Theory of long-lived nuclear spin states in methyl groups and quantum-rotor induced polarisation

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.

Spin Hyperpolarization in Modern Magnetic Resonance

Magnetic resonance techniques are successfully utilized in a broad range of scientific disciplines and in various practical applications, with medical magnetic resonance imaging being the most widely known example. Currently, both fundamental and applied magnetic resonance are enjoying a major boost owing to the rapidly developing field of spin hyperpolarization. Hyperpolarization techniques are able to enhance signal intensities in magnetic resonance by several orders of magnitude, and thus to largely overcome its major disadvantage of relatively low sensitivity. This provides new impetus for existing applications of magnetic resonance and opens the gates to exciting new possibilities. In this review, we provide a unified picture of the many methods and techniques that fall under the umbrella term "hyperpolarization" but are currently seldom perceived as integral parts of the same field. Specifically, before delving into the individual techniques, we provide a detailed analysis of the underlying principles of spin hyperpolarization. We attempt to uncover and classify the origins of hyperpolarization, to establish its sources and the specific mechanisms that enable the flow of polarization from a source to the target spins. We then give a more detailed analysis of individual hyperpolarization techniques: the mechanisms by which they work, fundamental and technical requirements, characteristic applications, unresolved issues, and possible future directions. We are seeing a continuous growth of activity in the field of spin hyperpolarization, and we expect the field to flourish as new and improved hyperpolarization techniques are implemented. Some key areas for development are in prolonging polarization lifetimes, making hyperpolarization techniques more generally applicable to chemical/biological systems, reducing the technical and equipment requirements, and creating more efficient excitation and detection schemes. We hope this review will facilitate the sharing of knowledge between subfields within the broad topic of hyperpolarization, to help overcome existing challenges in magnetic resonance and enable novel applications.

A flow electrochemistry-enabled synthesis of 2-substituted N-(methyl-d)piperidines

A synthesis of N-monodeuteriomethyl-2-substituted piperidines is described. An efficient and readily scalable anodic methoxylation of N-formylpiperidine in an undivided microfluidic electrolysis cell delivers methoxylated piperidine 3, which is a precursor to a N-formyliminium ion and enables C-nucleophiles to be introduced at the 2-position. The isotopically labelled N-deuteriomethyl group is installed using the Eschweiler-Clarke reaction with formic acid-d₂ and unlabelled formaldehyde. Monodeuterated N-methyl groups in these molecular systems possess small isotropic proton chemical shift differences important in the investigation of molecules that are able to support long-lived nuclear spin states in solution nuclear magnetic resonance.

Inversion of Hyperpolarized 13C NMR Signals through Cross-Correlated Cross-Relaxation in Dissolution DNP Experiments

Dissolution dynamic nuclear polarization (DDNP) is a versatile tool to boost signal amplitudes in solution-state nuclear magnetic resonance (NMR) spectroscopy. For DDNP, nuclei are spin-hyperpolarized "ex situ" in a dedicated DNP device and then transferred to an NMR spectrometer for detection. Dramatic signal enhancements can be achieved, enabling shorter acquisition times, real-time monitoring of fast reactions, and reduced sample concentrations. Here, we show how the sample transfer in DDNP experiments can affect NMR spectra through cross-correlated cross-relaxation (CCR), especially in the case of low-field passages. Such processes can selectively invert signals of ¹³C spins in proton-carrying moieties. For their investigations, we use schemes for simultaneous or "parallel" detection of hyperpolarized ¹H and ¹³C nuclei. We find that ¹H → ¹³C CCR can invert signals of ¹³C spins if the proton polarization is close to 100%. We deduce that low-field passage in a DDNP experiment, a common occurrence due to the introduction of so-called "ultra-shielded" magnets, accelerates these effects due to field-dependent paramagnetic relaxation enhancements that can influence CCR. The reported effects are demonstrated for various molecules, laboratory layouts, and DDNP systems. As coupled ¹³C-¹H spin systems are ubiquitous, we expect similar effects to be observed in various DDNP experiments. This might be exploited for selective spectroscopic labeling of hydrocarbons.

