High-Resolution Zero-Field NMR J-Spectroscopy of Aromatic Compounds

Low frequency signal detection via correlated Ramsey measurements

The low frequency region of the spectrum is a challenging regime for quantum probes. We support the idea that, in this regime, performing Ramsey measurements carefully controlling the time at which each measurement is initiated is an excellent signal detection strategy. We use the Fisher information to demonstrate a high quality performance in the low frequency regime, compared to more elaborated measurement sequences, and to optimize the correlated Ramsey sequence according to any given experimental parameters, showing that correlated Ramsey rivals with state-of-the-art protocols, and can even outperform commonly employed sequences such as dynamical decoupling in the detection of low frequency signals. Contrary to typical quantum detection protocols for oscillating signals, which require adjusting the time separation between pulses to match the half period of the target signal, and consequently see their scope limited to signals whose period is shorter than the characteristic decoherence time of the probe, or to those protocols whose target is primarily static signals, the time-tagged correlated Ramsey sequence simultaneously tracks the amplitude and the phase information of the target signal, regardless of its frequency, which crucially permits correlating measurements in post-processing, leading to efficient spectral reconstruction.

Zero-field J-spectroscopy of quadrupolar nuclei

Zero- to ultralow-field nuclear magnetic resonance (ZULF NMR) allows molecular structure elucidation via measurement of electron-mediated spin-spin J-couplings. This study examines zero-field J-spectra from molecules with quadrupolar nuclei, exemplified by solutions of various isotopologues of ammonium cations. The spectra reveal differences between various isotopologues upon extracting precise J-coupling values from pulse-acquire measurements. A primary isotope effect, △ J = γ 14 N / γ 15 N J 15 N H - J 14 N H ≈ - 58 mHz, is deduced by analysis of the proton-nitrogen J-coupling ratios. This study points toward further experiments with symmetric cations containing quadrupolar nuclei, promising applications in biomedicine, energy storage, and benchmarking quantum chemistry calculations.

Enzymatic Reactions Observed with Zero- and Low-Field Nuclear Magnetic Resonance

We demonstrate that enzyme-catalyzed reactions can be observed in zero- and low-field NMR experiments by combining recent advances in parahydrogen-based hyperpolarization methods with state-of-the-art magnetometry. Specifically, we investigated two model biological processes: the conversion of fumarate into malate, which is used in vivo as a marker of cell necrosis, and the conversion of pyruvate into lactate, which is the most widely studied metabolic process in hyperpolarization-enhanced imaging. In addition to this, we constructed a microfluidic zero-field NMR setup to perform experiments on microliter-scale samples of [1-13C]fumarate in a lab-on-a-chip device. Zero- to ultralow-field (ZULF) NMR has two key advantages over high-field NMR: the signals can pass through conductive materials (e.g., metals), and line broadening from sample heterogeneity is negligible. To date, the use of ZULF NMR for process monitoring has been limited to studying hydrogenation reactions. In this work, we demonstrate this emerging analytical technique for more general reaction monitoring and compare zero- vs low-field detection.

Detection of pyridine derivatives by SABRE hyperpolarization at zero field

Nuclear magnetic resonance (NMR) spectroscopy is a powerful analytical tool used in modern science and technology. Its novel incarnation, based on measurements of NMR signals without external magnetic fields, provides direct access to intramolecular interactions based on heteronuclear scalar J-coupling. The uniqueness of these interactions makes each zero-field NMR spectrum distinct and useful in chemical fingerprinting. However, the necessity of heteronuclear coupling often results in weak signals due to the low abundance of certain nuclei (e.g., ¹⁵N). Hyperpolarization of such compounds may solve the problem. In this work, we investigate molecules with natural isotopic abundance that are polarized using non-hydrogenative parahydrogen-induced polarization. We demonstrate that spectra of hyperpolarized naturally abundant pyridine derivatives can be observed and uniquely identified whether the same substituent is placed at a different position of the pyridine ring or different constituents are placed at the same position. To do so, we constructed an experimental system using a home-built nitrogen vapor condenser, which allows for consistent long-term measurements, crucial for identifying naturally abundant hyperpolarized molecules at a concentration level of ~1 mM. This opens avenues for future chemical detection of naturally abundant compounds using zero-field NMR.

