| 02 Apr 2026
Optimally controlled NMR in electrochemistry: Larmor and nutation frequency selective spin excitation for locally selective NMR experiments
Abstract. Spectroelectrochemical nuclear magnetic resonance (NMR) experiments are faced with numerous challenges originating from shielding effects and susceptibility gradients in samples, leading to inhomogeneous static magnetic fields B0 and radio frequency (rf) fields B1. Moreover, magnetic feedback caused by eddy currents in conductors can obstruct precise measurements. Previous works have shown that these eddy current induced magnetic field distortions can be accurately predicted by finite element method (FEM) simulations. In this work, we present a workflow combining FEM predictions with quantum optimal control (QOC) to tailor custom NMR pulses that exploit specific magnetic field distortions for selective excitation of affected sample regions. The desired selectivity was achieved using pattern pulses optimized for a particular B1 or Larmor frequency ν0. Experimental validation was performed on a heterogeneous phantom consisting of two cavities filled with two spectroscopically distinguishable liquids, one between copper disks to mimic an electrochemical cell, and one between polymer disks as reference. An over 30-fold suppression of the reference resonance in between polymer compared to the resonance in between copper disks was achieved, demonstrating how QOC-tailored pulses can selectively address FEM-predicted B1 distortions to achieve spatial selectivity. It was also demonstrated how QOC-tailored pulses can selectively excite specific ν0 despite of B0 distortions, which implies that difficulties with conventional solvent suppression techniques in electrochemical setups can be mitigated using the adjustable robustness of QOC-tailored pulses. The presented approach sets the stage for gradient-free, localized in operando NMR in electrochemistry and material sciences, with the prospect of surface selectivity down to the detection limit of the setup.
The paper describes the use of OC generated selective pulses in frequency and nutation space for use in electrochemical cells. It demonstrates the performance of such pulses on a phantom sample containing two different liquids between copper plates and PEEK plates. The two lines are clearly shifted in frequency space and also in the nutation space. I think the paper is suitable for MR but the presentation is sometimes confusing and should be improved.
I am not an expert on OC pulses so I cannot judge how demanding the generation of such pulses is. My impression is that this is quite standard and that the application to electrochemical problems is the new part. My expectation from the title and the first reading och Chapter 2.1, I expected the pulses to be simultaneously selective in frequency and nutation space. The title says "Larmor and nutation frequency selective pulses". After a more carefull reading, I think now that these are frequency selective pulses that are tolerant to deviations in the nutation frequency and nutation selective pulses that are insensitive to changes in the resonance frequency. If this is correct, I think this should be made clearer in phrasing of the title and the text. Later on, the paper always talks about B_0 selective or nutation-frequency selective pulses. I just realized that the phrasing in the SI is much clearer: "B1-robust selective excitation within ±500 Hz in a ±2000 Hz suppression band" and "Larmor frequency-robust selective excitation for 0 % artificial nutation frequency increase". It woould be nice if the phrasing in the main text and title would reflect that precision of the SI. By the way, I think the use of the term "B_0 selective" pulses is not a good choice since B_0 by definition is the same everywhere. I think it would be good to use a different term here like resonance frequency selective pulses.
I was wondering how much the improvement of these pulses are compared to "standard" frequency band selective pulses like BURP pulses (H. Geen, R. Freeman, J. Magn. Reson. 93 (1991) 93–141) or nutation-frequency selective pulses in the rotating frame (K. Aebischer, N. Wili, Z. Tosner, M. Ernst, Magn. Reson. 1 (2020) 187–195) that also have some inherent nutation or frequency frequency bandwidth. Can the authors comment, please, how important the simultaneous optimization for both parameters is for this application?
A second more general point is the use of the term "quantum optimal control" for the generation of the pulses. What is "quantum" about the optimal control methods used to generate pulses on a classical computer? I realize that "quantum" is very trendy and sells well but I really think that "optimal control" would be sufficient here.
The presentation of the results in Figs. 3 and 4 using double color coding of the spectra and the background is not easy to understand and interpret. Would it not be much simpler to plot the theoretical excitation profile over the spectra with a little arrow or dot indicating the irradiation frequency. What is especially grating is the fact that the color coding on the right goes to -1 but is in reality never smaller than 0.
minor points:
Fig. 2 and text: Why use ppm for the frequency axis if the ppm are meaningless. I think here a Hz scale would be much more meaningful since also the selectivity of the pulses was specified in Hz. (applies also to Figs. 3,4 and 7)
Fig. 2: Add a z scale to the drawing on the left to make the mapping from the drawing to the plot of the spectra clearer. Maybe even scale the drawing and the spectral plot such that the scale is the same.
Maybe Figures 1 and 2 could be combined in a singel figure that contains all the details.