Singlet Order Research Articles

Singulett‐Kontrast‐Magnetresonanztomographie: Freisetzung der Hyperpolarisation durch den Metabolismus**

AbstractHyperpolarisationsverstärkte Magnetresonanztomographie kann zur Untersuchung biomolekularer Prozesse im Körper verwendet werden, erfordert aber die Verwendung von Hetero‐Kernen wie 13C, 15N oder 129Xe. Hier stellen wir eine neue Art der Hyperpolarisierten Protonen Bildgebung vor, bei der die hyperpolarisierte Spinordnung in einem nicht magnetischen und langlebigen korrelierten (Singulett‐) Zustand eingeschlossen ist und nur durch eine spezifische biochemische Reaktion für die Bildgebung freigesetzt wird. In dieser Arbeit erzeugen wir hyperpolarisiertes Fumarat durch chemische Reaktion eines Eduktes mit para‐angereichertem Wasserstoffgas. Der Singulettzustand der Fumarat Protonen wird als Antiphasen‐NMR‐Signale durch enzymatische Umwandlung zu Malat in D2O freigesetzt. Anhand dieses Modellsystems zeigen wir zwei Pulssequenzen, um die NMR‐Signale für die Bildgebung zu rephasieren und die Hintergrundsignale von Wasser zu unterdrücken. Die hier vorgestellte hyperpolarisationsverstärkte Protonen Bildgebungstechnik ermöglicht eine hyperpolarisierte Bildgebung, ohne dass hierfür Hetero‐Kerne mit ihrer niedrigen natürlichen Häufigkeit und geringen Empfindlichkeit benötigt werden.

31P nuclear spin singlet lifetimes in a system with switchable magnetic inequivalence: experiment and simulation

31P NMR nuclear spin singlet order is reported for the first time. Experiments and molecular dynamics simulations indicate that the singlet order relaxes primarily via chemical shift anisotropy at high magnetic field strengths.

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.

Signatures of triplet correlations in density of states of Ising superconductors

The few-layer transition metal dichalcogenides (TMDs) have been recently suggested as a platform for controlled unconventional superconductivity. We study the manifestations of unconventional triplet pairing in the density of states of a disordered TMD based monolayer. The conventional singlet pairing attraction is assumed to be the dominant pairing interaction. We map the phase diagrams of disordered Ising superconductors in the plane of temperature and the in-plane magnetic field. The latter suppresses singlet and promote triplet correlations. The triplet order parameters of a trivial (non-trivial) symmetry compete (cooperate) with the singlet order parameter which gives rise to a rich phase diagram. We locate the model-dependent phase boundaries and compute the order parameters in each of the distinct phases. With this information, we obtain the density of states by solving the Gorkov equation. The triplet components of the order parameters may change an apparent width of the density of states by significantly increasing the critical field. The triplet components of the order parameters lead to the density of states broadening significantly exceeding the broadening induced by magnetic field and disorder in the singlet superconductor.

Robust transformation of singlet order into heteronuclear magnetisation over an extended coupling range

Several important NMR procedures involve the conversion of nuclear singlet order into heteronuclear magnetisation, including some experiments involving long-lived spin states and parahydrogen-induced hyperpolarisation. However most existing sequences suffer from a limited range of validity or a lack of robustness against experimental imperfections. We present a new radio-frequency scheme for the transformation of the singlet order of a chemically-equivalent homonuclear spin pair into the magnetisation of a heteronuclear coupling partner. The proposed radio-frequency (RF) scheme is called gS2hM (generalized singlet-to-heteronuclear magnetisation) and has good compensation for common experimental errors such as RF and static field inhomogeneities. The sequence retains its robustness for homonuclear spin pairs in the intermediate coupling regime, characterised by the in-pair coupling being of the same order of magnitude as the difference between the out-of-pair couplings. This is a substantial improvement to the validity range of existing sequences. Analytical solutions for the pulse sequence parameters are provided. Experimental results are shown for two test cases.

Geminal parahydrogen-induced polarization: accumulating long-lived singlet order on methylene proton pairs.

In the majority of hydrogenative parahydrogen-induced polarization (PHIP) experiments, the hydrogen molecule undergoes pairwise cis addition to an unsaturated precursor to occupy vicinal positions on the product molecule. However, some ruthenium-based hydrogenation catalysts induce geminal hydrogenation, leading to a reaction product in which the two hydrogen atoms are transferred to the same carbon centre, forming a methylene () group. The singlet order of parahydrogen is substantially retained over the geminal hydrogenation reaction, giving rise to a singlet-hyperpolarized group. Although the relaxation times of the methylene protons are often short, the singlet order has a long lifetime, provided that singlet-triplet mixing is suppressed, either by chemical equivalence of the protons or by applying a resonant radiofrequency field. The long lifetime of the singlet order enables the accumulation of hyperpolarization during the slow hydrogenation reaction. We introduce a kinetic model for the behaviour of the observed hyperpolarized signals, including both the chemical kinetics and the spin dynamics of the reacting molecules. Our work demonstrates the feasibility of producing singlet-hyperpolarized methylene moieties by parahydrogen-induced polarization. This potentially extends the range of molecular agents which may be generated in a hyperpolarized state by chemical reactions of parahydrogen.