Zero- to Ultralow-Field Nuclear Magnetic Resonance Enhanced with Dissolution Dynamic Nuclear Polarization

Zero- to ultralow-field nuclear magnetic resonance is a modality of magnetic resonance experiment which does not require strong superconducting magnets. Contrary to conventional high-field nuclear magnetic resonance, it has the advantage of allowing high-resolution detection of nuclear magnetism through metal as well as within heterogeneous media. To achieve high sensitivity, it is common to couple zero-field nuclear magnetic resonance with hyperpolarization techniques. To date, the most common technique is parahydrogen-induced polarization, which is only compatible with a small number of compounds. In this article, we establish dissolution dynamic nuclear polarization as a versatile method to enhance signals in zero-field nuclear magnetic resonance experiments on sample mixtures of [¹³C]sodium formate, [1-¹³C]glycine, and [2-¹³C]sodium acetate, and our technique is immediately extendable to a broad range of molecules with >1 s relaxation times. We find signal enhancements of up to 11,000 compared with thermal prepolarization in a 2 T permanent magnet. To increase the signal in future experiments, we investigate the relaxation effects of the TEMPOL radicals used for the hyperpolarization process at zero- and ultralow-fields.

Detection of natural abundance 13C J-couplings at Earth's magnetic field for spin system differentiation of small organic molecules

Nuclear magnetic resonance (NMR) spectroscopy routinely characterizes the unique spin systems of molecules using a combination of chemical shift and J-coupling interactions for the ¹H and ¹³C nuclei. However, at Earth's magnetic field, chemical shifts are unresolvable and the ability to characterize structure relies solely on the J-couplings. Fortuitously, the J-couplings at Earth's field provides the same spin system information as high field, but only requires detection of the ¹H nucleus. We report the first identification of the multiple natural abundance ¹H-¹³C spin systems on organic molecules detected at Earth's magnetic field. The results clearly demonstrate the feasibility of Earth's field NMR to characterize small organic molecules without costly enrichment strategies.

Quantum computation of molecular structure using data from challenging-to-classically-simulate nuclear magnetic resonance experiments

We propose a quantum algorithm for inferring the molecular nuclear spin Hamiltonian from time-resolved measurements of spin-spin correlators, which can be obtained via nuclear magnetic resonance (NMR). We focus on learning the anisotropic dipolar term of the Hamiltonian, which generates dynamics that are challenging to classically simulate in some contexts. We demonstrate the ability to directly estimate the Jacobian and Hessian of the corresponding learning problem on a quantum computer, allowing us to learn the Hamiltonian parameters. We develop algorithms for performing this computation on both noisy near-term and future fault-tolerant quantum computers. We argue that the former is promising as an early beyond-classical quantum application since it only requires evolution of a local spin Hamiltonian. We investigate the example of a protein (ubiquitin) confined on a membrane as a benchmark of our method. We isolate small spin clusters, demonstrate the convergence of our learning algorithm on one such example, and then investigate the learnability of these clusters as we cross the ergodic to non-ergodic phase transition by suppressing the dipolar interaction. We see a clear correspondence between a drop in the multifractal dimension measured across many-body eigenstates of these clusters, and a transition in the structure of the Hessian of the learning cost function (from degenerate to learnable). Our hope is that such quantum computations might enable the interpretation and development of new NMR techniques for analyzing molecular structure.

Relayed hyperpolarization for zero-field nuclear magnetic resonance

Zero- to ultralow-field nuclear magnetic resonance (ZULF NMR) is a rapidly developing form of spectroscopy that provides rich spectroscopic information in the absence of large magnetic fields. However, signal acquisition still requires a mechanism for generating a bulk magnetic moment for detection, and the currently used methods only apply to a limited pool of chemicals or come at prohibitively high cost. We demonstrate that the parahydrogen-based SABRE (signal amplification by reversible exchange)-Relay method can be used as a more general means of generating hyperpolarized analytes for ZULF NMR by observing zero-field J-spectra of [¹³C]-methanol, [1-¹³C]-ethanol, and [2-¹³C]-ethanol in both ¹³C-isotopically enriched and natural abundance samples. We explore the magnetic field dependence of the SABRE-Relay efficiency and show the existence of a second maximum at 19.0 ± 0.3 mT. Despite presence of water, SABRE-Relay is used to hyperpolarize ethanol extracted from a store-bought sample of vodka (%P_H ~ 0.1%).

