Exact simulation of multiple-quantum dynamics in solid-state NMR: implications for spin counting

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Abstract
Multiple-quantum NMR has recently been shown to be an effective method for measuring the sizes of spin clusters in solids, with initial applications reported for hydrogenated amorphous silicon, zeolites and surface-bound species. The present analysis traces the time development of multiple-quantum coherence in polycrystalline materials containing clusters of two to five spin-½ nuclei. Numerical solutions to the Liouville-von Neumann equation are given for a series of different configurations in order to gauge the dependence of the coherence magnitudes on the geometry of the cluster, and to follow the simplification and damping of the macroscopic signal. Exact coherence magnitudes after prolonged excitation are compared with those predicted by statistical models, and found to differ significantly for most of the small polycrystalline systems.