Spinning-sideband patterns in multiple-quantum magic-angle spinning NMR spectroscopy

Recent interest has focused on solid-state NMR experiments which excite multiple-quantum (MQ) coherences in the presence of magic-angle spinning (MAS). Such experiments have been applied to both dipolar-coupled spin I = 1/2 and half-integer quadrupolar systems. A feature common to both cases is the observation of interesting spinning sideband patterns in the indirect (MQ) dimension. In this paper, the origin of these patterns is reviewed in terms of two distinct mechanisms: first, rotor encoding of the dipolar or quadrupolar interaction caused by the change in the Hamiltonian active during the MQ reconversion period relative to the excitation period (reconversion rotor encoding, RRE); and, second, rotor modulation of the interaction during the evolution of the MQ coherences in the tl dimension (evolution rotor modulation, ERM). Only the first mechanism is present for total spin coherences, while for lower-order MQ coherences both mechanisms contribute to the pattern. For dipolar and quadrupolar model systems, i.e., the three protons of a methyl group and quadrupolar nuclei with spin I = 3/2 and I = 5/2 and axially symmetric first-order quadrupolar interactions, analytical expressions are derived for all orders of MQ MAS signals. Simulations based on these analytical expressions and numerical density matrix simulations are compared with experimental spectra. Additional perturbing influences, such as the heteronuclear dipolar coupling between a quadrupolar and a spin I=1/2 nucleus, are taken into account. The effect of dipolar couplings on a quadrupolar MQ spectrum is found to be enhanced by the order of the observed MQ coherence.