Practical dissolution dynamic nuclear polarization

This review article intends to provide insightful advice for dissolution-dynamic nuclear polarization in the form of a practical handbook. The goal is to aid research groups to effectively perform such experiments in their own laboratories. Previous review articles on this subject have covered a large number of useful topics including instrumentation, experimentation, theory, etc. The topics to be addressed here will include tips for sample preparation and for checking sample health; a checklist to correctly diagnose system faults and perform general maintenance; the necessary mechanical requirements regarding sample dissolution; and aids for accurate, fast and reliable polarization quantification. Herein, the challenges and limitations of each stage of a typical dissolution-dynamic nuclear polarization experiment are presented, with the focus being on how to quickly and simply overcome some of the limitations often encountered in the laboratory.

Nuclear singlet relaxation by chemical exchange

The population imbalance between nuclear singlet states and triplet states of strongly coupled spin-1/2 pairs, also known as nuclear singlet order, is well protected against several common relaxation mechanisms. We study the nuclear singlet relaxation of ¹³C pairs in aqueous solutions of 1,2-¹³C₂ squarate over a range of pH values. The ¹³C singlet order is accessed by introducing ¹⁸O nuclei in order to break the chemical equivalence. The squarate dianion is in chemical equilibrium with hydrogen-squarate (SqH^-) and squaric acid (SqH₂) characterized by the dissociation constants pK₁ = 1.5 and pK₂ = 3.4. Surprisingly, we observe a striking increase in the singlet decay time constants T_S when the pH of the solution exceeds ∼10, which is far above the acid-base equilibrium points. We derive general rate expressions for chemical-exchange-induced nuclear singlet relaxation and provide a qualitative explanation of the T_S behavior of the squarate dianion. We identify a kinetic contribution to the singlet relaxation rate constant, which explicitly depends on kinetic rate constants. Qualitative agreement is achieved between the theory and the experimental data. This study shows that infrequent chemical events may have a strong effect on the relaxation of nuclear singlet order.

An Examination of Factors Influencing Small Proton Chemical Shift Differences in Nitrogen-Substituted Monodeuterated Methyl Groups

Monodeuterated methyl groups have previously been demonstrated to provide access to long-lived nuclear spin states. This is possible when the CH2D rotamers have sufficiently different populations and the local environment is chiral, which foments a non-negligible isotropic chemical shift difference between the two CH2D protons. In this article, the focus is on the N-CH2D group of N-CH2D-2-methylpiperidine and other suitable CH2D-piperidine derivatives. We used a combined experimental and computational approach to investigate how rotameric symmetry breaking leads to a 1H CH2D chemical shift difference that can subsequently be tuned by a variety of factors such as temperature, acidity and 2-substituted molecular groups.

Centralizer theory for long-lived spin states

Nuclear long-lived spin states represent spin density operator configurations that are exceptionally well protected against spin relaxation phenomena. Their long-lived character is exploited in a variety of Nuclear Magnetic Resonance (NMR) techniques. Despite the growing importance of long-lived spin states in modern NMR, strategies for their identification have changed little over the last decade. The standard approach heavily relies on a chain of group theoretical arguments. In this paper, we present a more streamlined method for the calculation of such configurations. Instead of focusing on the symmetry properties of the relaxation superoperator, we focus on its corresponding relaxation algebra. This enables us to analyze long-lived spin states with Lie algebraic methods rather than group theoretical arguments. We show that the centralizer of the relaxation algebra forms a basis for the set of long-lived spin states. The characterization of the centralizer, on the other hand, does not rely on any special symmetry arguments, and its calculation is straightforward. We outline a basic algorithm and illustrate advantages by considering long-lived spin states for some spin-1/2 pairs and rapidly rotating methyl groups.

Hyperpolarization and the physical boundary of Liouville space

The quantum state of a spin ensemble is described by a density operator, which corresponds to a point in the Liouville space of orthogonal spin operators. Valid density operators are confined to a particular region of Liouville space, which we call the physical region and which is bounded by multidimensional figures called simplexes. Each vertex of a simplex corresponds to a pure-state density operator. We provide examples for spins I = 1 / 2 , I = 1 , I = 3 / 2 and for coupled pairs of spins-1/2. We use the von Neumann entropy as a criterion for hyperpolarization. It is shown that the inhomogeneous master equation for spin dynamics leads to non-physical results in some cases, a problem that may be avoided by using the Lindbladian master equation.

