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

NMR spectroscopy of a 18O-labeled rhodium paddlewheel complex: Isotope shifts, 103Rh-103Rh spin-spin coupling, and 103Rh singlet NMR

Despite the importance of rhodium complexes in catalysis, and the favorable 100% natural abundance of the spin-1/2 103Rh nucleus, there are few reports of 103Rh nuclear magnetic resonance (NMR) parameters in the literature. In part, this is the consequence of the very low gyromagnetic ratio of 103Rh and its dismal NMR sensitivity. In a previous paper [Harbor-Collins et al., J. Chem. Phys. 159, 104 307 (2023)], we demonstrated an NMR methodology for 1H-enhanced 103Rh NMR and demonstrated an application to the 103Rh NMR of the dirhodium formate paddlewheel complex. In this paper, we employ selective 18O labeling to break the magnetic equivalence of the 103Rh spin pair of dirhodium formate. This allows the estimation of the 103Rh-103Rh spin-spin coupling and provides access to the 103Rh singlet state. We present the first measurement of a 18O-induced 103Rh secondary isotope shift as well as the first instance of singlet order generated in a 103Rh spin pair. The field-dependence of 103Rh singlet relaxation is measured by field-cycling NMR experiments.

Selective filtration of NMR signals arising from weakly- and strongly-coupled spin systems

Nuclear magnetic resonance (NMR) spectroscopy is a powerful technique for analyzing chemical and biological systems. However, in complex solutions with similar molecular components, NMR signals can overlap, making it challenging to distinguish and quantify individual species. In this paper, we introduce new spectral editing sequences that exploit the differences in nuclear spin interactions (J-couplings) between weakly- and strongly-coupled two-spin systems. These sequences selectively attenuate or nullify undesired spin magnetization while they preserve the desired signals, resulting in simplified NMR spectra and potentially facilitating single-species imaging applications. We demonstrate the effectiveness of our approach using a 31P spectral filtration method on a model system of nicotinamide dinucleotide (NAD), which exists in oxidized (NAD+) and reduced (NADH) forms. The presented sequences are robust to field inhomogeneity, do not require additional sub-spectra, and retain a significant portion of the original signal.

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.

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).

Selective Excitation of Long-Lived Nuclear Spin States

Nuclear magnetization storage, once limited by longitudinal and transverse relaxation lifetimes, T₁ and T₂, can be prolonged by symmetry-adapted nuclear spin order, i.e. long-lived states (LLS) and long-lived coherences (LLC), which have significantly extended relaxation time constants compared to T₁ and T₂, respectively. Excitation and/or detection of LLS currently involves pulses covering wide frequency ranges in high-magnetic-field spectrometers. This leads to excitation of unwanted signals that may overlap and interfere with the resonances of interest. Herein, we present a new pulse sequence that converts longitudinal magnetization to LLS and further to detectable magnetization using only frequency-selective pulses. We demonstrate the suitability of this sequence for different J-coupled spin pairs in dipeptide AlaGly and protein Ubiquitin. The newly developed method is adapted for investigations of LLS in complex systems such as proteins and mixtures of metabolites where selected molecular groups are to be investigated separately.

Adaptable Singlet-Filtered Nuclear Magnetic Resonance Spectroscopy for Chemical and Biological Applications

Proton nuclear magnetic resonance (¹H NMR) spectroscopy presents a powerful detection tool for studying chemical compositions and molecular structures. In practical chemical and biological applications, ¹H NMR experiments are generally confronted with the challenge of spectral congestions caused by abundant observable components and intrinsic limitations of a narrow frequency distribution range and extensive J coupling splitting. Herein, a one-dimensional (1D) general NMR method is proposed to individually extract the signals of targeted proton groups based on their endogenous spin singlet states excited from J coupling interactions, and it is suitable for high-resolution detections on complex chemical and biological samples. The applicability of the proposed method is demonstrated by experimental observations on chemical solutions containing different coupled components, intact grape tissues subjected to crowded resonances, and in vitro pig brain with various metabolites. Moreover, the proposed method is further exploited for magnetic resonance spectroscopy applications by directly combining the spatial localization module, showing promise in in vivo biological metabolite studies.

Early Divergence in Misfolding Pathways of Amyloid-Beta Peptides

The amyloid cascade hypothesis proposes that amyloid‐beta (Aβ) aggregation is the initial triggering event in Alzheimer's disease. Here, we utilize NMR spectroscopy and monitor the structural dynamics of two variants of Aβ, Aβ40 and Aβ42, as a function of temperature. Despite having identical amino acid sequence except for the two additional C‐terminal residues, Aβ42 has higher aggregation propensity than Aβ40. As revealed by the NMR data on dynamics, including backbone chemical shifts, intra‐methyl cross‐correlated relaxation rates and glycine‐based singlet‐states, the C‐terminal region of Aβ, especially the G33‐L34‐M35 segment, plays a particular role in the early steps of temperature‐induced Aβ aggregation. In Aβ42, the distinct dynamical behaviour of C‐terminal residues at higher temperatures is accompanied with marked changes in the backbone dynamics of residues V24‐K28. The distinctive role of the C‐terminal region of Aβ42 in the initiation of aggregation defines a target for the rational design of Aβ42 aggregation inhibitors.