Decoupling of Spin Decoherence Paths near Zero Magnetic Field

We demonstrate a method to quantify and manipulate nuclear spin decoherence mechanisms that are active in zero to ultralow magnetic fields. These include (i) nonadiabatic switching of spin quantization axis due to residual background fields and (ii) scalar pathways due to through-bond couplings between ¹H and heteronuclear spin species, such as ²H used partially as an isotopic substitute for ¹H. Under conditions of free evolution, scalar relaxation due to ²H can significantly limit nuclear spin polarization lifetimes and thus the scope of magnetic resonance procedures near zero field. It is shown that robust trains of pulsed dc magnetic fields that apply π flip angles to one or multiple spin species may switch the effective symmetry of the nuclear spin Hamiltonian, imposing decoupled or coupled dynamic regimes on demand. The method should broaden the spectrum of hyperpolarized biomedical contrast-agent compounds and hyperpolarization procedures that are used near zero field.

Zero-Field NMR of Urea: Spin-Topology Engineering by Chemical Exchange

Well-resolved and information-rich J-spectra are the foundation for chemical detection in zero-field NMR. However, even for relatively small molecules, spectra exhibit complexity, hindering the analysis. To address this problem, we investigate an example biomolecule with a complex J-coupling network─urea, a key metabolite in protein catabolism─and demonstrate ways of simplifying its zero-field spectra by modifying spin topology. This goal is achieved by controlling pH-dependent chemical exchange rates of 1H nuclei and varying the composition of the D2O/H2O mixture used as a solvent. Specifically, we demonstrate that by increasing the proton exchange rate in the [13C,15N2]-urea solution, the spin system simplifies, manifesting through a single narrow spectral peak. Additionally, we show that the spectra of 1H/D isotopologues of [15N2]-urea can be understood easily by analyzing isolated spin subsystems. This study paves the way for zero-field NMR detection of complex biomolecules, particularly in biofluids with a high concentration of water.

Improvement in the signal amplitude and bandwidth of an optical atomic magnetometer via alignment-to-orientation conversion

We evaluated the alignment-to-orientation conversion (AOC) at the cesium D1 line to improve a nonlinear magneto-optical rotation (NMOR) optical atomic magnetometer's signal amplitude and bandwidth. For the 6 ²S_1/2 F = 3 → 6 ²P_1/2 F' = 4 transition, the AOC-related NMOR achieves a 1.7-fold enhancement in signal amplitude compared to the conventional NMOR, benefiting from narrow linewidth and ultraweak power broadening. Therefore, an effective amplitude-to-linewidth ratio is maintained in the high-laser-power region. This method is beneficial for detecting high-frequency magnetic signals in nuclear magnetic resonance and biomagnetism, as the NMOR magnetometer bandwidth increases with laser power.

Lower than low: Perspectives on zero- to ultralow-field nuclear magnetic resonance

The less-traveled low road in nuclear magnetic resonance is discussed, honoring the contributions of Prof. Bernhard Blümich, aspiring towards reaching 'a new low.' A history of the subject and its current status are briefly reviewed, followed by an effort to prophesy possible directions for future developments.

Zero-Field NMR J-Spectroscopy of Organophosphorus Compounds

Organophosphorus compounds are a wide and diverse class of chemicals playing a crucial role in living organisms. This aspect has been often investigated using nuclear magnetic resonance (NMR), which provides information about molecular structure and function. In this paper, we report the results of theoretical and experimental studies on basic organophosphorus compounds using zero-field NMR, where spin dynamics are investigated in the absence of a magnetic field with the dominant heteronuclear J-coupling. We demonstrate that the zero-field NMR enables distinguishing the chemicals owing to their unique electronic environment even though their spin systems have the same alphabetic designation. Such information can be obtained just in a single measurement, while amplitudes and widths of observed low-field NMR resonances enable the study of processes affecting spin dynamics. An excellent agreement between simulations and measurements of the spectra, particularly in the largest frequency J-couplings range ever reported in zero-field NMR, is demonstrated.