Nuclear Spin Relaxation of Longitudinal and Singlet Order in Liquid-CO2 Solutions

Hyperpolarization techniques can enormously enhance the NMR signal thus allowing the exploitation of hyperpolarized substrates for in-vivo MRI applications. The short lifetime of hyperpolarized spin order poses significant limitations in such applications. Spin order storage can be prolonged through the use of long-lived spin states. Additionally, the storage of spin polarization-either in the form of longitudinal or singlet order-can be prolonged in low viscosity solutions. Here, we report the use of low viscosity liquid-CO₂ solutions to store nuclear spin polarization in the form of longitudinal and singlet order for extended periods. Our results demonstrate that this storage time can be considerably sustained in liquid-CO₂ solutions in comparison to other low viscosity solvents, opening up the possibility of new, exciting storage experiments in the future.

Single-scan measurements of nuclear spin singlet order decay rates

Measurements of singlet spin order decay rates are time consuming due to the long-lived nature of this form of order and the typical pseudo-2D mode of acquisition. Additionally, this acquisition modality is not ideal for experiments run on hyperpolarized order because of the single-shot nature of hyperpolarization techniques. We present a methodology based on spatial encoding that not only significantly reduces the duration of these experiments but also confers compatibility using spin hyperpolarization techniques. The method condenses in a single shot the variable delay array used to measure decay rates in conventional pseudo-2D relaxation experiments. This results in a substantial time saving factor and, more importantly, makes the experiment compatible with hyperpolarization techniques since only a single hyperpolarized sample is required. Furthermore, the presented method, besides offering savings on time and costs, avoids reproducibility concerns associated with repetition in the hyperpolarization procedure. The method accelerates the measurement and characterization of singlet order decay times, and, when coupled with hyperpolarization techniques, can facilitate the quest for systems with very long decay times.

Rotational-permutational dual-pairing and long-lived spin order

Quantum systems in contact with a thermal environment experience coherent and incoherent dynamics. These drive the system back toward thermal equilibrium after an initial perturbation. The relaxation process involves the reorganization of spin state populations and the decay of spin state coherences. In general, individual populations and coherences may exhibit different relaxation time constants. Particular spin configurations may exhibit exceptionally long relaxation time constants. Such spin configurations are known as long-lived spin order. The existence of long-lived spin order is a direct consequence of the symmetries of the system. For nuclear spin systems, rotational and permutational symmetries are of fundamental importance. Based on the Schur-Weyl duality theorem, we describe a theoretical framework for the study of rotational and permutational dual-symmetries in the context of long-lived spin order. Making use of the proposed formalism, we derive refined bounds on the number on long-lived spin populations and coherences for systems exhibiting rotational-permutational dual-symmetries.

A master equation for spin systems far from equilibrium

The quantum dynamics of spin systems is often treated by a differential equation known as the master equation, which describes the trajectories of spin observables such as magnetization components, spin state populations, and coherences between spin states. The master equation describes how a perturbed spin system returns to a state of thermal equilibrium with a finite-temperature environment. The conventional master equation, which has the form of an inhomogeneous differential equation, applies to cases where the spin system remains close to thermal equilibrium, which is well satisfied for a wide variety of magnetic resonance experiments conducted on thermally polarized spin systems at ordinary temperatures. However, the conventional inhomogeneous master equation may fail in the case of hyperpolarized spin systems, when the spin state populations deviate strongly from thermal equilibrium, and in general where there is a high degree of nuclear spin order. We highlight a simple case in which the inhomogeneous master equation clearly fails, and propose an alternative master equation based on Lindblad superoperators which avoids most of the deficiencies of previous proposals. We discuss the strengths and limitations of the various formulations of the master equation, in the context of spin systems which are far from thermal equilibrium. The method is applied to several problems in nuclear magnetic resonance and to spin-isomer conversion.

