Essential Tools of Linear Algebra for Calculating Nuclear Spin Dynamics of Chemically Exchanging Systems

In this work, we describe essential tools of linear algebra necessary for calculating the effect of chemical exchange on spin dynamics and polarization transfer in various nuclear magnetic resonance (NMR) experiments. We show how to construct Hamiltonian, relaxation, and chemical exchange superoperators in the Liouville space, as well as demonstrate corresponding code in Python. Examples of applying the code are given for problems involving chemical exchange between NH3 and NH4+ at zero and high magnetic field and polarization transfer from parahydrogen relevant in SABRE (signal amplification by reversible exchange) at low magnetic field (0-20 mT). The presented methodology finds utility for describing the effect of chemical exchange on NMR spectra and can be extended further by taking into account non-linearities in the master equation

Visualization of dynamics in coupled multi-spin systems

Since the dawn of quantum mechanics, ways to visualize spins and their interactions have attracted the attention of researchers and philosophers of science. In this work we present a generalized measurement-based 3D-visualization approach for describing dynamics in strongly coupled spin ensembles. The approach brings together angular momentum probability surfaces (AMPS), Husimi Q functions, and DROPS (discrete representations of operators for spin systems) and finds particular utility when the total angular momentum basis is used for describing Hamiltonians. We show that, depending on the choice of a generalized measurement operator, the plotted surfaces either represent probabilities of finding the maximal projection of an angular momentum along any direction in space or represent measurable coherences between the states with different total angular momenta. Such effects are difficult to grasp by looking at (time-dependent) numerical values of density-matrix elements. The approach is complete in a sense that there is one-to-one correspondence between the plotted surfaces and the density matrix. Three examples of nuclear spin dynamics in two-spin systems are visualized: (i) a zero- to ultralow-field (ZULF) nuclear magnetic resonance (NMR) experiment in the presence of a magnetic field applied perpendicularly to the sensitive axis of the detector, (ii) interplay between chemical exchange and spin dynamics during high-field signal amplification by reversible exchange (SABRE), and (iii) a high-field spin-lock-induced crossing (SLIC) sequence, with the initial state being the singlet state between two spins. The presented visualization technique facilitates intuitive understanding of spin dynamics during complex experiments as exemplified here by the considered cases. Temporal sequences (“the movies”) of such surfaces show phenomena like interconversion of spin order between the coupled spins and are particularly relevant in ZULF NMR

Proton relaxometry of tree leaves at hypogeomagnetic fields

We report on a cross-species proton-relaxometry study in ex vivo tree leaves using nuclear magnetic resonance (NMR) at 7µT. Apart from the intrinsic interest of probing nuclear-spin relaxation in biological tissues at magnetic fields below Earth field, our setup enables comparative analysis of plant water dynamics without the use of expensive commercial spectrometers. In this work, we focus on leaves from common Eurasian evergreen and deciduous tree families: Pinaceae (pine, spruce), Taxaceae (yew), Betulaceae (hazel), Prunus (cherry), and Fagaceae (beech, oak). Using a nondestructive protocol, we measure their effective proton T2 relaxation times as well as track the evolution of water content associated with leaf dehydration. Newly developed “gradiometric quadrature” detection and data-processing techniques are applied in order to increase the signal-to-noise ratio (SNR) of the relatively weak measured signals. We find that while measured relaxation times do not vary significantly among tree genera, they tend to increase as leaves dehydrate. Such experimental modalities may have particular relevance for future drought-stress research in ecology, agriculture, and space exploration

13^{13}C and 15^{15}N benchtop NMR detection of metabolites via relayed hyperpolarization

Parahydrogen-based nuclear spin hyperpolarization allows various magnetic-resonance applications, and it is particularly attractive because of its technical simplicity, low cost, and ability to quickly (in seconds) produce large volumes of hyperpolarized material. Although many parahydrogen-based techniques have emerged, some of them remain unexplored due to the lack of careful optimization studies. In this work, we investigate and optimize a novel parahydrogen-induced polarization (PHIP) technique that relies on proton exchange referred to below as PHIP-relay. An INEPT (insensitive nuclei enhanced by polarization transfer) sequence is employed to transfer polarization from hyperpolarized protons to heteronuclei ($^{15}$N and $^{13}$C) and nuclear signals are detected using benchtop NMR spectrometers (1 T and 1.4 T, respectively). We demonstrate the applicability of the PHIP-relay technique for hyperpolarization of a wide range of biochemicals by examining such key metabolites as urea, ammonium, glucose, amino acid glycine, and a drug precursor benzamide. By optimizing chemical and NMR parameters of the PHIP-relay, we achieve a 17,100-fold enhancement of $^{15}$N signal of [$^{13}$C, $^{15}$N$_{2}$]-urea compared to the thermal signal measured at 1 T. We also show that repeated measurements with shorter exposure to parahydrogen provide a higher effective signal-to-noise ratio compared to longer parahydrogen bubbling

