Solid-state nuclear magnetic resonance spectra of dipolar-coupled multi-spin systems under fast magic angle spinning

A general treatment of nuclear magnetic resonance (NMR) spectra under magic-angle spinning (MAS) conditions is provided that is applicable both to homogeneously and inhomogeneously broadened lines. It is based on a combination of Floquet theory and perturbation theory, and allows the factorization of the spin system response into three factors that describe different aspects of the resulting MAS spectrum. The first factor directly reflects the Floquet theorem and describes the appearance of sidebands. The other two terms give the integral intensities of the resulting sidebands and their line shapes and depend on the specific features of the considered interaction. The analytical form of these two factors is derived for multi-spin dipolar interactions under fast MAS. The leading term in the expansion of the integral intensities involves products of only two spin operators whereas the linewidths, which are found to be different for the different sideband orders, are determined predominantly by three-spin te...