Chemical Reaction Monitoring using Zero-Field Nuclear Magnetic Resonance Enables Study of Heterogeneous Samples in Metal Containers

We demonstrate that heterogeneous/biphasic chemical reactions can be monitored with high spectroscopic resolution using zero-field nuclear magnetic resonance spectroscopy. This is possible because magnetic susceptibility broadening is negligible at ultralow magnetic fields. We show the two-step hydrogenation of dimethyl acetylenedicarboxylate with para-enriched hydrogen gas in conventional glass NMR tubes, as well as in a titanium tube. The low frequency zero-field NMR signals ensure that there is no significant signal attenuation arising from shielding by the electrically conductive sample container. This method paves the way for in situ monitoring of reactions in complex heterogeneous multiphase systems and in reactors made of conductive materials while maintaining resolution and chemical specificity.

Robustness of the NV-NMR Spectrometer Setup to Magnetic Field Inhomogeneities

The NV-NMR spectrometer is a promising candidate for detection of NMR signals at the nanoscale. Field inhomogeneities, however, are a major source of noise that limits spectral resolution in state of the art NV-NMR experiments and constitutes a major bottleneck in the development of nanoscale NMR. Here we propose, a route in which this limitation could be circumvented in NV-NMR spectrometer experiments, by utilizing the nanometric scale and the quantumness of the detector.

Two-dimensional single- and multiple-quantum correlation spectroscopy in zero-field nuclear magnetic resonance

We present single- and multiple-quantum correlation J-spectroscopy detected in zero (<1μG) magnetic field using a ⁸⁷Rb vapor-cell magnetometer. At zero field the spectrum of ethanol appears as a mixture of ¹³C isotopomers, and correlation spectroscopy is useful in separating the two composite spectra. We also identify and observe the zero-field equivalent of a double-quantum transition in ¹³C₂-acetic acid, and show that such transitions are of use in spectral assignment. Two-dimensional spectroscopy further improves the high resolution attained in zero-field NMR since selection rules on the coherence-transfer pathways allow for the separation of otherwise overlapping resonances into distinct cross-peaks.

Design and implementation of a J-coupled spectrometer for multidimensional structure and relaxation detection at low magnetic fields

In recent years, it has been realized that low and ultra-low field (mT-nT magnetic field range) nuclear magnetic resonance spectroscopy can be used for molecular structural analysis. However, spectra are often hindered by lengthy acquisition times or require large sample volumes and high concentrations. Here, we report a low field (50 μT) instrument that employs a linear actuator to shuttle samples between a 1 T prepolarization field and a solenoid detector in a laboratory setting. The current experimental setup is benchmarked using water and ¹³C-methanol with a single scan detection limit of 2 × 10²⁰ spins (3 µl, 55M H₂O) and detection limit of 2.9 × 10¹⁹ (200 µl, 617 mM ¹³C-methanol) spins with signal averaging. The system has a dynamic range of >3 orders of magnitude. Investigations of room-temperature relaxation dynamics of ¹³C-methanol show that sample dilution can be used in lieu of sample heating to acquire spectra with linewidths comparable to high-temperature spectra. These results indicate that the T₁ and T₂ mechanisms are governed by both the proton exchange rate and the dissolved oxygen in the sample. Finally, a 2D correlation spectroscopy experiment is reported, performed in the strong coupling regime that resolves the multiple resonances associated with the heteronuclear J-coupling. The spectrum was collected using 10 times less sample and in less than half the time from previous reports in the strong coupling limit.

Zero- to ultralow-field nuclear magnetic resonance J-spectroscopy with commercial atomic magnetometers

Zero- to ultralow-field nuclear magnetic resonance (ZULF NMR) is an alternative spectroscopic method to high-field NMR, in which samples are studied in the absence of a large magnetic field. Unfortunately, there is a large barrier to entry for many groups, because operating the optical magnetometers needed for signal detection requires some expertise in atomic physics and optics. Commercially available magnetometers offer a solution to this problem. Here we describe a simple ZULF NMR configuration employing commercial magnetometers, and demonstrate sufficient functionality to measure samples with nuclear spins prepolarized in a permanent magnet or initialized using parahydrogen. This opens the possibility for other groups to use ZULF NMR, which provides a means to study complex materials without magnetic susceptibility-induced line broadening, and to observe samples through conductive materials.

Extreme nuclear magnetic resonance: Zero field, single spins, dark matter…

An unusual regime for liquid-state nuclear magnetic resonance (NMR) where the magnetic field strength is so low that the J-coupling (intramolecular spin-spin) interactions dominate the spin Hamiltonian opens a new paradigm with applications in spectroscopy, quantum control, and in fundamental-physics experiments, including searches for well-motivated dark-matter candidates. An interesting possibility is to bring this kind of "extreme NMR" together with another one-single nuclear spin detected with a single-spin quantum sensor. This would enable single-molecule J-spectroscopy.

