A unified heteronuclear decoupling picture in solid-state NMR under low radio-frequency amplitude and fast magic-angle-spinning frequency regime

Heteronuclear spin decoupling is a highly important component of solid-state NMR experiments to remove undesired coupling interactions between unlike spins for spectral resolution. Recently, experiments using a unification strategy of standard decoupling schemes were presented for high radio-frequency (RF) amplitudes and slow-intermediate magic-angle-spinning (MAS) frequencies, in the pursuit of deeper understanding of spin decoupling under phase-modulated RF irradiation [A. Equbal et al., J. Chem. Phys. 142, 184201 (2015)]. The approach, unified two-pulse heteronuclear decoupling (UTPD), incorporates the simultaneous time- and phase-modulation strategies, commonly used in solid-state NMR. Here, the UTPD based decoupling scheme is extended to the experimentally increasingly important regime of low RF amplitudes and fast MAS frequencies. The unified decoupling approach becomes increasingly effective in identifying the deleterious dipole-dipole and, in particular, J recoupling conditions which become critical for the low-amplitude RF regime. This is because J coupling is isotropic and therefore not averaged out by sample spinning unlike the anisotropic dipole-dipole coupling. Numerical simulations and analytic theory are used to understand the effects of various nuclear spin interactions on the decoupling performance of UTPD, in particular, the crucial difference between the low-phase and high-phase UTPD conditions with respect to J coupling. In the UTPD scheme, when the cycle-frequency of the pulse-sequence is comparable to the RF nutation frequency, the existence of a non-zero effective rotation in the basic two-pulse scheme becomes an essential feature for the efficient and robust averaging out of the scalar J coupling. This broad viewpoint is expected to bring different optimum low-power decoupling pulse schemes under a common footing.