Multiple-pulse NMR in inhomogeneously broadened rotating solids: Theory of sideband suppression experiments

A detailed analysis of a wide range of magic angle sample spinning (MASS)/multiple-pulse NMR experiments is presented. The analysis depends upon the calculation of the magnetization trajectories of individual crystallites, and thus is valid for inhomogeneously broadened systems. Using this model we examine a variety of experiments used to control and manipulate rotational sidebands in MASS spectra. This model provides a straightforward analysis of both the two and four π pulse experiments used for total suppression of sidebands (TOSS), and allows us to derive new timings for both sequences. We are able to provide the first proof that the TOSS sequence exactly eliminates sidebands, and that the two-pulse sequence eliminates first-order sidebands. We also demonstrate that the TOSS cycle can actually lead to inverted spectra, and we have accurately quantified intensity losses which occur in both the two- and four-pulse versions. The effect of pulse errors on sideband suppression experiments is also briefly discussed, as well as one possible means to reintroduce information about shift anisotropies into TOSS-type experiments.