Residual dipolar line width in magic-angle spinning proton solid-state NMR

Abstract. Magic-angle spinning is routinely used to average anisotropic interactions in solid-state nuclear magnetic resonance (NMR). Due the fact that homonuclear dipolar Hamiltonian of a strongly coupled spin system does not commute with itself at different time points during rotation, second-order and higher-order terms lead residual line broadening observed resonances. Additional truncation due isotropic chemical-shift differences can be observed. We analyze proton systems based on theoretical calculations effective Hamiltonians up third order using Floquet theory compare these results numerically obtained small systems. show frequencies beyond 75 kHz, dominate width, leading 1/?r dependence second moment which we use characterize width. However, leads partial ?r-2 width looks as if third-order are contributing significantly. At slower frequencies, cross between chemical shift coupling contribute Hamiltonians. contributions only broaden line, but also center gravity line. Experimental data reveal such spinning-frequency-dependent shifts spectra model substances explained by induced Hamiltonian.