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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{H}}_4^ +$$\end{document}H4+) 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.

Zero-field nuclear magnetic resonance can identify species and collective behaviors in mixtures without applied magnetic fields. Here the authors demonstrate its use for resolving proton exchange in ammonium and for the detection of hyperpolarized pyruvic acid, an important imaging biomarker.

Scalar relaxation of NMR transitions at ultralow magnetic field

Nuclear magnetic resonance signals for ¹H in simple chlorinated, brominated and deuterated liquids were detected at field strengths between 1 nT and a few μT to investigate the influence of scalar relaxation of the second kind (SR2K). SR2K describes the acceleration in magnetization decay rate for a spin-1/2 nucleus that is scalar coupled to a fast-relaxing quadrupolar nucleus. In agreement with simple theoretical models, the experimental data show that couplings to nuclei with small, nonzero quadrupole moments (²H) give rise to higher transverse relaxation rates at ultralow field than rapidly relaxing quadrupolar nuclei (Cl and Br). This behavior is opposite to the case normally encountered in high-field NMR, and demonstrates that certain nuclei in the spin system may be "weakly coupled" or even decoupled when the applied magnetic field is zero. The results show that the capability for precision determination of NMR frequencies and molecular structural information depends strongly on the composition and topology of the nuclear spin system.

High-resolution methods for the measurement of scalar coupling constants

Scalar couplings provide important information regarding molecular structure and dynamics. The measurement of scalar coupling constants constitutes a topic of interest and significance in NMR spectroscopy. However, the measurement of J values is often not straightforward because of complex signal splitting patterns and signal overlap. Many methods have been proposed for the measurement of scalar coupling constants, both for homonuclear and heteronuclear cases. Different approaches to the measurement of scalar coupling constants are reviewed here with several applications presented. The accurate measurement of scalar coupling constants can greatly facilitate molecular structure elucidation and the study of molecule dynamics.

NMR relaxation in porous materials at zero and ultralow magnetic fields

NMR detection in the ultralow-field regime (below 10 μT) was used to measure the nuclear spin relaxation rates of liquids imbibed into silica pellets with mean pore diameters in the 10-50 nm range. Heptane, formic acid and acetic acid were studied and relaxation rate data were compared with a conventional field-cycling NMR technique. Detection of ¹H-¹³C spin coupling NMR signals at zero field (∼0.1 nT) allowed spectroscopic identification of molecules inside the porous material and unambiguous measurements of the chemistry-specific relaxation rates in liquid mixtures. In the case of molecules that contain ¹H and ¹³C, spin-singlet state relaxation can provide additional information about the dynamics. Applications and future improvements to the methodology are discussed.

Multinuclear Detection of Nuclear Spin Optical Rotation at Low Field

We describe the multinuclear detection of nuclear spin optical rotation (NSOR), an effect dependent on the hyperfine interaction between nuclear spins and electrons. Signals of ¹H and ¹⁹F are discriminated by frequency in a single spectrum acquired at sub-millitesla field. The simultaneously acquired optical signal along with the nuclear magnetic resonance signal allows the calculation of the relative magnitude of the NSOR constants corresponding to different nuclei within the sample molecules. This is illustrated by a larger NSOR signal measured at the ¹⁹F frequency despite a smaller corresponding spin concentration. Second, it is shown that heteronuclear J-coupling is observable in the NSOR signal, which can be used to retrieve chemical information. Multinuclear frequency and J resolution can localize optical signals in the molecule. Properties of electronic states at multiple sites in a molecule may therefore ultimately be determined by frequency-resolved NSOR spectroscopy at low field.

Experimental benchmarking of quantum control in zero-field nuclear magnetic resonance

Demonstration of coherent control and characterization of the control fidelity is important for the development of quantum architectures such as nuclear magnetic resonance (NMR). We introduce an experimental approach to realize universal quantum control, and benchmarking thereof, in zero-field NMR, an analog of conventional high-field NMR that features less-constrained spin dynamics. We design a composite pulse technique for both arbitrary one-spin rotations and a two-spin controlled-not (CNOT) gate in a heteronuclear two-spin system at zero field, which experimentally demonstrates universal quantum control in such a system. Moreover, using quantum information-inspired randomized benchmarking and partial quantum process tomography, we evaluate the quality of the control, achieving single-spin control for ¹³C with an average fidelity of 0.9960(2) and two-spin control via a CNOT gate with a fidelity of 0.9877(2). Our method can also be extended to more general multispin heteronuclear systems at zero field. The realization of universal quantum control in zero-field NMR is important for quantum state/coherence preparation, pulse sequence design, and is an essential step toward applications to materials science, chemical analysis, and fundamental physics.

