Real-space imaging of macroscopic diffusion and slow flow by singlet tagging MRI

Singlet-assisted diffusion-NMR (SAD-NMR): extending the scope of diffusion tensor imaging via singlet NMR

In this study, long-lived nuclear singlet order methods are combined with diffusion tensor imaging with the purpose of characterizing the full diffusion tensor of molecules diffusing freely in large pores of up to a millimeter in size. Such sizes are out of reach in conventional diffusion tensor imaging because of the limitations imposed by the relaxation decay constant of the longitudinal magnetization. A singlet-assisted diffusion tensor imaging methodology able to circumvent such limitations is discussed, and the new possibilities that it offers are demonstrated through simulation and experiments on plastic phantoms containing cylindrical channels of 1 mm in diameter.

A dual-core NMR system for field-cycling singlet assisted diffusion NMR

Long-lived singlet spin order offers the possibility to extend the spin memory by more than an order of magnitude. This enhancement can be used, among other applications, to assist NMR diffusion experiments in porous media where the extended lifetime of singlet spin order can be used to gain information about structural features of the medium as well as the dynamics of the imbibed phase. Other than offering the possibility to explore longer diffusion times of the order of many minutes that, for example, gives unprecedented access to tortuosity in structures with interconnected pores, singlet order has the important advantage to be immune to the internal field gradients generated by magnetic susceptibility inhomogeneities. These inhomogeneities, however, are responsible for very short T₂ decay constants in high magnetic field and this precludes access to the singlet order in the first instance. To overcome this difficulty and take advantage of singlet order in diffusion experiments in porous media, we have here developed a dual-core system with radiofrequency and 3-axis pulsed field gradients facilities in low magnetic field, for preparation and manipulation of singlet order and a probe, in high magnetic field, for polarisation and detection. The system operates in field-cycling and can be used for a variety of NMR experiments including diffusion tensor imaging (both singlet assisted and not). In this paper we present and discuss the new hardware and its calibration, and demonstrate its capabilities through a variety of examples.

Long-Lived States Provide Insights from NMR into the β-Cyclodextrin Drug Assemblies

In the last two decades, extending spin memory in NMR has been used for several purposes. Long-lived states (LLS) or singlet states are one of the first spin memory enhancement techniques used. LLS have the potential to extract structural information and intra- and intermolecular interactions of complex systems other than studying slow phenomenon. The motional regime of β-cyclodextrin (β-CD) drug inclusion complexes generally lies in the intermediate region, where ωτ_c ≈ 1, and the standard methods of studying these interactions, i.e., NOE and chemical shift monitoring, suffer from insufficient output information. The sensitivity of LLS toward the environmental changes is utilized here to gain insights into the drug assemblies formed by β-CD. One can use change in relaxation of LLS to study the structural changes during complexation. The examples of β-CD with the drugs indomethacin, paracetamol, gliclazide, and CI-933 (a precursor 4-methoxybenzamide) were studied. Indomethacin, paracetamol, and 4-methoxybenzamide show strong interaction through the para-substituted benzene ring, unlike gliclazide. Relaxation of LLS in β-CD-drug complexes is modeled using standard Redfield Relaxation Theory. Computational studies performed support the experimental observations. Docking and molecular dynamics simulation provided the explanation of the relaxation properties of these drug molecules.

In vivo singlet state filtered nuclear magnetic resonance: towards monitoring toxic responses inside living organisms

In line with recent paradigm shifts in toxicity testing, in vivo nuclear magnetic resonance (NMR) is a powerful tool for studying the biological impacts and perturbations caused by toxicants in living organisms. However, despite the excellent molecular insights that can be obtained through this technique, in vivo NMR applications are hampered by considerable experimental challenges such as poor line shape and spectral overlap. Here, we demonstrate the application of singlet-filtered NMR to target specific metabolites and facilitate the study of metabolite fluxes in living Daphnia magna, an aquatic keystone species and model organism. Informed by mathematical simulations and experiments on ex vivo organisms, singlet state NMR is used to monitor the flux of metabolites such as d-glucose and serine in living D. magna, during the environmentally relevant processes of anoxic stress and reduced food availability. Overall, singlet state NMR is shown to have significant future potential for studying metabolic processes in vivo.