SABRE: Chemical kinetics and spin dynamics of the formation of hyperpolarization

In this review, we present the physical principles of the SABRE (Signal Amplification By Reversible Exchange) method. SABRE is a promising hyperpolarization technique that enhances NMR signals by transferring spin order from parahydrogen (an isomer of the H₂ molecule that is in a singlet nuclear spin state) to a substrate that is to be polarized. Spin order transfer takes place in a transient organometallic complex which binds both parahydrogen and substrate molecules; after dissociation of the SABRE complex, free hyperpolarized substrate molecules are accumulated in solution. An advantage of this method is that the substrate is not modified chemically, and its polarization can be regenerated multiple times by bubbling fresh parahydrogen through the solution. Thus, SABRE requires two key ingredients: (i) polarization transfer and (ii) chemical exchange of both parahydrogen and substrate. While there are several excellent reviews on applications of SABRE, the background of the method is discussed less frequently. In this review we aim to explain in detail how SABRE hyperpolarization is formed, focusing on key aspects of both spin dynamics and chemical kinetics, as well as on the interplay between them. Hence, we first cover the known spin order transfer methods applicable to SABRE - cross-relaxation, coherent spin mixing at avoided level crossings, and coherence transfer - and discuss their practical implementation for obtaining SABRE polarization in the most efficient way. Second, we introduce and explain the principle of SABRE hyperpolarization techniques that operate at ultralow (<1 μT), at low (1μT to 0.1 T) and at high (>0.1 T) magnetic fields. Finally, chemical aspects of SABRE are discussed in detail, including chemical systems that are amenable to SABRE and the exchange processes that are required for polarization formation. A theoretical treatment of the spin dynamics and their interplay with chemical kinetics is also presented. This review outlines known aspects of SABRE and provides guidelines for the design of new SABRE experiments, with the goal of solving practical problems of enhancing weak NMR signals.

Long live the singlet state!

The field of long-lived states in NMR is reviewed. The relationship of long-lived-state phenomena to those associated with spin isomerism is discussed. A brief overview is given of key developments in the field of long-lived states, including chemical symmetry-switching, the role of magnetic equivalence and magnetic inequivalence, long-lived coherences, hyperpolarized NMR involving long-lived states, quantum-rotor-induced polarization, and parahydrogen-induced hyperpolarization. Current application areas of long-lived states are reviewed, and a peer into the crystal ball reveals future developments in the field.

Application and methodology of dissolution dynamic nuclear polarization in physical, chemical and biological contexts

Dissolution dynamic nuclear polarization (d-DNP) is a versatile method to enhance nuclear magnetic resonance (NMR) spectroscopy. It boosts signal intensities by four to five orders of magnitude thereby providing the potential to improve and enable a plethora of applications ranging from the real-time monitoring of chemical or biological processes to metabolomics and in-cell investigations. This perspectives article highlights possible avenues for developments and applications of d-DNP in biochemical and physicochemical studies. It outlines how chemists, biologists and physicists with various fields of interest can transform and employ d-DNP as a powerful characterization method for their research.

Relaxation Dynamics of Nuclear Long-Lived Spin States in Propane and Propane-d6 Hyperpolarized by Parahydrogen

We report a systematic study of relaxation dynamics of hyperpolarized (HP) propane and HP propane-d₆ prepared by heterogeneous pairwise parahydrogen addition to propylene and propylene-d₆ respectively. Long-lived spin states (LLS) created for these molecules at the low magnetic field of 0.0475 T were employed for this study. The parahydrogen-induced overpopulation of a HP propane LLS decays exponentially with time constant (T_LLS) approximately 3-fold greater than the corresponding T₁ values. Both T_LLS and T₁ increase linearly with propane pressure in the range from 1 atm (the most biomedically relevant conditions for pulmonary MRI) to 5 atm. The T_LLS value of HP propane gas at 1 atm is ~3 s. Deuteration of the substrate (propylene-d₆) yields hyperpolarized propane-d₆ gas with T_LLS values approximately 20% shorter than those of hyperpolarized fully protonated propane gas, indicating that deuteration does not benefit the lifetime of the LLS HP state. The use of pH₂ or Xe/N₂ buffering gas during heterogeneous hydrogenation reaction (leading to production of 100% HP propane (no buffering gas) versus 43% HP propane gas (with 57% buffering gas) composition mixtures) results in (i) no significant changes in T₁, (ii) decrease of T_LLS values (by 35±7% and 8±7% respectively); and (iii) an increase of the polarization levels of HP propane gas with a propane concentration decrease (by 1.6±0.1-fold and 1.4±0.1-fold respectively despite the decrease in T_LLS, which leads to disproportionately greater polarization losses during HP gas transport). Moreover, we demonstrate the feasibility of HP propane cryo-collection (which can be potentially useful for preparing larger amounts of concentrated HP propane, when buffering gas is employed), and T_LLS of liquefied HP propane reaches 14.7 seconds, which is greater than the T_LLS value of HP propane gas at any pressure studied. Finally, we have explored the utility of using a partial Spin-Lock Induced Crossing (SLIC) radio frequency (RF) pulse sequence for converting the overpopulated LLS into observable ¹H nuclear magnetization at low magnetic field. We find that (i) the bulk of the overpopulated LLS is retained even when the optimal or near-optimal values of SLIC pulse duration are employed, and (ii) the overpopulated LLS of propane is also relatively immune to strong RF pulses-thereby, indicating that LLS is highly suitable as a spin-polarization reservoir in the context of NMR/MRI detection applications. The presented findings may be useful for improving the levels of polarization of HP propane produced by HET-PHIP via the use of an inert buffer gas; increasing the lifetime of the HP state during preparation and storage; and developing efficient approaches for ultrafast MR imaging of HP propane in the context of biomedical applications of HP propane gas, including its potential use as an inhalable contrast agent.

