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Autori: C. Filip, S. Hafner, I. Schnell, D.E. Demco, H.W. Spiess
Editorial: J. Chem. Phys, 110, p.423-440, 1999.
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 terms. The higher-spin contributions in both cases scale
with increasing powers of the inverse rotor frequency 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 frequencies of
the order of the strongest couplings are sufficient to allow the analysis of the sideband intensities
within the approximation of two-spin terms. This scaling of the different contributions together with
the strong distance 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 structural information.
Cuvinte cheie: solid sate NMR, spin dynamics, magic angle spinning