Magnetic impurities in thin films and 2D Ising superconductors

In the theory of dilute magnetic impurities in superconductors, the effect of all impurity spin-components is expressed via a single magnetic scattering rate Γm. In a more realistic setting, magnetic impurities are anisotropic. In this case, the spatial randomness of three spin-components of impurities gives rise to generally different scattering rates Γi (i=1,2,3). We explore the effects of anisotropic magnetic impurities on the in-plane critical field in 2D superconductors. We discuss singlet, triplet, and parity-mixed order parameters allowed in systems without the inversion center. Also, the addition of a small amount of magnetic impurities may cause singlet to triplet crossovers. In all cases, different components of impurity spin affect the magnetic field—temperature phase diagram differently. We show that anisotropy of the magnetic impurities can serve as a probe of unconventional triplet or parity-mixed superconductivity.

A temperature-controlled sample shuttle for field-cycling NMR

We present a design for a temperature-controlled sample shuttle for use in NMR measurements at variable magnetic field strength. Accurate temperature control was achieved using a mixture of water-ethylene glycol as a heat transfer fluid, reducing temperature gradients across the sample to < 0.05 °C and minimising convection. Using the sample shuttle, we show how the longitudinal (T1) and singlet order (TS) relaxation time constants were measured for two molecules capable of supporting long-lived states, with new record lifetimes observed at low field and above ambient temperatures.

Algorithmic cooling of nuclear spins using long-lived singlet order.

Algorithmic cooling methods manipulate an open quantum system in order to lower its temperature below that of the environment. We achieve significant cooling of an ensemble of nuclear spin-pair systems by exploiting the long-lived nuclear singlet state, which is an antisymmetric quantum superposition of the "up" and "down" Zeeman states. The effect is demonstrated by nuclear magnetic resonance experiments on a molecular system containing a coupled pair of near-equivalent 13C nuclei. The populations of the system are subjected to a repeating sequence of cyclic permutations separated by relaxation intervals. The long-lived nuclear singlet order is pumped well beyond the unitary limit. The pumped singlet order is converted into nuclear magnetization which is enhanced by 21% relative to its thermal equilibrium value.

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.

Fast destruction of singlet order in NMR experiments.

Some nuclear spin systems support long-lived states, which display greatly extended relaxation times relative to the relaxation time of nuclear spin magnetization. In spin-1/2 pairs, such a long-lived state is given by singlet order, representing the difference of the population of the nuclear singlet state and the mean population of the three triplets. In many cases, the experiments with long-lived singlet order are very time-consuming because of the need to wait for singlet order decay before the experiment can be repeated; otherwise, spin order remaining from a previous measurement may lead to experimental artifacts. Here, we propose techniques for fast and efficient singlet order destruction. These methods exploit coherent singlet-triplet conversion; in some cases, multiple conversion steps are introduced. We demonstrate that singlet order destruction enables a dramatic reduction of the waiting time between consecutive experiments and suggest to use this approach in singlet-state Nuclear Magnetic Resonance (NMR) experiments with nearly equivalent spins.

Quasi-Resonance Fluorine-19 Signal Amplification by Reversible Exchange.

We report on an extension of the quasi-resonance (QUASR) pulse sequence used for signal amplification by reversible exchange (SABRE), showing that we may target distantly J-coupled 19F-spins. Polarization transfer from the parahydrogen-derived hydrides to the 19F nucleus is accomplished via weak five-bond J-couplings using a shaped QUASR radio frequency pulse at a 0.05 T magnetic field. The net result is the direct generation of hyperpolarized 19F z-magnetization, derived from the parahydrogen singlet order. An accumulation of 19F polarization on the free ligand is achieved with subsequent repetition of this pulse sequence. The hyperpolarized 19F signal exhibits clear dependence on the pulse length, irradiation frequency, and delay time in a manner similar to that reported for 15N QUASR-SABRE. Moreover, the hyperpolarized 19F signals of 3-19F-14N-pyridine and 3-19F-15N-pyridine isotopologues are similar, suggesting that (i) polarization transfer via QUASR-SABRE is irrespective of the nitrogen isotopologue and (ii) the presence or absence of the spin-1/2 15N nucleus has no impact on the efficiency of QUASR-SABRE polarization transfer. Although optimization of polarization transfer efficiency to 19F (P19F ≈ 0.1%) was not the goal of this study, we show that high-field SABRE can be efficient and broadly applicable for direct hyperpolarization of 19F spins.

Polarization transfer via field sweeping in parahydrogen-enhanced nuclear magnetic resonance.