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.

31P spin-lattice and singlet order relaxation mechanisms in pyrophosphate studied by isotopic substitution, field shuttling NMR, and molecular dynamics simulation

Nuclear spin relaxation mechanisms are often difficult to isolate and identify, especially in molecules with internal flexibility. Here we combine experimental work with computation in order to determine the major mechanisms responsible for ³¹P spin-lattice and singlet order (SO) relaxation in pyrophosphate, a physiologically relevant molecule. Using field-shuttling relaxation measurements (from 2 μT to 9.4 T) and rates calculated from molecular dynamics (MD) trajectories, we identified chemical shift anisotropy (CSA) and spin-rotation as the major mechanisms, with minor contributions from intra- and intermolecular coupling. The significant spin-rotation interaction is a consequence of the relatively rapid rotation of the -PO₃^2- entities around the bridging P-O bonds, and is treated by a combination of MD simulations and quantum chemistry calculations. Spin-lattice relaxation was predicted well without adjustable parameters, and for SO relaxation one parameter was extracted from the comparison between experiment and computation (a correlation coefficient between the rotational motion of the groups).

Theory and Simulation Framework for the Relaxation of Nuclear Spin Order in Porous Media

The theory of nuclear spin relaxation in a liquid permeating a solid structure of irregular geometry is examined. The effects of restricted diffusion and the demagnetizing field generated by an inhomogeneous distribution of magnetic susceptibility in the system are explored. A framework comprising Brownian Dynamics, average Hamiltonian theory, and Liouville-space spin dynamics is proposed for simulating nuclear spin relaxation in 3D models of random structures obtained from CT scans of actual samples. Simulations results are compared with experimental data. An analytical solution valid within approximation is also reported.

Prediction of 1H Singlet Relaxation via Intermolecular Dipolar Couplings Using the Molecular Dynamics Method

Dissolution dynamic nuclear polarization has been applied in various fields, including chemistry, biology, and medical science. To expand the scope of these applications, the nuclear singlet state, which is decoherence-free against dipolar relaxation between spin pairs, has been studied experimentally, theoretically, and numerically. The singlet state composed of proton spins is used in several applications, such as enhanced polarization preservation, molecular tagging to probe slow dynamic processes, and detection of ligand-protein complexes. In this study, we predict the lifetimes of the nuclear spin states composed of proton spin pairs using the molecular dynamics method and quantum chemistry simulations. We consider intramolecular dipolar, intermolecular dipolar between solvent and solute, chemical shift anisotropy, and spin-rotation interactions. In particular, the relaxation rate of intermolecular dipolar interactions is calculated using the molecular dynamics method for various solvents. The calculated values and the experimental values are of the same order of magnitude. Our program would provide insight into the molecular design of several NMR applications and would be helpful in predicting the nuclear spin relaxation time of synthetic molecules in advance.

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.

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.

Localized singlet-filtered MRS in vivo

MR is a prominent technology to investigate diseases, with millions of clinical procedures performed every year. Metabolic dysfunction is one common aspect associated with many diseases. Thus, understanding and monitoring metabolic changes is essential to develop cures for many illnesses, including for example cancer and neurodegeneration. MR methodologies are especially suited to study endogenous metabolites and processes within an organism in vivo, which has led to many insights about physiological functions. Advancing metabolic MR techniques is therefore key to further understand physiological processes. Here, we introduce an approach based on nuclear spin singlet states to specifically filter metabolic signals and particularly show that singlet-filtered glutamate can be observed distinctly in the hippocampus of a living mouse in vivo. This development opens opportunities to make use of the singlet spin phenomenon in vivo and besides its use as a filter to provide scope for new contrast agents.

Large-scale magnetic resonance simulations: A tutorial

Computational modeling is becoming an essential tool in magnetic resonance to design and optimize experiments, test the performance of theoretical models, and interpret experimental data. Recent theoretical research and software development made possible simulations of large spin systems, for example, proteins with thousands of spins, in reasonable time. In the last few years, the Fokker-Planck formalism also re-emerged due to its ability to handle spatial dynamics. The purpose of this tutorial is to describe advantages and disadvantages of the most common formalisms, the latest developments and strategies to improve the computational efficiency, and to guide users in the setting up of a simulation using the Spinach software.

