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

Recent interest has focused on solid-state NMR experiments which excite mul tiple-quantum (MQ) coherences in the presence of magic-angle spinning (MAS) . Such experiments have been applied to both dipolar-coupled spin I = 1/2 a nd 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 quadru polar interaction caused by the change in the Hamiltonian active during the MQ reconversion period relative to the excitation period (reconversion rot or encoding, RRE); and, second, rotor modulation of the interaction during the evolution of the MQ coherences in the tl dimension (evolution rotor mod ulation, ERM). Only the first mechanism is present for total spin coherence s, while for lower-order MQ coherences both mechanisms contribute to the pa ttern. For dipolar and quadrupolar model systems, i.e., the three protons o f a methyl group and quadrupolar nuclei with spin I = 3/2 and I = 5/2 and a xially symmetric first-order quadrupolar interactions, analytical expressio ns are derived for all orders of MQ MAS signals. Simulations based on these analytical expressions and numerical density matrix simulations are compar ed with experimental spectra. Additional perturbing influences, such as the heteronuclear dipolar coupling between a quadrupolar and a spin I=1/2 nucl eus, are taken into account. The effect of dipolar couplings on a quadrupol ar MQ spectrum is found to be enhanced by the order of the observed MQ cohe rence.