A test for the number of coupled spins I = 1/2 in magic-angle-spinning solids: zero-quantum recoupling of multiple-quantum coherences.

Current methodologies for estimating the number of coupled spins I = 1/2 in solids are based upon the maximum multiple-quantum order that can be observed. This strategy establishes a clear lower bound on the number of coupled spins I = 1/2. However, it is difficult to ascertain the exact number of coupled spins, since the absence of a peak could be due either to the limited size of the spin system or to the experimental difficulty of exciting high-quantum orders and recovering those coherences into detectable signals. Herein, a supplementary test is proposed that allows one to determine whether a given coherence has the highest possible order in the spin system. The sample is subjected to magic-angle spinning and the behaviour of the coherence under a rotor-synchronised spin-echo sequence is compared to its behaviour under a zero-quantum recoupling sequence. A similar decay of the coherence in these two experiments is strong evidence for the coherence order being the maximum possible. We propose applications to biomolecular solid-state NMR spectroscopy.