21 Feb 2024
 | 21 Feb 2024
Status: this preprint is currently under review for the journal MR.

Dynamic averaging of anisotropic interactions and its dependence on motional time scales in MAS solid-state NMR

Kathrin Aebischer, Lea Marie Becker, Paul Schanda, and Matthias Ernst

Abstract. Dynamic processes in molecules can occur on a large range of time scales, and it is important to understand which time scales of motion contribute to different parameters used in dynamics measurements. For spin relaxation, this can easily be understood from the sampling of the spectral-density function by different relaxation-rate constants. In addition to data from relaxation measurements, determining dynamically-averaged anisotropic interactions in magic-angle spinning (MAS) solid-state NMR allows better quantification of the amplitude of molecular motion. For partially averaged anisotropic interactions, the relevant time scales of motion are not so clearly defined and whether the averaging depends on the experimental methods (e.g., pulse sequences) or conditions (e.g., MAS frequency, magnitude of anisotropic interaction, rf-field amplitudes) is not fully understood. To investigate these questions, we performed numerical simulations of dynamic systems based on the stochastic Liouville equation using several experiments for recoupling the dipolar-coupling, CSA or quadrupolar coupling. The transition between slow motion, where parameters characterizing the anisotropic interaction are not averaged, and fast motion, where the tensors are averaged leading to a scaled anisotropic quantity, occurs over a window of motional rate constants that depends mainly on the strength of the interaction. This transition region can span two orders of magnitude in exchange-rate constants (typically in the μs range) but depends only marginally on the employed recoupling scheme or sample spinning frequency. Residual couplings in off-magic-angle experiments, however, average over longer time scales of motion. While in principle one may gain information on the time scales of motion from the transition area, extracting such information is hampered by low signal-to-noise ratio in experimental spectra due to fast relaxation that occurs in the same region.

Kathrin Aebischer, Lea Marie Becker, Paul Schanda, and Matthias Ernst

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-2024-4', Kay Saalwächter, 05 Mar 2024
    • AC1: 'Reply on RC1', Matthias Ernst, 06 Mar 2024
      • RC2: 'Reply on AC1', Kay Saalwächter, 08 Mar 2024
        • AC4: 'Reply on RC2', Matthias Ernst, 14 Mar 2024
  • RC3: 'Comment on mr-2024-4', Anonymous Referee #2, 09 Mar 2024
    • AC2: 'Reply on RC3', Matthias Ernst, 12 Mar 2024
  • RC4: 'Comment on mr-2024-4', Anonymous Referee #3, 13 Mar 2024
    • AC3: 'Reply on RC4', Matthias Ernst, 14 Mar 2024
Kathrin Aebischer, Lea Marie Becker, Paul Schanda, and Matthias Ernst
Kathrin Aebischer, Lea Marie Becker, Paul Schanda, and Matthias Ernst


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Short summary
To characterize the amplitude of dynamic processes in molecules, anisotropic parameters can be measured using solid-state NMR. However, it is not clear motions on which time scales lead to such a scaling of the anisotropic interactions. Using numerical simulations in small spin systems we could show that mostly the magnitude of the anisotropic interaction determines the range of time scales detected by the scaled anisotropic interaction and experimental parameters play a very minor role.