Theoretical description of hyperpolarization formation in the SABRE-relay method

SABRE (Signal Amplification By Reversible Exchange) has become a widely used method for hyper-polarizing nuclear spins, thereby enhancing their Nuclear Magnetic Resonance (NMR) signals by orders of magnitude. In SABRE experiments, the non-equilibrium spin order is transferred from parahydrogen to a substrate in a transient organometallic complex. The applicability of SABRE is expanded by the methodology of SABRE-relay in which polarization can be relayed to a second substrate either by direct chemical exchange of hyperpolarized nuclei or by polarization transfer between two substrates in a second organometallic complex. To understand the mechanism of the polarization transfer and study the transfer efficiency, we propose a theoretical approach to SABRE-relay, which can treat both spin dynamics and chemical kinetics as well as the interplay between them. The approach is based on a set of equations for the spin density matrices of the spin systems involved (i.e., SABRE substrates and complexes), which can be solved numerically. Using this method, we perform a detailed study of polarization formation and analyze in detail the dependence of the attainable polarization level on various chemical kinetic and spin dynamic parameters. We foresee the applications of the present approach for optimizing SABRE-relay experiments with the ultimate goal of achieving maximal NMR signal enhancements for substrates of interest

Towards large-scale steady-state enhanced nuclear magnetization with in situ detection

Signal amplification by reversible exchange (SABRE) boosts NMR signals of various nuclei enabling new applications spanning from magnetic resonance imaging to analytical chemistry and fundamental physics. SABRE is especially well positioned for continuous generation of enhanced magnetization on a large scale; however, several challenges need to be addressed for accomplishing this goal. Specifically, SABRE requires (i) a specialized catalyst capable of reversible H2 activation and (ii) physical transfer of the sample from the point of magnetization generation to the point of detection (e.g., a high-field or a benchtop nuclear magnetic resonance [NMR] spectrometer). Moreover, (iii) continuous parahydrogen bubbling accelerates solvent (e.g., methanol) evaporation, thereby limiting the experimental window to tens of minutes per sample. In this work, we demonstrate a strategy to rapidly generate the best-to-date precatalyst (a compound that is chemically modified in the course of the reaction to yield the catalyst) for SABRE, [Ir(IMes)(COD)Cl] (IMes = 1,3-bis-[2,4,6-trimethylphenyl]-imidazol-2-ylidene; COD = cyclooctadiene) via a highly accessible synthesis. Second, we measure hyperpolarized samples using a home-built zero-field NMR spectrometer and study the field dependence of hyperpolarization directly in the detection apparatus, eliminating the need to physically move the sample during the experiment. Finally, we prolong the measurement time and reduce evaporation by presaturating parahydrogen with the solvent vapor before bubbling into the sample. These advancements extend opportunities for exploring SABRE hyperpolarization by researchers from various fields and pave the way to producing large quantities of hyperpolarized material for long-lasting detection of SABRE-derived nuclear magnetization

Zero-Field J-spectroscopy of Quadrupolar Nuclei

Zero- to ultralow-field (ZULF) nuclear magnetic resonance (NMR) is a version of NMR that allows studying molecules and their transformations in the regime dominated by intrinsic spin-spin interactions. While spin dynamics at zero magnetic field can be probed indirectly, J-spectra can also be measured at zero field by using non-inductive sensors, for example, optically-pumped magnetometers (OPMs). A J-spectrum can be detected when a molecule contains at least two different types of magnetic nuclei (i.e., nuclei with different gyromagnetic ratios) that are coupled via J-coupling. Up to date, no pure J-spectra of molecules featuring the coupling to quadrupolar nuclei were reported. Here we show that zero-field J-spectra can be collected from molecules containing quadrupolar nuclei with I = 1 and demonstrate this for solutions containing various isotopologues of ammonium cations. Lower ZULF NMR signals are observed for molecules containing larger numbers of deuterons compared to protons; this is attributed to less overall magnetization and not to the scalar relaxation of the second kind. We analyze the energy structure and allowed transitions for the studied molecular cations in detail using perturbation theory and demonstrate that in the studied systems, different lines in J-spectra have different dependencies on the magnetic pulse length allowing for unique on-demand zero-field spectral editing. Precise values for the 15N-1H, 14N-1H, and D-1H coupling constants are extracted from the spectra and the difference in the reduced coupling constants is explained by the secondary isotope effect. Simple symmetric cations such as ammonium do not require expensive isotopic labeling for the observation of J-spectra and, thus, may expand applicability of ZULF NMR spectroscopy in biomedicine and energy storage.Comment: 39 pages, 5 figure

Possible Applications of Dissolution Dynamic Nuclear Polarization in Conjunction with Zero- to Ultralow-Field Nuclear Magnetic Resonance

The combination of a powerful and broadly applicable nuclear hyperpolarization technique with emerging (near-)zero-field modalities offer novel opportunities in a broad range of nuclear magnetic resonance spectroscopy and imaging applications, including biomedical diagnostics, monitoring catalytic reactions within metal reactors and many others. These are discussed along with a roadmap for future developments.Comment: 12 pages, 5 figure

Zero-field nuclear magnetic resonance of chemically exchanging systems.

Zero- to ultralow-field (ZULF) nuclear magnetic resonance (NMR) is an emerging tool for precision chemical analysis. In this work, we study dynamic processes and investigate the influence of chemical exchange on ZULF NMR J-spectra. We develop a computational approach that allows quantitative calculation of J-spectra in the presence of chemical exchange and apply it to study aqueous solutions of [15N]ammonium (15N[Formula: see text]) as a model system. We show that pH-dependent chemical exchange substantially affects the J-spectra and, in some cases, can lead to degradation and complete disappearance of the spectral features. To demonstrate potential applications of ZULF NMR for chemistry and biomedicine, we show a ZULF NMR spectrum of [2-13C]pyruvic acid hyperpolarized via dissolution dynamic nuclear polarization (dDNP). We foresee applications of affordable and scalable ZULF NMR coupled with hyperpolarization to study chemical exchange phenomena in vivo and in situations where high-field NMR detection is not possible to implement