In-Vivo NMR Spectroscopy: A Powerful and Complimentary Tool for Understanding Environmental Toxicity

Part review, part perspective, this article examines the applications and potential of in-vivo Nuclear Magnetic Resonance (NMR) for understanding environmental toxicity. In-vivo NMR can be applied in high field NMR spectrometers using either magic angle spinning based approaches, or flow systems. Solution-state NMR in combination with a flow system provides a low stress approach to monitor dissolved metabolites, while magic angle spinning NMR allows the detection of all components (solutions, gels and solids), albeit with additional stress caused by the rapid sample spinning. With in-vivo NMR it is possible to use the same organisms for control and exposure studies (controls are the same organisms prior to exposure inside the NMR). As such individual variability can be reduced while continual data collection over time provides the temporal resolution required to discern complex interconnected response pathways. When multidimensional NMR is combined with isotopic labelling, a wide range of metabolites can be identified in-vivo providing a unique window into the living metabolome that is highly complementary to more traditional metabolomics studies employing extracts, tissues, or biofluids.

A method for measurement of spin-spin couplings with sub-mHz precision using zero- to ultralow-field nuclear magnetic resonance

We present a method which allows for the extraction of physical quantities directly from zero- to ultralow-field nuclear magnetic resonance (ZULF NMR) data. A numerical density matrix evolution is used to simulate ZULF NMR spectra of several molecules in order to fit experimental data. The method is utilized to determine the indirect spin-spin couplings (J-couplings) in these systems, which is achieved with precision of 10^-2-10^-4Hz. The simulated and measured spectra are compared to earlier research. Agreement and improved precision are achieved for most of the J-coupling estimates. The availability of fast, flexible fitting method for ZULF NMR enables a new generation of precision-measurement experiments for spin-dependent interactions and physics beyond the Standard Model.

Invited Review Article: Instrumentation for nuclear magnetic resonance in zero and ultralow magnetic field

We review experimental techniques in our laboratory for nuclear magnetic resonance (NMR) in zero and ultralow magnetic field (below 0.1 μT) where detection is based on a low-cost, non-cryogenic, spin-exchange relaxation free ⁸⁷Rb atomic magnetometer. The typical sensitivity is 20-30 fT/Hz^1/2 for signal frequencies below 1 kHz and NMR linewidths range from Hz all the way down to tens of mHz. These features enable precision measurements of chemically informative nuclear spin-spin couplings as well as nuclear spin precession in ultralow magnetic fields.

Evolution-Free Hamiltonian Parameter Estimation through Zeeman Markers

We provide a protocol for Hamiltonian parameter estimation which relies only on the Zeeman effect. No time-dependent quantities need to be measured; it fully suffices to observe spectral shifts induced by fields applied to local "markers." We demonstrate the idea with a simple tight-binding Hamiltonian and numerically show stability with respect to Gaussian noise on the spectral measurements. Then we generalize the result to show applicability to a wide range of systems, including quantum spin chains, networks of qubits, and coupled harmonic oscillators, and suggest potential experimental implementations.

13C-Decoupled J-Coupling Spectroscopy Using Two-Dimensional Nuclear Magnetic Resonance at Zero-Field

We present a two-dimensional method for obtaining ¹³C-decoupled, ¹H-coupled nuclear magnetic resonance (NMR) spectra in zero magnetic field using coherent spin-decoupling. The result is a spectrum determined only by the proton-proton J-coupling network. Detection of NMR signals in zero magnetic field requires at least two different nuclear spin species, but the proton J-spectrum is independent of isotopomer, thus potentially simplifying spectra and thereby improving the analytical capabilities of zero-field NMR. The protocol does not rely on a difference in Larmor frequency between the coupled nuclei, allowing for the direct determination of J-coupling constants between chemically equivalent spins. We obtain the ¹³C-decoupled zero-field spectrum of [1-¹³C]-propionic acid and identify conserved quantum numbers governing the appearance of cross peaks in the two-dimensional spectrum.

