Residual proton line width under refocused frequency-switched Lee-Goldburg decoupling in MAS NMR

Despite many decades of research, homonuclear decoupling in solid-state NMR under magic-angle spinning (MAS) has yet to reach a point where the achievable proton line widths become comparable to the resolution obtained in solution-state NMR. This makes the precise determination of isotropic chemical shifts difficult and thus presents a limiting factor in the application of proton solid-state NMR to biomolecules and small molecules. In this publication we analyze the sources of the residual line width in refocused homonuclear-decoupled spectra in detail by comparing numerical simulations and experimental data. Using a hybrid analytical/numerical approach based on Floquet theory, we find that third-order effective Hamiltonian terms are required to realistically characterize the line shape and line width under frequency-switched Lee-Goldburg (FSLG) decoupling under MAS. Increasing the radio-frequency field amplitude enhances the influence of experimental rf imperfections such as pulse transients and the MAS-modulated radial rf-field inhomogeneity. While second- and third-order terms are, as expected, reduced in size at higher rf-field amplitudes, the line width becomes dominated by first-order terms which severely limits the achievable line width. We expect, therefore, that significant improvements in the line width of FSLG-decoupled spectra can only be achieved by reducing the influence of MAS-modulated rf-field inhomogeneity and pulse transients.