Preparation of Long-Lived States in a Multi-Spin System by Using an Optimal Control Method

The lifetime Ts of a long-lived nuclear spin state (LLS) could be much longer than the longitudinal order T₁ . Many spin systems were used to produce long-lived states, including two or more homonuclear spins that couple to each other. For multiple homonuclear spins with rather small chemical shift difference, normally it is difficult to selectively control the spins and then to prepare a LLS. Herein, we present a scheme that prepares different spin orders in a multi-spin system by using optimal control and numerical calculation. By experimentally measuring the lifetime of the states, we find that for a three-spin physical system, although there are many forms of state combinations with different spin orders, each component has its own lifetime.

Generalised magnetisation-to-singlet-order transfer in nuclear magnetic resonance

A variety of pulse sequences have been described for converting nuclear spin magnetisation into long-lived singlet order for nuclear spin-1/2 pairs. Existing sequences operate well in two extreme parameter regimes. The magnetisation-to-singlet (M2S) pulse sequence performs a robust conversion of nuclear spin magnetisation into singlet order in the near-equivalent limit, meaning that the difference in chemical shift frequencies of the two spins is much smaller than the spin-spin coupling. Other pulse sequences operate in the strong-inequivalence regime, where the shift difference is much larger than the spin-spin coupling. However both sets of pulse sequences fail in the intermediate regime, where the chemical shift difference and the spin-spin coupling are roughly equal in magnitude. We describe a generalised version of M2S, called gM2S, which achieves robust singlet order excitation for spin systems ranging from the near-equivalence limit well into the intermediate regime. This closes an important gap left by existing pulse sequences. The efficiency of the gM2S sequence is demonstrated numerically and experimentally for near-equivalent and intermediate-regime cases.

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.

Generating and sustaining long-lived spin states in 15N,15N'-azobenzene

Long-Lived spin States (LLSs) hold a great promise for sustaining non-thermal spin order and investigating various slow processes by Nuclear Magnetic Resonance (NMR) spectroscopy. Of special interest for such application are molecules containing nearly equivalent magnetic nuclei, which possess LLSs even at high magnetic fields. In this work, we report an LLS in trans-¹⁵N,¹⁵N′-azobenzene. The singlet state of the ¹⁵N spin pair exhibits a long-lived character. We solve the challenging problem of generating and detecting this LLS and further increase the LLS population by converting the much higher magnetization of protons into the ¹⁵N singlet spin order. As far as the longevity of this spin order is concerned, various schemes have been tested for sustaining the LLS. Lifetimes of 17 minutes have been achieved at 16.4 T, a value about 250 times longer than the longitudinal relaxation time of ¹⁵N in this magnetic field. We believe that such extended relaxation times, along with the photochromic properties of azobenzene, which changes conformation upon light irradiation and can be hyperpolarized by using parahydrogen, are promising for designing new experiments with photo-switchable long-lived hyperpolarization.

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.

Terminal Diazirines Enable Reverse Polarization Transfer from 15 N2 Singlets

Diazirine moieties are chemically stable and have been incorporated into biomolecules without impediment of biological activity. The ¹⁵ N₂ labeled diazirines are appealing motifs for hyperpolarization supporting relaxation protected states with long-lived lifetimes. The (-CH¹⁵ N₂ ) diazirine groups investigated here are analogues to methyl groups, which provides the opportunity to transfer polarization stored on a relaxation protected (-CH¹⁵ N₂ ) moiety to ¹ H, thus combining the advantages of long lifetimes of ¹⁵ N polarization with superior sensitivity of ¹ H detection. Despite the proximity of ¹ H to ¹⁵ N nuclei in the diazirine moiety, ¹⁵ N T₁ times of up to (4.6±0.4) min and singlet lifetimes T_s of up to (17.5±3.8) min are observed. Furthermore, we found terminal diazirines to support hyperpolarized ¹ H₂ singlet states in CH₂ groups of chiral molecules. The singlet lifetime of ¹ H singlets is up to (9.2±1.8) min, thus exceeding ¹ H T₁ relaxation time (at 8.45 T) by a factor of ≈100.

