Low-power WALTZ decoupling under magic-angle spinning NMR

Heteronuclear low-power decoupling using the solution-state wideband alternating-phase low-power technique for zero-residual splitting (WALTZ) sequences has become quite popular in solid-state protein NMR and seems to work well. However, there are no systematic studies that characterize these sequences under magic-angle spinning (MAS) and give recommendations on which parameter should be used. We have studied in detail the use of WALTZ-16 and WALTZ-64 as low-power decoupling sequences under 100 kHz MAS by characterizing the resonance conditions analytically using numerical simulations and experiments on model substances. The recoupling heteronuclear resonance conditions between the modulation frequency of the sequences and the MAS frequency is the most important feature. Pulse lengths corresponding to areas with vanishing first-order heteronuclear recoupling are good candidates for efficient decoupling. We have characterized two such conditions which can be defined using the nutation frequency of the radio frequency (RF) field ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>ν</mml:mi> <mml:mn>1</mml:mn></mml:msub> </mml:mrow> </mml:math> ) and the spinning frequency ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>ν</mml:mi> <mml:mi>r</mml:mi></mml:msub> </mml:mrow> </mml:math> ) by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>ν</mml:mi> <mml:mn>1</mml:mn></mml:msub> <mml:mo>=</mml:mo> <mml:msub><mml:mi>ν</mml:mi> <mml:mi>r</mml:mi></mml:msub> <mml:mo>/</mml:mo> <mml:mn>10</mml:mn></mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>ν</mml:mi> <mml:mn>1</mml:mn></mml:msub> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> <mml:msub><mml:mi>ν</mml:mi> <mml:mi>r</mml:mi></mml:msub> <mml:mo>/</mml:mo> <mml:mn>5</mml:mn></mml:mrow> </mml:math> , which both lead to narrow lines and are stable against RF-field variations and chemical-shift offsets. More such conditions might exist but were not investigated here.