Mechanisms of coherent re-arrangement for long-lived spin order

Long-lived spin order-based approaches for magnetic resonance rely on the transition between two magnetic environments of different symmetries, one governed by the magnetic field of the spectrometer and the other where this strong magnetic field is inconsequential. Research on the excitation of magnetic-symmetry transitions in nuclear spins is a scientific field that debuted in Southampton in the year 2000. We advanced in this field carrying the baggage of pre-established directions in NMR spectroscopy. We propose to reveal herein the part of discoveries that may have been obscured by our choice to only look at them through the experience of such pre-established directions at the time. The methodological developments that are emphasised herein are the mechanisms of translation between the symmetric and non-symmetric environments with respect to the main magnetic field B 0 . More specifically, we look again thoroughly at zero-quantum rotations in the starting blocks of long-lived state populations, magnetisation transfers between hyperpolarised heteronuclei, and protons. These pulse sequences seed subsequent magnetic mechanisms that contribute to further applications. For instance, we show how some of the introduced coherence rotations were combined with classical pulse blocks to obtain two-dimensional correlations between protons and heteronuclei. We hope the pulse sequence building blocks discussed herein will open further perspectives for magnetic resonance experiments with long-lived spin order.

Rotating-Frame Overhauser Transfer via Long-Lived Coherences

Solution-state distance restraints for protein structure determination with Ångström-level resolution rely on through-space transfer of magnetization between nuclear spins. Such magnetization transfers, named Overhauser effects, occur via dipolar magnetic couplings. We demonstrate improvements in magnetization transfer using long-lived coherences (LLCs)—singlet-triplet superpositions that are antisymmetric with respect to spin-permutation within pairs of coupled magnetic nuclei—as the magnetization source. Magnetization transfers in the presence of radio-frequency irradiation, known as ‘rotating-frame’ Overhauser effects (ROEs), are predicted by theory to improve by the use of LLCs; calculations are matched by preliminary experiments herein. The LLC-ROE transfers were compared to the transmission of magnetization via classical transverse routes. Long-lived coherences accumulate magnetization on an external third proton, K, with transfer rates that depended on the tumbling regime. I,S →K transfers in the LLC configuration for (I,S) are anticipated to match, and then overcome, the same transfer rates in the classical configuration as the molecular rotational correlation times increase. Experimentally, we measured the LLC-ROE transfer in dipeptide AlaGly between aliphatic protons in different residues K = Ala − Hα and (I,S) = Gly − Hα1,2 over a distance dK,I,S = 2.3 Å. Based on spin dynamics calculations, we anticipate that, for such distances, a superior transfer of magnetization occurs using LLC-ROE compared to classical ROE at correlation times above τC=10 ns. The LLC-ROE effect shows potential for improving structural studies of large proteins and offering constraints of increased precision for high-affinity protein-ligand complexes in slow tumbling in the liquid state.

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.

Singlet-Contrast Magnetic Resonance Imaging: Unlocking Hyperpolarization with Metabolism*

Hyperpolarization-enhanced magnetic resonance imaging can be used to study biomolecular processes in the body, but typically requires nuclei such as 13 C, 15 N, or 129 Xe due to their long spin-polarization lifetimes and the absence of a proton-background signal from water and fat in the images. Here we present a novel type of 1 H imaging, in which hyperpolarized spin order is locked in a nonmagnetic long-lived correlated (singlet) state, and is only liberated for imaging by a specific biochemical reaction. In this work we produce hyperpolarized fumarate via chemical reaction of a precursor molecule with para-enriched hydrogen gas, and the proton singlet order in fumarate is released as antiphase NMR signals by enzymatic conversion to malate in D2 O. Using this model system we show two pulse sequences to rephase the NMR signals for imaging and suppress the background signals from water. The hyperpolarization-enhanced 1 H-imaging modality presented here can allow for hyperpolarized imaging without the need for low-abundance, low-sensitivity heteronuclei.