Antisymmetric Couplings Enable Direct Observation of Chirality in Nuclear Magnetic Resonance Spectroscopy

Here we demonstrate that a term in the nuclear spin Hamiltonian, the antisymmetric J-coupling, is fundamentally connected to molecular chirality. We propose and simulate a nuclear magnetic resonance (NMR) experiment to observe this interaction and differentiate between enantiomers without adding any additional chiral agent to the sample. The antisymmetric J-coupling may be observed in the presence of molecular orientation by an external electric field. The opposite parity of the antisymmetric coupling tensor and the molecular electric dipole moment yields a sign change of the observed coupling between enantiomers. We show how this sign change influences the phase of the NMR spectrum and may be used to discriminate between enantiomers.

Nuclear magnetic resonance at millitesla fields using a zero-field spectrometer

We describe new analytical capabilities for nuclear magnetic resonance (NMR) experiments in which signal detection is performed with chemical resolution (via spin-spin J couplings) in the zero to ultra-low magnetic field region, below 1μT. Using magnetic fields in the 100μT to 1mT range, we demonstrate the implementation of conventional NMR pulse sequences with spin-species selectivity.

Milli-tesla NMR and spectrophotometry of liquids hyperpolarized by dissolution dynamic nuclear polarization

Hyperpolarization methods offer a unique means of improving low signal strength obtained in low-field NMR. Here, simultaneous measurements of NMR at a field of 0.7mT and laser optical absorption from samples hyperpolarized by dissolution dynamic nuclear polarization (D-DNP) are reported. The NMR measurement field closely corresponds to a typical field encountered during sample injection in a D-DNP experiment. The optical spectroscopy allows determination of the concentration of the free radical required for DNP. Correlation of radical concentration to NMR measurement of spin polarization and spin-lattice relaxation time allows determination of relaxivity and can be used for optimization of the D-DNP process. Further, the observation of the nuclear Overhauser effect originating from hyperpolarized spins is demonstrated. Signals from (1)H and (19)F in a mixture of trifluoroethanol and water are detected in a single spectrum, while different atoms of the same type are distinguished by J-coupling patterns. The resulting signal changes of individual peaks are indicative of molecular contact, suggesting a new application area of hyperpolarized low-field NMR for the determination of intermolecular interactions.

Transition-Selective Pulses in Zero-Field Nuclear Magnetic Resonance

We use low-amplitude, ultralow frequency pulses to drive nuclear spin transitions in zero and ultralow magnetic fields. In analogy to high-field NMR, a range of sophisticated experiments becomes available as these allow narrow-band excitation. As a first demonstration, pulses with excitation bandwidths 0.5-5 Hz are used for population redistribution, selective excitation, and coherence filtration. These methods are helpful when interpreting zero- and ultralow-field NMR spectra that contain a large number of transitions.

Zero-field nuclear magnetic resonance spectroscopy of viscous liquids

We report zero-field NMR measurements of a viscous organic liquid, ethylene glycol. Zero-field spectra were taken showing resolved scalar spin-spin coupling (J-coupling) for ethylene glycol at different temperatures and water contents. Molecular dynamics strongly affects the resonance linewidth, which closely follows viscosity. Quantum chemical calculations have been used to obtain the relative stability and coupling constants of all ethylene glycol conformers. The results show the potential of zero-field NMR as a probe of molecular structure and dynamics in a wide range of environments, including viscous fluids.

Two-dimensional NMR spectroscopy of (13)C methanol at less than 5 μT

Two-dimensional (2D) spectroscopy is one of the most significant applications of nuclear magnetic resonance (NMR). Here, we demonstrate that the 2D NMR can be performed even at a low magnetic field of less than 5μT, which is ten times less than the Earth's magnetic field. The pulses used in the experiment were composed of circularly polarized fields for coherent as well as wideband excitations. Since the excitation band covers the entire spectral range, the simplest two-pulse sequence delivered the full 2D spectrum. At 5μT, methanol with (13)C enriched up to 99% belongs to a strongly coupled regime, and thus its 2D spectrum exhibits complicated spectral correlations, which can be exploited as a fingerprint in chemical analysis. In addition, we show that, with compressive sensing, the acquisition of the 2D spectrum can be accelerated to take only 45% of the overall duration.

