The effect of methyl group rotation on ¹H-¹H solid-state NMR spin-diffusion spectra

Fast magic-angle spinning (MAS) NMR experiments open the way for proton-detected NMR studies and have been explored in the past years for a broad range of materials, comprising biomolecules and pharmaceuticals. Proton-spin diffusion (SD) is a versatile polarization-transfer mechanism and plays an important role in resonance assignment and structure determination. Recently, the occurrence of negative cross peaks in 2D ¹H-¹H SD-based spectra has been reported and explained with higher-order SD effects, in which the chemical shifts of the involved quadruple of nuclei need to compensate each other. We herein report negative cross peaks in SD-based spectra observed for a variety of small organic molecules involving methyl groups. We combine experimental observations with numerical and analytical simulations to demonstrate that the methyl groups can give rise to coherent (SD) as well as incoherent (Nuclear Overhauser Enhancement, NOE) effects, both in principle manifesting themselves as negative cross peaks in the 2D spectra. Analytical calculations and simulations however show that higher-order coherent contributions dominate the experimentally observed negative peaks in our systems. Methyl groups are prone to the observation of such higher order coherent effects. Due to their low-frequency shifted ¹H resonances, the chemical-shift separation relative to for instance aromatic protons in spatial proximity is substantial (>4.7 ppm in the studied examples) preventing any sizeable second-order spin-diffusion processes, which would mask the negative contribution to the peaks.