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 hom ogeneously and inhomogeneously broadened lines. It is based on a combinatio n of Floquet theory and perturbation theory, and allows the factorization o f the spin system response into three factors that describe different aspec ts of the resulting MAS spectrum. The first factor directly reflects the Fl oquet theorem and describes the appearance of sidebands, The other two term s give the integral intensities of the resulting sidebands and their line s hapes and depend on the specific features of the considered interaction. Th e analytical form of these two factors is derived for multi-spin dipolar in teractions under fast MAS. The leading term in the expansion of the integra l intensities involves products of only two spin operators whereas the line widths, which are found to be different for the different sideband orders, are determined predominantly by three-spin terms. The higher-spin contribut ions in both cases scale with increasing powers of the inverse rotor freque ncy and thus becomes less and less important when approaching the limit of fast spinning. From numerical simulations and the analysis of experimental MAS NMR spectra it was found that for typical spin systems, spinning freque ncies of the order of the strongest couplings are sufficient to allow the a nalysis of the sideband intensities within the approximation of two-spin te rms. This scaling of the different contributions together with the strong d istance dependence of the dipolar interaction thus leads to a considerable simplification in the fast spinning limit and provides the basis for using the dipolar interaction in high-resolution MAS spectra to obtain local stru ctural information. (C) 1999 American Institute of Physics. [S0021-9606(98) 00346-8].