Preprints
https://doi.org/10.5194/mr-2021-45
https://doi.org/10.5194/mr-2021-45

  20 May 2021

20 May 2021

Review status: this preprint is currently under review for the journal MR.

Residual Linewidth in Magic-Angle Spinning Solid-State NMR

Matías Chávez, Thomas Wiegand, Alexander A. Malär, Beat H. Meier, and Matthias Ernst Matías Chávez et al.
  • Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland

Abstract. Magic-angle spinning is routinely used to average anisotropic interactions in solid-state NMR. Due to the fact, that the Hamiltonian of a strongly-coupled spin system does not commute with itself at different time points during the rotation, second-order and higher-order terms lead to a residual line broadening in the observed resonances. Additional truncation of the residual broadening due to isotropic chemical-shift differences can be observed. We analyze the residual line broadening in coupled proton spin systems based on theoretical calculations of effective Hamiltonians up to third order using Floquet theory and compare these results to numerically obtained effective Hamiltonians in small spin systems. We show that at spinning frequencies beyond 50 kHz, second-order terms dominate the residual line width leading to a 1/ωr dependence of the second moment which we use to characterize the line width. However, chemical-shift truncation leads to a partial ωr-2 dependence of the line width which looks as if third-order effective Hamiltonian terms are contributing significantly. We show that second-order contributions not only broaden the line but also lead to a shift of the center of gravity of the line. Experimental data reveals such spinning-frequency dependent line shifts in proton spectra in model substances that can be explained by line shifts induced by the second-order dipolar Hamiltonian.

Matías Chávez et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on mr-2021-45', Anonymous Referee #1, 02 Jun 2021
    • AC1: 'Reply on RC1', Matthias Ernst, 02 Jun 2021
  • RC2: 'Comment on mr-2021-45', Anonymous Referee #2, 04 Jun 2021
    • AC2: 'Reply on RC2', Matthias Ernst, 07 Jun 2021

Matías Chávez et al.

Matías Chávez et al.

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Short summary
Sample rotation around the magic angle averages out the dipolar couplings in homonuclear spin systems in a first-order approximation. However, in higher orders, residual coupling terms remain and lead to a broadening of the spectral lines. We investigate the source of this broadening and the effects on the powder line shape in small spin systems with and without chemical shifts. We show that one can expect different scaling behavior as a function of the spinning frequency for the two cases.