Spectroelectrochemical nuclear magnetic resonance (NMR) experiments are faced with numerous challenges originating from shielding effects and susceptibility gradients in samples, leading to inhomogeneities in the static magnetic fields B0 and the 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 either 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 a 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 in the vicinity of electrical conductors to achieve spatial selectivity with simultaneous ν0 robustness. It was also demonstrated how QOC-tailored pulses can selectively excite specific ν0 despite 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 segmented-overlap Fourier filtering and averaging (SOFFA) data acquisition method is described in detail for magnetic resonance spectroscopy. In this work, the four processes that encompass the SOFFA data acquisition method are detailed: (i) oversampling spectral segments, (ii) Fourier block-filtering, (iii) segment-overlap averaging, and (iv) decimation. Three experimental examples are shown: first, conventional continuous-wave (CW) electron paramagnetic resonance (EPR) is compared to SOFFA-CW of a single reduced [4Fe-4S]+ (S=1/2) at concentrations of 1 mM, 100 µM, and 10 µM, showing an average increase in concentration sensitivity by a factor of 5.6 in a 100 min measurement time. Second, an experimental comparison of CW and SOFFA non-adiabatic rapid-scan (SOFFA-NARS) data with similar filter parameters and field modulation amplitude demonstrates a factor of 10.3 in signal-to-noise (SNR) improvement (32 min measurement time) for a 150 µM site-directed spin-labeled hemoglobin in 82 % glycerol at 18 °C. Finally, an SNR-matched experiment of free TEMPO at 10 µM concentration is presented, where CW was performed at 400 scans (273 min) compared to SOFFA-CW with an overlap factor of 100 (20 min). Also shown is the effect of 1/f noise on these CW and SOFFA-CW experiments. Ultimately, the SOFFA algorithm achieves sensitivity enhancement by combining massive digital oversampling and out-of-band noise filtration with coherent spatial accumulation of highly overlapped spectral segments. The gains reported here are phenomenological and are grounded in established digital signal processing principles but are validated through experiments rather than closed-form analytical prediction. This fundamental restructuring of the acquisition chain successfully decouples high-frequency filtering from low-frequency averaging while providing a data collection scheme that suppresses 1/f noise. The SOFFA method can be implemented to perform real-time segmented processing and, combined with more sophisticated averaging methods, will push the state-of-the-art sensitivity in magnetic resonance spectroscopy.
Long-lived states (LLSs) can be excited in geminal protons of aliphatic chains by mono- or poly-chromatic spin-lock-induced crossings (SLICs), i.e., by application of one or more selective radio frequency (RF) fields, to create delocalized population imbalances between states belonging to different symmetry under spin permutations. At low fields (in this work at 1.4 T or 60 MHz for proton NMR), these experiments are challenging due to the proximity of the chemical shifts and the need to consider the full untruncated J -coupling Hamiltonian. Five molecules were studied in this work: ethanolamine, lysine, vitamin B1, metronidazole, and phenoxyethylamine (POEA). For POEA and metronidazole, the LLSs are reported for the first time. Measurements were carried out at low and high magnetic fields (1.4 and 11.7 T or 60 and 500 MHz for protons) using 60 MHz Magritek and 500 MHz Bruker NEO spectrometers. The rates R LLS = 1 / T LLS and R 1 = 1 / T 1 were determined using monochromatic SLIC excitation at both fields. We describe strategies for optimizing SLIC conditions in cases where the signals of neighboring CH2 groups are relatively close to each other.
Bilinear rotations imply differing rotations on a spin I depending on the presence or absence of a bilinear coupling Hamiltonian in connection to a heteronucleus S. As such, spin system selective inversions using BIRD elements, excitations using TANGO, or general (effective) rotations using BANGO and/or BIG-BIRD, as well as multiplicity-edited rotations, are achievable. So far, the well-defined rotations were only imposed on a single spin, e.g., I, while the coupled heteronucleus experienced only an inversion or no rotation at all. Here, we introduce dual bilinear rotations that simultaneously allow spin system selective manipulations on both spins I and S as compared to the coupled spin system IS. Particularly with the advent of multi-receive experiments and/or super-sequences with the necessity of exciting and storing specific spin systems in a flexible way, this may open new possibilities in pulse sequence design. A general derivation of the approach is given, and a quadruple-J-resolved-type experiment for obtaining fully decoupled spectra optimized for different spin systems is introduced for demonstration.
This work presents a theoretical framework for quantitative, scalable modeling of signal amplification by reversible exchange (SABRE) experiments under zero- and ultralow-field (ZULF) conditions. SABRE exploits the singlet spin order of parahydrogen to hyperpolarize nuclear spins of substrates without chemical modification, enhancing NMR signals. In the ZULF SABRE method, polarization transfer occurs in ultralow magnetic fields where Zeeman interactions are comparable to or weaker than scalar couplings, enabling coherent mixing of spin states and revealing interactions often suppressed at high fields. Our approach captures the full quantum dynamics of SABRE, including coherent evolution, chemical exchange, and relaxation, within a Liouville space formalism. We demonstrate that the Hamiltonian, relaxation, and exchange superoperators possess symmetry with respect to the total spin, allowing the dynamics to be rigorously restricted to the zero-quantum coherence subspace. This symmetry-based reduction yields a scalable framework for efficient simulation of multi-spin SABRE systems, allowing the treatment of arbitrary spin ensembles, including those containing 15N, 13C, 1H, and other nuclei. The approach is validated against full Liouville space calculations for small systems and is further applied to a 14-spin SABRE complex, demonstrating its ability to treat spin systems of a complexity well beyond the reach of conventional full Liouville space simulations. The framework thus provides a predictive tool for optimal polarization fields, ZULF NMR spectra, and the design of novel hyperpolarization experiments.