Long-Lived States in Hyperpolarized Deuterated Methyl Groups Reveal Weak Binding of Small Molecules to Proteins

We introduce a method for the detection of weak interactions of small molecules such as metabolites or medicaments that contain deuterated methyl groups with proteins in solution. The technique relies on long-lived imbalances of spin state populations, which are generated by dissolution dynamic nuclear polarization (D-DNP) and feature lifetimes that depend on the frequency of internal rotation of deuterated methyl groups. We demonstrate the technique for interactions between deuterated dimethyl sulfoxide (DMSO- d₆) and bovine serum albumin (BSA) or trypsin, where the methyl group rotation is slowed down upon protein binding, which causes a marked reduction in the lifetime of the population imbalances.

Homonuclear ADAPT: A general preparation route to long-lived nuclear singlet order

We introduce a simple strategy to access and readout nuclear singlet order based on the alternate repetition of hard pulses and delays. We demonstrate the general applicability of the method by accessing nuclear singlet order in spin systems characterized by diverse coupling regimes. We show that the method is highly efficient in the strong-coupling and chemical equivalence regimes, and can overcome some limitations of other well-established and more elaborated pulse sequences. A simulation package is provided which allows the determination of pulse sequence parameters.

Assessment of heteronuclear long-lived states at ultralow magnetic fields

A study of long-lived spin states in hetero-nuclear spin systems is presented.

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.

Relaxation of long-lived modes in NMR of deuterated methyl groups

Long-lived imbalances of spin state populations can circumvent fast quadrupolar relaxation by reducing effective longitudinal relaxation rates by about an order of magnitude. This opens new avenues for the study of dynamic processes in deuterated molecules. Here we present an analysis of the relaxation properties of deuterated methyl groups CD₃. The number of coupled equations that describe cross-relaxation between the 27 symmetry-adapted spin states of a D₃ system can be reduced to only 2 non-trivial "lumped modes" by (i) taking the sums of the populations of all states that equilibrate rapidly within each irreducible representation of the symmetry group, and (ii) by combining populations that have similar relaxation rates although they belong to different irreducible representations. The quadrupolar relaxation rates of the spin state imbalances in CD₃ groups are determined not by the correlation time of overall tumbling of the molecule, but by the frequency of jumps of methyl groups about their three-fold symmetry axis. We access these states via dissolution dynamic nuclear polarization (D-DNP), a method that allows one to populate the desired long-lived states at cryogenic temperatures and their subsequent detection at ambient temperatures after rapid dissolution. Experimental examples of DMSO-d₆ and ethanol-d₆ demonstrate that long-lived deuterium spin states are indeed accessible and that their lifetimes can be determined. Our analysis of the system via "lumped" modes allows us to visualize different possible spin-state populations of symmetry A, B, or E. Thus, we identify a long-lived spin state involving all three deuterons in a CD₃ group as an A/E imbalance that can be populated through DNP at low temperatures.

Quantum-rotor-induced polarization

Quantum-rotor-induced polarization is closely related to para-hydrogen-induced polarization. In both cases, the hyperpolarized spin order derives from rotational interaction and the Pauli principle by which the symmetry of the rotational ground state dictates the symmetry of the associated nuclear spin state. In quantum-rotor-induced polarization, there may be several spin states associated with the rotational ground state, and the hyperpolarization is typically generated by hetero-nuclear cross-relaxation. This review discusses preconditions for quantum-rotor-induced polarization for both the 1-dimensional methyl rotor and the asymmetric rotor H₂¹⁷ O@C₆₀ , that is, a single water molecule encapsulated in fullerene C₆₀ . Experimental results are presented for both rotors.