Symmetry versus entropy: Long-lived states and coherences

In recent years, new molecular symmetry-based approaches for magnetic resonance have been invented. The implications of these discoveries will be significant for molecular imaging via magnetic resonance, in vitro as well as in vivo, for quantum computing and for other fields. Since the initial observation in 2004 in Southampton that effective spin symmetry can be instilled in a molecule during magnetic resonance experiments, spin states that are resilient to relaxation mechanisms have been increasingly used. Most of these states are related to the nuclear singlet in a pair of J-coupled spins. Tailored relaxation rate constants for magnetization became available in molecules of different sizes and structures, as experimental developments broadened the scope of symmetry-adapted spin states. The ensuing access to timescales longer than the classically-attained ones by circa one order of magnitude allows the study of processes such as slow diffusion or slow exchange that were previously beyond reach. Long-lived states formed by differences between populations of singlets and triplets have overcome the limitations imposed by longitudinal relaxation times (T₁) by factors up to 40. Long-lived coherences formed by superpositions of singlets and triplets have overcome the limit of classical transverse coherence (T₂) by a factor 9. We present here an overview of the development and applications of long-lived states (LLS) and long-lived coherences (LLC's) and considerations on future perspectives.

Representation of population exchange at level anti-crossings

A theoretical framework is proposed to describe the spin dynamics driven by coherent spin mixing at level anti-crossings (LACs). We briefly introduce the LAC concept and propose to describe the spin dynamics using a vector of populations of the diabatic eigenstates. In this description, each LAC gives rise to a pairwise redistribution of eigenstate populations, allowing one to construct the total evolution operator of the spin system. Additionally, we take into account that in the course of spin evolution a "rotation" of the eigenstate basis case take place. The approach is illustrated by a number of examples, dealing with magnetic field inversion, cross-polarization, singlet-state nuclear magnetic resonance and parahydrogen-induced polarization.

Magnetization Lifetimes Prediction and Measurements Using Long-Lived Spin States in Endogenous Molecules

Nuclear magnetization storage in biologically-relevant molecules opens new possibilities for the investigation of metabolic pathways, provided the lifetimes of magnetization are sufficiently long. Dissolution-dynamic nuclear polarization-based spin-order enhancement, sustained by long-lived states can measure the ratios between concentrations of endogenous molecules on a cellular pathway. These ratios can be used as meters of enzyme function. Biological states featuring intracellular amino-acid concentrations that are depleted or replenished in the course of in-cell or in-vivo tests of drugs or radiation treatments can be revealed. Progressing from already-established long-lived states, we investigated related spin order in the case of amino acids and other metabolites featuring networks of coupled spins counting up to eight nuclei. We detail a new integrated theoretical approach between quantum chemistry simulations, chemical shifts, J-couplings information from databanks, and spin dynamics calculations to deduce a priori magnetization lifetimes in biomarkers. The lifetimes of long-lived states for several amino acids were also measured experimentally in order to ascertain the approach. Experimental values were in fair agreement with the computed ones and prior data in the literature.

In vitro singlet state and zero-quantum encoded magnetic resonance spectroscopy: Illustration with N-acetyl-aspartate

Magnetic resonance spectroscopy (MRS) allows the analysis of biochemical processes non-invasively and in vivo. Still, its application in clinical diagnostics is rare. Routine MRS is limited to spatial, chemical and temporal resolutions of cubic centimetres, mM and minutes. In fact, the signal of many metabolites is strong enough for detection, but the resonances significantly overlap, exacerbating identification and quantification. Besides, the signals of water and lipids are much stronger and dominate the entire spectrum. To suppress the background and isolate selected signals, usually, relaxation times, J-coupling and chemical shifts are used. Here, we propose methods to isolate the signals of selected molecular groups within endogenous metabolites by using long-lived spin states (LLS). We exemplify the method by preparing the LLSs of coupled protons in the endogenous molecules N-acetyl-L-aspartic acid (NAA). First, we store polarization in long-lived, double spin states, followed by saturation pulses before the spin order is converted back to observable magnetization or double quantum filters to suppress background signals. We show that LLS and zero-quantum coherences can be used to selectively prepare and measure the signals of chosen metabolites or drugs in the presence of water, inhomogeneous field and highly concentrated fatty solutions. The strong suppression of unwanted signals achieved allowed us to measure pH as a function of chemical shift difference.

