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

Abstract

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.

Origins of linewidth in H1 magic-angle spinning NMR

“…20 We and others have previously discussed the significance of this parameter and its quantification from the 1 H NMR spectrum. 12,19 19 A similar level of uncertainty is predicted for these NMR measurements.…”

“…͑4͔͒ could be predicted ab initio. Unfortunately, this is an extremely complex problem, 12 and the empirical relationship between the local coupling strength and the resulting linewidth given by Eq. ͑7͒ is sufficient to provide good estimates of the achievable resolution.…”

“…This limitation can be overcome, at the expense of significantly increased complexity, using Floquet treatments. [11][12][13] In general, however, exact treatments rapidly become intractable once more than two spins are involved. The resulting expressions provide little insight into the factors that determine what the effective 1 H resolution will be for a given sample and set of experimental conditions.…”

Multi-Frequency Resonances in Pure Multiple-Pulse NQR

“…Multiple resonance modes of higher orders have been detected by microwave spectroscopy [6], molecular beam technique [7], optical pumping [8] and observed previously in NMR experiments [9][10][11][12][13]. However the amplitude of these resonances decreased abruptly with the mode order of the resonance.…”

GAVA: Spectral simulation for in vivo MRS applications

“…Despite the increase in available tools, GAMMA has maintained a strong presence in the field due to its flexibility, performance, straightforward elegant design and standard C++ implementation. There have been numerous reports of spectral simulations that have made use of the GAMMA library [3,[8][9][10][11][12][13][14]19,21,22,25,26,30,34,[37][38][39]41,50,51]. However, use of the GAMMA library also requires familiarity with C++ programming and it provides only rudimentary tools for the display, storage and analysis of results.…”