The role of level anti-crossings in nuclear spin hyperpolarization

Nuclear spin hyperpolarization is an important resource for increasing the sensitivity of NMR spectroscopy and MRI. Signal enhancements can be as large as 3-4 orders of magnitude. In hyperpolarization experiments, it is often desirable to transfer the initial polarization to other nuclei of choice, either protons or insensitive nuclei such as (13)C and (15)N. This situation arises primarily in Chemically Induced Dynamic Nuclear Polarization (CIDNP), Para-Hydrogen Induced Polarization (PHIP), and the related Signal Amplification By Reversible Exchange (SABRE). Here we review the recent literature on polarization transfer mechanisms, in particular focusing on the role of Level Anti-Crossings (LACs) therein. So-called "spontaneous" polarization transfer may occur both at low and high magnetic fields. In addition, transfer of spin polarization can be accomplished by using especially designed pulse sequences. It is now clear that at low field spontaneous polarization transfer is primarily due to coherent spin-state mixing under strong coupling conditions. However, thus far the important role of LACs in this process has not received much attention. At high magnetic field, polarization may be transferred by cross-relaxation effects. Another promising high-field technique is to generate the strong coupling condition by spin locking using strong radio-frequency fields. Here, an analysis of polarization transfer in terms of LACs in the rotating frame is very useful to predict which spin orders are transferred depending on the strength and frequency of the B1 field. Finally, we will examine the role of strong coupling and LACs in magnetic-field dependent nuclear spin relaxation and the related topic of long-lived spin-states.

Long-lived heteronuclear spin-singlet states in liquids at a zero magnetic field

We report an observation of long-lived spin-singlet states in a 13C-1H spin pair in a zero magnetic field. In 13C-labeled formic acid, we observe spin-singlet lifetimes as long as 37 s, about a factor of 3 longer than the T1 lifetime of dipole polarization in the triplet state. In contrast to common high-field experiments, the observed coherence is a singlet-triplet coherence with a lifetime T2 longer than the T1 lifetime of dipole polarization in the triplet manifold. Moreover, we demonstrate that heteronuclear singlet states formed between a 1H and a 13C nucleus can exhibit longer lifetimes than the respective triplet states even in the presence of additional spins that couple to the spin pair of interest. Although long-lived homonuclear spin-singlet states have been extensively studied, this is the first experimental observation of analogous singlet states in heteronuclear spin pairs.

Low-field permanent magnets for industrial process and quality control

In this review we focus on the technology associated with low-field NMR. We present the current state-of-the-art in low-field NMR hardware and experiments, considering general magnet designs, rf performance, data processing and interpretation. We provide guidance on obtaining the optimum results from these instruments, along with an introduction for those new to low-field NMR. The applications of lowfield NMR are now many and diverse. Furthermore, niche applications have spawned unique magnet designs to accommodate the extremes of operating environment or sample geometry. Trying to capture all the applications, methods, and hardware encompassed by low-field NMR would be a daunting task and likely of little interest to researchers or industrialists working in specific subject areas. Instead we discuss only a few applications to highlight uses of the hardware and experiments in an industrial environment. For details on more particular methods and applications, we provide citations to specialized review articles.

Symmetry-amplified J splittings for quadrupolar spin pairs: a solid-state NMR probe of homoatomic covalent bonds

Chemically informative J couplings between pairs of quadrupolar nuclei in dimetallic and dimetalloid coordination motifs are measured using J-resolved solid-state NMR experiments. It is shown that the application of a double-quantum filter is necessary to observe the J splittings and that, under these conditions, only a simple doublet is expected. Interestingly, the splitting is amplified if the spins are magnetically equivalent, making it possible to measure highly precise J couplings and unambiguously probe the symmetry of the molecule. This is demonstrated experimentally by chemically breaking the symmetry about a pair of boron spins by reaction with an N-heterocyclic carbene to form a β-borylation reagent. The results show that the J coupling is a sensitive probe of bonding in diboron compounds and that the J values quantify the weakening of the B-B bond which occurs when forming an sp(2)-sp(3) diboron compound, which is relevant to their reactivity. Due to the prevalence of quadrupolar nuclei among transition metals, this work also provides a new approach to probe metal-metal bonding; results for Mn2(CO)10 are provided as an example.