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.

Diffusional attenuation during soft pulses: A Zangger-Sterk pure shift iDOSY experiment

Diffusion-ordered spectroscopy experiments in which existing delays in a parent pulse sequence are used for diffusion encoding - iDOSY experiments - are potentially attractive because of their simplicity and sensitivity. However the calculation of diffusional attenuation in Zangger-Sterk pure shift iDOSY experiments is a very difficult problem to attack analytically, and is more easily approached numerically. Numerical simulations show that for typical experimental conditions, the dependence of diffusional attenuation on diffusion-encoding gradient amplitude is well represented by a shifted Gaussian function. The shift in gradient can be calculated analytically for the limiting case where the selective pulse is replaced by a hard 180° pulse at its midpoint; numerical simulations show that the effect of using different shapes of selective pulse is to scale down this limiting gradient shift by a constant factor that depends on the pulse shape used. The practical consequence is that under the experimental conditions appropriate for small molecules, the pure shift iDOSY method should allow good diffusion coefficient measurements to be made if appropriate allowance is made for the change in effective diffusion-encoding gradient. Parallel sets of numerical simulations and experiments are presented, and a practical application of a Zangger-Sterk pure shift iDOSY experiment to a simple test mixture is illustrated.

Nuclear singlet relaxation by scalar relaxation of the second kind in the slow-fluctuation regime

The singlet state of nuclear spin-1/2 pairs is protected against many common relaxation mechanisms. Singlet order, which is defined as the population difference between the nuclear singlet and triplet states, usually decays more slowly than the nuclear magnetization. Nevertheless, some decay mechanisms for nuclear singlet order persist. One such mechanism is called scalar relaxation of the second kind (SR2K) and involves the relaxation of additional nuclei ("third spins") which have scalar couplings to the spin-1/2 pair. This mechanism requires a difference between the couplings of at least one third spin with the two members of the spin-1/2 pair, and depends on the longitudinal relaxation time of the third spin. The SR2K mechanism of nuclear singlet relaxation has previously been examined in the case where the relaxation rate of the additional spins is on the time scale of the nuclear Larmor frequency. In this paper, we consider a different regime, in which the longitudinal relaxation of the third spins is on a similar time scale to the J-coupling between the members of the spin pair. This regime is often encountered when the spin-1/2 pair has scalar couplings to nearby deuterium nuclei. We show that the SR2K mechanism may be suppressed in this regime by applying a radiofrequency field which is resonant either with the members of the spin pair, or with the third spins. These phenomena are analyzed theoretically and by numerical simulations, and demonstrated experimentally on a diester of [¹³C₂, ²H₂]-labeled fumarate in solution.

Assessment of heteronuclear long-lived states at ultralow magnetic fields

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

Experimental evidence for the role of paramagnetic oxygen concentration on the decay of long-lived nuclear spin order

The sensitivity of longitudinal magnetization and singlet order to relaxation from dissolved paramagnetic oxygen sources in solution is investigated experimentally.

Singlet excitation in the intermediate magnetic equivalence regime and field-dependent study of singlet–triplet leakage

Measuring field-dependence of singlet lifetimes in the intermediate magnetic equivalence regime.

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.

Using optimal control methods with constraints to generate singlet states in NMR

A method is proposed for optimizing the performance of the APSOC (Adiabatic-Passage Spin Order Conversion) technique, which can be exploited in NMR experiments with singlet spin states. In this technique magnetization-to-singlet conversion (and singlet-to-magnetization conversion) is performed by using adiabatically ramped RF-fields. Optimization utilizes the GRAPE (Gradient Ascent Pulse Engineering) approach, in which for a fixed search area we assume monotonicity to the envelope of the RF-field. Such an approach allows one to achieve much better performance for APSOC; consequently, the efficiency of magnetization-to-singlet conversion is greatly improved as compared to simple model RF-ramps, e.g., linear ramps. We also demonstrate that the optimization method is reasonably robust to possible inaccuracies in determining NMR parameters of the spin system under study and also in setting the RF-field parameters. The present approach can be exploited in other NMR and EPR applications using adiabatic switching of spin Hamiltonians.

