Multiple-quantum dynamics in solid state NMR

Recently developed solid state multiple-quantum NMR methods are applied to extended coupling networks, where direct dipole–dipole interactions can be used to create coherences of very high order (∼100). The progressive development of multiple-quantum coherence over time depends upon the formation of multiple-spin correlations, a phenomenon which also accompanies the normal decay to equilibrium of the free induction signal in a solid. Both the time development and the observed distributions of coherence can be approached statistically, with the spin system described by a time-dependent density operator whose elements are completely uncorrelated at sufficiently long times. With this point of view, we treat the distribution of coherence in a multiple-quantum spectrum as Gaussian, and characterize a spectrum obtained for a given preparation time by its variance. The variance of the distribution is associated roughly with the number of coupled spins effectively interacting, and its steady growth with time reflects the continual expansion of the system under the action of the dipolar interactions. The increase in effective system ‘‘size’’ is accounted for by a random walk model for the time development of the density operator. Experimental results are presented for hexamethylbenzene, adamantane, and squaric acid. The formation of coherence in systems containing physically isolated clusters is also investigated, and a simple method for estimating the number of spins involved is demonstrated.