A simple and cost-efficient technique to generate hyperpolarized long-lived 15N-15N nuclear spin order in a diazine by signal amplification by reversible exchange

Signal Amplification by Reversible Exchange (SABRE) is an inexpensive and simple hyperpolarization technique that is capable of boosting nuclear magnetic resonance sensitivity by several orders of magnitude. It utilizes the reversible binding of para-hydrogen, as hydride ligands, and a substrate of interest to a metal catalyst to allow for polarization transfer from para-hydrogen into substrate nuclear spins. While the resulting nuclear spin populations can be dramatically larger than those normally created, their lifetime sets a strict upper limit on the experimental timeframe. Consequently, short nuclear spin lifetimes are a challenge for hyperpolarized metabolic imaging. In this report, we demonstrate how both hyperpolarization and long nuclear spin lifetime can be simultaneously achieved in nitrogen-15 containing derivatives of pyridazine and phthalazine by SABRE. These substrates were chosen to reflect two distinct classes of ¹⁵N₂-coupled species that differ according to their chemical symmetry and thereby achieve different nuclear spin lifetimes. The pyridazine derivative proves to exhibit a signal lifetime of ∼2.5 min and can be produced with a signal enhancement of ∼2700. In contrast, while the phthalazine derivative yields a superior 15 000-fold ¹⁵N signal enhancement at 11.7 T, it has a much shorter signal lifetime.

Water hydrogen uptake in biomolecules detected via nuclear magnetic phosphorescence

We introduce a new symmetry-based method for structural investigations of areas surrounding water-exchanging hydrogens in biomolecules by liquid-state nuclear magnetic resonance spectroscopy. Native structures of peptides and proteins can be solved by NMR with fair resolution, with the notable exception of labile hydrogen sites. The reason why biomolecular structures often remain elusive around exchangeable protons is that the dynamics of their exchange with the solvent hampers the observation of their signals. The new spectroscopic method we report allows to locate water-originating hydrogens in peptides and proteins via their effect on nuclear magnetic transitions similar to electronic phosphorescence, long-lived coherences. The sign of long-lived coherences excited in coupled protons can be switched by the experimenter. The different effect of water-exchanging hydrogens on long-lived coherences with opposed signs allows to pinpoint the position of these labile hydrogen atoms in the molecular framework of peptides and proteins.

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.

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.

Progress in low-field benchtop NMR spectroscopy in chemical and biochemical analysis

The employment of spectroscopically-resolved NMR techniques as analytical probes have previously been both prohibitively expensive and logistically challenging in view of the large sizes of high-field facilities. However, with recent advances in the miniaturisation of magnetic resonance technology, low-field, cryogen-free "benchtop" NMR instruments are seeing wider use. Indeed, these miniaturised spectrometers are utilised in areas ranging from food and agricultural analyses, through to human biofluid assays and disease monitoring. Therefore, it is both intrinsically timely and important to highlight current applications of this analytical strategy, and also provide an outlook for the future, where this approach may be applied to a wider range of analytical problems, both qualitatively and quantitatively.

Proton Relaxometry of Long-Lived Spin Order

A study of long-lived spin order in chlorothiophene carboxylates at both high and low magnetic fields is presented. Careful sample preparation (removal of dissolved oxygen in solution, chelating of paramagnetic impurities, reduction of convection) allows one to obtain very long-lived singlet order of the two coupled protons in chlorothiophene derivatives, having lifetimes of about 130 s in D₂ O and 240 s in deuterated methanol, which are much longer than the T₁ -relaxation times (18 and 30 s, respectively, at a field B 0 =9.4 T). In protonated solvents the relaxation times become shorter, but the lifetime is still substantially longer than T 1 . In addition, long-lived coherences are shown to have lifetimes as long as 30 s. Thiophene derivatives can be used as molecular tags to study slow transport, slow dynamics and slow chemical processes, as has been shown in recent years.

Excitation of singlet–triplet coherences in pairs of nearly-equivalent spins

We present approaches for an efficient excitation of singlet–triplet coherences in pairs of nearly-equivalent spins.

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.

cis Versus trans-Azobenzene: Precise Determination of NMR Parameters and Analysis of Long-Lived States of 15N Spin Pairs

We provide a detailed evaluation of nuclear magnetic resonance (NMR) parameters of the cis- and trans-isomers of azobenzene (AB). For determining the NMR parameters, such as proton-proton and proton-nitrogen J-couplings and chemical shifts, we compared NMR spectra of three different isotopomers of AB: the doubly ¹⁵N labeled azobenzene, ¹⁵N,¹⁵N'-AB, and two partially deuterated AB isotopomers with a single ¹⁵N atom. For the total lineshape analysis of NMR spectra, we used the recently developed ANATOLIA software package. The determined NMR parameters allowed us to optimize experiments for investigating singlet long-lived spin states (LLSs) of ¹⁵N spin pairs and to measure LLS lifetimes in cis-AB and trans-AB. Magnetization-to-singlet-to-magnetization conversion has been performed using the SLIC and APSOC techniques, providing a degree of conversion up to 17 and 24% of the initial magnetization, respectively. Our approach is useful for optimizing the performance of experiments with singlet LLSs; such LLSs can be exploited for preserving spin hyperpolarization, for probing slow molecular dynamics, slow chemical processes and also slow transport processes.

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.

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.

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.