Spin-Isomer Conversion of Water at Room Temperature and Quantum-Rotor-Induced Nuclear Polarization in the Water-Endofullerene H_{2}O@C_{60}

Water exists in two forms, para and ortho, that have nuclear spin states with different symmetries. Here we report the conversion of fullerene-encapsulated para water to ortho water. The enrichment of para water at low temperatures is monitored via changes in the electrical polarizability of the material. Upon rapid dissolution of the material in toluene the excess para water converts to ortho water. In H_{2}^{16}O@C_{60} the conversion leads to a slow increase in the NMR signal. In H_{2}^{17}O@C_{60} the conversion gives rise to weak signal enhancements attributed to quantum-rotor-induced nuclear spin polarization. The time constants for the para-to-ortho conversion of fullerene-encapsulated water in ambient temperature solution are estimated as 30±4  s for the ^{16}O isotopolog of water, and 16±3  s for the ^{17}O isotopolog.

SpinDynamica: Symbolic and numerical magnetic resonance in a Mathematica environment

SpinDynamica is a set of Mathematica packages for performing numerical and symbolic analysis of a wide range of magnetic resonance experiments and phenomena. An overview of the SpinDynamica architecture and functionality is given, with some simple representative examples.

Testing signal enhancement mechanisms in the dissolution NMR of acetone

In cryogenic dissolution NMR experiments, a substance of interest is allowed to rest in a strong magnetic field at cryogenic temperature, before dissolving the substance in a warm solvent, transferring it to a high-resolution NMR spectrometer, and observing the solution-state NMR spectrum. In some cases, negative enhancements of the ¹³C NMR signals are observed, which have been attributed to quantum-rotor-induced polarization. We show that in the case of acetone (propan-2-one) the negative signal enhancements of the methyl ¹³C sites may be understood by invoking conventional cross-relaxation within the methyl groups. The ¹H nuclei acquire a relative large net polarization through thermal equilibration in a magnetic field at low temperature, facilitated by the methyl rotation which acts as a relaxation sink; after dissolution, the ¹H magnetization slowly returns to thermal equilibrium at high temperature, in part by cross-relaxation processes, which induce a transient negative polarization of nearby ¹³C nuclei. We provide evidence for this mechanism experimentally and theoretically by saturating the ¹H magnetization using a radiofrequency field pulse sequence before dissolution and comparing the ¹³C magnetization evolution after dissolution with the results obtained from a conventional ¹H-¹³C cross relaxation model of the CH₃ moieties in acetone.

Dipolar relaxation mechanism of long-lived states of methyl groups

We analyze the symmetry properties of the dipolar Hamiltonian as the main relaxation mechanism responsible for the observed NMR spectra of long-lived states of methyl groups. Long-lived states exhibit relaxation times that are considerably longer than the spin-lattice relaxation time, T 1 . The analysis is complementary to previous studies and provides insight into the relaxation mechanism of long-lived states by focusing exclusively on the symmetry of the spin Hamiltonian. Our study shows that the dipole-dipole coupling between protons of a methyl group and between the protons and an external spin are both symmetry breaking interactions that can lead to relaxation pathways that transform the polarization from symmetry order to Zeeman order. The net contribution of the internal dipolar interaction to the NMR observation of long-lived states is zero. Our calculation is in good agreement with the reported features of the observed spectra and previous theoretical studies.

Bang-bang optimal control of large spin systems: Enhancement of 13C-13C singlet-order at natural abundance

Using a bang-bang optimal control technique, we transfer polarization from a set of abundant high-γ nuclei directly to singlet order of a low-γ spin-pair. This approach is analogous to algorithmic cooling (AC) procedure used in quantum state purification. Specifically, we apply this method for enhancing the singlet order in a natural abundant ¹³C- ¹³C spin pair by exploiting nine equivalent protons of an 11-spin system. Compared to the standard method not involving polarization transfer, we find an enhancement of singlet order by about 3.4 times. In addition, since the singlet magnetization is contributed by the faster relaxing protons, the recycle delay is halved. Thus effectively we observe a reduction in the overall experimental time by a factor of 23. We also discuss a possible extension of AC, known as heat-bath algorithmic cooling (HBAC).

Dynamic Nuclear Polarization of Long-Lived Nuclear Spin States in Methyl Groups

We have induced hyperpolarized long-lived states in compounds containing ¹³C-bearing methyl groups by dynamic nuclear polarization (DNP) at cryogenic temperatures, followed by dissolution with a warm solvent. The hyperpolarized methyl long-lived states give rise to enhanced antiphase ¹³C NMR signals in solution, which often persist for times much longer than the ¹³C and ¹H spin-lattice relaxation times under the same conditions. The DNP-induced effects are similar to quantum-rotor-induced polarization (QRIP) but are observed in a wider range of compounds because they do not depend critically on the height of the rotational barrier. We interpret our observations with a model in which nuclear Zeeman and methyl tunnelling reservoirs adopt an approximately uniform temperature, under DNP conditions. The generation of hyperpolarized NMR signals that persist for relatively long times in a range of methyl-bearing substances may be important for applications such as investigations of metabolism, enzymatic reactions, protein-ligand binding, drug screening, and molecular imaging.