Hyperpolarized long-lived nuclear spin states in monodeuterated methyl groups

Monodeuterated methyl groups may support a long-lived nuclear spin state, with a relaxation time exceeding the conventional spin-lattice relaxation time T1. Dissolution-DNP (dynamic nuclear polarization) may be used to hyperpolarize such a long-lived spin state. This is demonstrated for the CH2D groups of a piperidine derivative. The polarized sample is manipulated in the ambient magnetic field of the laboratory, without destruction of the hyperpolarized singlet order. Strongly enhanced CH2D signals are observed more than one minute after dissolution, even in the presence of paramagnetic radicals, by which time the NMR signal from the hyperpolarized proton magnetization has completely disappeared.

Singlet-assisted diffusion-NMR (SAD-NMR): redefining the limits when measuring tortuosity in porous media

Long-lived singlet order is exploited in diffusion NMR experiments to successfully measure the tortuosity of randomly packed spheres with diameters ranging from 500 to 1000 μm.

Accessing the long-time limit in diffusion NMR: The case of singlet assisted diffusive diffraction q-space

The latest developments in the field of long-lived spin states are merged with pulsed-field gradient techniques to extend the diffusion time beyond what is currently achievable in standard q-space diffusive-diffraction studies. The method uses nearly-equivalent spin-1/2 pairs that let diffusion times of the order of many minutes to be measured allowing access to the long-time limit in cavities of macroscopic size (millimeters). A pulse sequence suitable to exploit this regime has been developed and validated with the use of numerical simulations and experiments.

Effect of convection and B1 inhomogeneity on singlet relaxation experiments

Nuclear spin singlet lifetimes can often exceed the T₁ length scales by a large factor. This property makes them suitable for polarization storage. The measurement of such long lifetimes itself can become challenging due to the influence of even very weak relaxation mechanisms. Here we show that a judicious choice of the singlet-to-triplet conversion method is highly important in order to achieve reliable singlet relaxation measurements. In particular, we identify thermal convection, in connection with B₁ field gradients, asa significant apparent decay mechanism, which limits the ability to measure the true singlet state lifetimes. Highly B₁-compensated broadband singlet excitation/detection sequences are shown to minimize the influence of macroscopic molecular motion and B₁ inhomogeneity.

Origins of Small Proton Chemical Shift Differences in Monodeuterated Methyl Groups

We have recently shown that the small proton chemical shift difference in 2-methyl-1-(methyl-d)piperidine supports a long-lived nuclear spin state. To identify additional candidate molecules with CH₂D groups exhibiting accessible long-lived states, and to investigate the factors governing the magnitude of the shift differences, we report a computational and experimental investigation of methyl rotational equilibria and proton chemical shifts in a variety of 2-substituted 1-(methyl-d)piperidines. The polarity and size of the 2-substituent affect the 1,2-stereoisomeric relationship, and consequently, the strength of the rotational asymmetry within the CH₂D group. Nonpolar and large 2-substituents prefer the equatorial position, and relatively large shift differences (i.e., > 13 ppb) are observed. Polar and small substituents, however, increasingly prefer the axial position, and medium to small shift differences (i.e., 0 to 9 ppb) are observed. In addition, the diastereotopic CH₂D proton chemical shift difference for tricarbonyl(1-chloro-2-deuteriomethylbenzene) chromium(0) was computed, showing that reasonable predictions of these small shift differences can be extended to more complex, organometallic species.

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.

Efficient simulation of ultrafast magnetic resonance experiments

We present a convenient and powerful simulation formalism for ultrafast NMR spectroscopy. The formalism is based on the Fokker–Planck equation that supports systems with complicated combinations of classical spatial dynamics and quantum mechanical spin dynamics.

