the 2D spectrum consists of a set of rotational sidebands spaced at the spinning frequency in each dimension. Projection of these sidebands onto the chemical shift or dipolar axis yields either the chemical shift or the dipolar spectrum fully separated from the other interaction. The projections may be used to extract the principal values of either the chemical shift or dipolar tensor, and from the latter, internuclear distances may be calculated. In addition, it is shown that sets of dipolar sidebands, corresponding to individual chemical shift sidebands, exhibit some unusual features. In particular, in the slow spinning regime, the dipolar rotational sideband patterns are asymmetric and in some instances, individual sidebands are inverted. The physical origin of this effect is discussed, and experimental results and computer simulations are in excellent agreement. Finally, it is shown that the intensity distribution of the sidebands permits a determination of the relative orientation of the shift and dipolar tensors.