Unexpected effects of third-order cross-terms in heteronuclear spin systems under simultaneous radio-frequency irradiation and magic-angle spinning NMR

We recently noted [R. K. Harris, P. Hodgkinson, V. Zorin, J.-N. Dumez, B. Elena, L. Emsley, E. Salager, and R. Stein, Magn. Reson. Chem. 48, S103 (2010)] anomalous shifts in apparent (1)H chemical shifts in experiments using (1)H homonuclear decoupling sequences to acquire high-resolution (1)H NMR spectra for organic solids under magic-angle spinning (MAS). Analogous effects were also observed in numerical simulations of model (13)C,(1)H spin systems under homonuclear decoupling and involving large (13)C,(1)H dipolar couplings. While the heteronuclear coupling is generally assumed to be efficiently suppressed by sample spinning at the magic angle, we show that under conditions typically used in solid-state NMR, there is a significant third-order cross-term from this coupling under the conditions of simultaneous MAS and homonuclear decoupling for spins directly bonded to (1)H. This term, which is of the order of 100 Hz under typical conditions, explains the anomalous behaviour observed on both (1)H and (13)C spins, including the fast dephasing observed in (13)C{(1)H} heteronuclear spin-echo experiments under (1)H homonuclear decoupling. Strategies for minimising the impact of this effect are also discussed.