Prediction of low-field nuclear singlet lifetimes with molecular dynamics and quantum-chemical property surface

Molecular dynamics and quantum chemistry methods are implemented to quantify nuclear spin-1/2 pair singlet-state relaxation rates. Illustrated is the relevant spin-internal-motion mechanism (SIM).

Robust conversion of singlet spin order in coupled spin-1/2 pairs by adiabatically ramped RF-fields

We propose a robust and highly efficient NMR technique to create singlet spin order from longitudinal spin magnetization in coupled spin-½ pairs and to perform backward conversion (singlet order)→magnetization. In this method we exploit adiabatic ramping of an RF-field in order to drive transitions between the singlet state and the T_± triplet states of a spin pair under study. We demonstrate that the method works perfectly for both strongly and weakly coupled spin pairs, providing a conversion efficiency between the singlet spin order and magnetization, which is equal to the theoretical maximum. We anticipate that the proposed technique is useful for generating long-lived singlet order, for preserving spin hyperpolarization and for analyzing singlet spin order in nearly equivalent spin pairs in specially designed molecules and in low-field NMR studies.

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.

Fokker-Planck formalism in magnetic resonance simulations

This paper presents an overview of the Fokker-Planck formalism for non-biological magnetic resonance simulations, describes its existing applications and proposes some novel ones. The most attractive feature of Fokker-Planck theory compared to the commonly used Liouville - von Neumann equation is that, for all relevant types of spatial dynamics (spinning, diffusion, stationary flow, etc.), the corresponding Fokker-Planck Hamiltonian is time-independent. Many difficult NMR, EPR and MRI simulation problems (multiple rotation NMR, ultrafast NMR, gradient-based zero-quantum filters, diffusion and flow NMR, off-resonance soft microwave pulses in EPR, spin-spin coupling effects in MRI, etc.) are simplified significantly in Fokker-Planck space. The paper also summarises the author's experiences with writing and using the corresponding modules of the Spinach library - the methods described below have enabled a large variety of simulations previously considered too complicated for routine practical use.

Limits in Proton Nuclear Singlet-State Lifetimes Measured with para-Hydrogen-Induced Polarization

The synthesis of a hyperpolarized molecule was developed, where the polarization and the singlet state were preserved over two controlled chemical steps. Nuclear singlet-state lifetimes close to 6 min for protons are reported in dimethyl fumarate. Owing to the high symmetry (AA'X₃ X₃ ' and A₂ systems), the singlet-state readout requires either a chemical desymmetrization or a long and repeated spin lock. Using DFT calculations and relaxation models, we further determine nuclear spin singlet lifetime limiting factors, which include the intramolecular dipolar coupling mechanism (proton-proton and proton-deuterium), the chemical shift anisotropy mechanism (symmetric and antisymmetric), and the intermolecular dipolar coupling mechanism (to oxygen and deuterium). If the limit of paramagnetic relaxation caused by residual oxygen could be lifted, the intramolecular dipolar coupling to deuterium would become the limiting relaxation mechanism and proton lifetimes upwards of 26 min could become available in the molecules considered here (dimethyl maleate and dimethyl fumarate).

Long-lived spin states as a source of contrast in magnetic resonance spectroscopy and imaging

A method is proposed to create Long-Lived spin States (LLSs) from longitudinal spin magnetization, which is based on adiabatic switching of a Radio-Frequency (RF) field with proper frequency. The technique is simple to implement with standard Nuclear Magnetic Resonance (NMR) equipment, providing an excellent conversion of population from the triplet T+ (or T-) state to the singlet state of a pair of spins and back. The method has been tested for the amino acid tyrosine and its partially deuterated isotopomer; for the deuterated compound, we have achieved a LLS lifetime, which exceeds the longitudinal relaxation time by a factor of 21. Furthermore, by slightly modifying the method, an enhanced contrast with respect to LLSs in NMR spectra is achieved; contrast enhancements of more than 1200 are feasible. This enables efficient suppression of longitudinal spin magnetization in NMR allowing one to look selectively at LLSs. Using this method we have demonstrated that not only spectral but also spatial contrast can be achieved: we have obtained spatial NMR images with strongly improved contrast originating from the difference of LLS lifetimes at different positions in the sample.