Communication: Dissolution DNP reveals a long-lived deuterium spin state imbalance in methyl groups

We report the generation and observation of long-lived spin states in deuterated methyl groups by dissolution DNP. These states are based on population imbalances between manifolds of spin states corresponding to irreducible representations of the C_3v point group and feature strongly dampened quadrupolar relaxation. Their lifetime depends on the activation energies of methyl group rotation. With dissolution DNP, we can reduce the deuterium relaxation rate by a factor up to 20, thereby extending the experimentally available time window. The intrinsic limitation of NMR spectroscopy of quadrupolar spins by short relaxation times can thus be alleviated.

A pulse sequence for singlet to heteronuclear magnetization transfer: S2hM

We have recently demonstrated, in the context of para-hydrogen induced polarization (PHIP), the conversion of hyperpolarized proton singlet order into heteronuclear magnetisation can be efficiently achieved via a new sequence named S2hM (Singlet to heteronuclear Magnetisation). In this paper we give a detailed theoretical description, supported by an experimental illustration, of S2hM. Theory and experiments on thermally polarized samples demonstrate the proposed method is robust to frequency offset mismatches and radiofrequency field inhomogeneities. The simple implementation, optimisation and the high conversion efficiency, under various regimes of magnetic equivalence, makes S2hM an excellent candidate for a widespread use, particularly within the PHIP arena.

NMR Spin-Lock Induced Crossing (SLIC) dispersion and long-lived spin states of gaseous propane at low magnetic field (0.05T)

When parahydrogen reacts with propylene in low magnetic fields (e.g., 0.05T), the reaction product propane develops an overpopulation of pseudo-singlet nuclear spin states. We studied how the Spin-Lock Induced Crossing (SLIC) technique can be used to convert these pseudo-singlet spin states of hyperpolarized gaseous propane into observable magnetization and to detect ¹H NMR signal directly at 0.05T. The theoretical simulation and experimental study of the NMR signal dependence on B₁ power (SLIC amplitude) exhibits a well-resolved dispersion, which is induced by the spin-spin couplings in the eight-proton spin system of propane. We also measured the exponential decay time constants (T_LLSS or T_S) of these pseudo-singlet long-lived spin states (LLSS) by varying the time between hyperpolarized propane production and SLIC detection. We have found that, on average, T_S is approximately 3 times longer than the corresponding T₁ value under the same conditions in the range of pressures studied (up to 7.6atm). Moreover, T_S may exceed 13s at pressures above 7atm in the gas phase. These results are in agreement with the previous reports, and they corroborate a great potential of long-lived hyperpolarized propane as an inhalable gaseous contrast agent for lung imaging and as a molecular tracer to study porous media using low-field NMR and MRI.

Singlet NMR methodology in two-spin-1/2 systems

This paper discusses methodology developed over the past 12years in order to access and manipulate singlet order in systems comprising two coupled spin-1/2 nuclei in liquid-state nuclear magnetic resonance. Pulse sequences that are valid for different regimes are discussed, and fully analytical proofs are given using different spin dynamics techniques that include product operator methods, the single transition operator formalism, and average Hamiltonian theory. Methods used to filter singlet order from byproducts of pulse sequences are also listed and discussed analytically. The theoretical maximum amplitudes of the transformations achieved by these techniques are reported, together with the results of numerical simulations performed using custom-built simulation code.

Methyl rotor quantum states and the effect of chemical environment in organic crystals: γ-picoline and toluene

Using a set of first-principles calculations, we have studied the methyl tunnel splitting for molecular crystals of γ-picoline and toluene. The effective rotational potential energy surface of the probe methyl rotor along the tunneling path is evaluated using first-principles electronic structure calculations combined with the nudged elastic band method. The tunnel splitting is calculated by an explicit diagonalization of the one-dimensional time-independent Hamiltonian matrix. The effects of chemical environment and rotor-rotor coupling on the rotational energy barriers were investigated. It is found that more dense packing of the molecules in toluene compared to that in γ-picoline gives rise to a larger rotational barrier which in turn yields a considerably smaller tunnel splitting. Moreover, it turned out that coupled motion of the face-to-face methyl groups in γ-picoline has a significant effect on the reduction of the rotational barrier. Our results are in good agreement with the experimentally observed tunnel splitting.

NMR of molecular endofullerenes dissolved in a nematic liquid crystal

We report the NMR of the molecular endofullerenes H₂@C₆₀, H₂O@C₆₀ and HF@C₆₀ dissolved in the nematic liquid crystal N-(4-methoxybenzylidene)-4-butylaniline (MBBA).

Long-lived nuclear spin states in rapidly rotating CH2D groups

Although monodeuterated methyl groups support proton long-lived states, hindering of the methyl rotation limits the singlet relaxation time. We demonstrate an experimental case in which the rapid rotation of the CH₂D group extends the singlet lifetime but does not quench the chemical shift difference between the CH₂D protons, induced by the chiral environment. Proton singlet order is accessed using Spin-Lock Induced Crossing (SLIC) experiments, showing that the singlet relaxation time T_S is over 2min, exceeding the longitudinal relaxation time T₁ by a factor of more than 10. This result shows that proton singlet states may be accessible and long-lived in rapidly rotating CH₂D groups.

Challenges in preparing, preserving and detecting para-water in bulk: overcoming proton exchange and other hurdles

Para-water is an analogue of para-hydrogen, where the two proton spins are in a quantum state that is antisymmetric under permutation, also known as singlet state. The populations of the nuclear spin states in para-water are believed to have long lifetimes just like other Long-Lived States (LLSs). This hypothesis can be verified by measuring the relaxation of an excess or a deficiency of para-water, also known as a "Triplet-Singlet Imbalance" (TSI), i.e., a difference between the average population of the three triplet states T (that are symmetric under permutation) and the population of the singlet state S. In analogy with our recent findings on ethanol and fumarate, we propose to adapt the procedure for Dissolution Dynamic Nuclear Polarization (D-DNP) to prepare such a TSI in frozen water at very low temperatures in the vicinity of 1.2 K. After rapid heating and dissolution using an aprotic solvent, the TSI should be largely preserved. To assess this hypothesis, we studied the lifetime of water as a molecular entity when diluted in various solvents. In neat liquid H2O, proton exchange rates have been characterized by spin-echo experiments on oxygen-17 in natural abundance, with and without proton decoupling. One-dimensional exchange spectroscopy (EXSY) has been used to study proton exchange rates in H2O, HDO and D2O mixtures diluted in various aprotic solvents. In the case of 50 mM H2O in dioxane-d8, the proton exchange lifetime is about 20 s. After dissolving, one can observe this TSI by monitoring intensities in oxygen-17 spectra of H2O (if necessary using isotopically enriched samples) where the AX2 system comprising a "spy" oxygen A and two protons X2 gives rise to binomial multiplets only if the TSI vanishes. Alternatively, fast chemical addition to a suitable substrate (such as an activated aldehyde or ketone) can provide AX2 systems where a carbon-13 acts as a spy nucleus. Proton signals that relax to equilibrium with two distinct time constants can be considered as a hallmark of a TSI. We optimized several experimental procedures designed to preserve and reveal dilute para-water in bulk.

Symmetry constraints on spin dynamics: Application to hyperpolarized NMR

Spin dynamical evolution is constrained by the symmetries of the spin Hamiltonians that generate the quantum dynamics. The consequences of symmetry-induced constraints are examined for some common hyperpolarized NMR experiments, including the excitation of singlet order in spin-pair systems, and the transfer of parahydrogen-induced hyperpolarized singlet order to magnetization in systems displaying chemical and magnetic equivalence.

Long-lived nuclear spin states in monodeuterated methyl groups

It is possible to access long-lived nuclear singlet order in monodeuterated methyl groups, in the case that a significant chemical shift difference exists between the CH₂D protons.

Nonexponential (1)H spin-lattice relaxation and methyl group rotation in molecular solids

We report a quantitative measure of the nonexponential (1)H spin-lattice relaxation resulting from methyl group (CH3) rotation in six polycrystalline van der Waals solids. We briefly review the subject in general to put the report in context. We then summarize several significant issues to consider when reporting (1)H or (19)F spin-lattice relaxation measurements when the relaxation is resulting from the rotation of a CH3 or CF3 group in a molecular solid.