We show that in a spin system of two magnetically inequivalent protons coupled to a heteronucleus such as 13C, an adiabatic magnetic field sweep, passing through zero field, transfers the proton singlet order into magnetization of the coupled heteronucleus. This effect is potentially useful in parahydrogen-enhanced nuclear magnetic resonance and is demonstrated on singlet-hyperpolarized [1-13C]maleic acid, which is prepared via the reaction between [1-13C]acetylene dicarboxylic acid and para-enriched hydrogen gas. The magnetic field sweeps are of microtesla amplitudes and have durations on the order of seconds. We show a polarization enhancement by a factor of 104 in the 13C spectra of [1-13C]maleic acid in a 1.4 T magnetic field.

Quantitative quantum mechanical approach to SABRE hyperpolarization at high magnetic fields.

A theoretical approach is proposed for quantitative modeling of SABRE (Signal Amplification by Reversible Exchange) experiments performed using an NMR spectrometer at a high magnetic field. SABRE is a method that exploits the spin order of parahydrogen (the H2 molecule in its nuclear singlet state) for hyper-polarizing the spins of various substrates to enhance their NMR signals. An important feature of SABRE is that the substrate is not modified chemically; instead, spin order transfer takes place in a transient complex with parahydrogen. In high-field SABRE experiments, such a transfer is achieved by using suitable NMR excitation schemes. The approach presented here can explicitly treat the spin dynamics in the SABRE complex as well as the kinetics of substrate exchange (between the free and bound form) and complex interplay of spin evolution and chemical processes. One more important effect included in the model is the alteration of the spin state of parahydrogen giving rise to the formation of anti-phase spin order from the initial singlet order. Such a treatment enables a detailed analysis of known high-field SABRE schemes, quantitative comparison with experiments, and elucidation of the key factors that limit the resulting NMR signal enhancement.

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.

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.

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 =9.4 T). In protonated solvents the relaxation times become shorter, but the lifetime is still substantially longer than . 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.

Multiplet-to-net CIDEP conversion by MW-pulses with adiabatically ramped amplitude

ABSTRACTA method is proposed to manipulate electron spin order of spin-correlated radical pairs. As radical pairs are often born in a well-defined spin state, e.g. in the singlet state, they acquire Chemically Induced Dynamic Electron Polarisation (CIDEP). In the case of singlet-state preparation CIDEP is of the multiplet (or anti-phase) type resulting in reduction of EPR (electron paramagnetic resonance) signals due to overlap of absorptive and emissive lines in the spectrum. Here we propose to convert the singlet spin order into net magnetisation of the radical pair by applying a microwave field, with its amplitude slowly (adiabatically) reduced to zero. We demonstrate that by properly choosing the microwave frequency one can completely convert the singlet order into net polarisation of the radical pair with significant enhancement of the signal as compared to multiplet CIDEP. Calculations show that the technique is operative for both weakly coupled and strongly coupled spin pairs. Potential applications of the method are discussed.

Using coligands to gain mechanistic insight into iridium complexes hyperpolarized with para-hydrogen.

We report the formation of a series of novel [Ir(H)2(IMes)(α-13C2-carboxyimine)L] complexes in which the identity of the coligand L is varied. When examined with para-hydrogen, complexes in which L is benzylamine or phenethylamine show significant 1H hydride and 13C2 imine enhancements and may exist in 13C2 singlet spin order. Isotopic labeling techniques are used to double 13C2 enhancements (up to 750-fold) and singlet state lifetimes (up to 20 seconds) compared to those previously reported. Exchange spectroscopy and Density Functional Theory are used to investigate the stability and mechanism of rapid hydrogen exchange in these complexes, a process driven by dissociative coligand loss to form a key five coordinate intermediate. When L is pyridine or imidazole, competitive binding to such intermediates leads to novel complexes whose formation, kinetics, behaviour, structure, and hyperpolarization is investigated. The ratio of the observed PHIP enhancements were found to be affected not only by the hydrogen exchange rates but the identity of the coligands. This ligand reactivity is accompanied by decoherence of any 13C2 singlet order which can be preserved by isotopic labeling. Addition of a thiol coligand proved to yield a thiol oxidative addition product which is characterized by NMR and MS techniques. Significant 870-fold 13C enhancements of pyridine can be achieved using the Signal Amplification By Reversible Exchange (SABRE) process when α-carboxyimines are used to block active coordination sites. [Ir(H)2(IMes)(α-13C2-carboxyimine)L] therefore acts as unique sensors whose 1H hydride chemical shifts and corresponding hyperpolarization levels are indicative of the identity of a coligand and its binding strength.

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

Nuclear singlet lifetimes are often dependent on the quantity of paramagnetic oxygen species present in solution, although the extent to which quenching or removing molecular oxygen has on extending singlet lifetimes is typically an unknown factor. Here we investigate the behaviour of the singlet relaxation time constant as a function of the oxygen concentration in solution. An experimental demonstration is presented for a chemically inequivalent proton pair of the tripeptide alanine–glycine–glycine in solution. We introduce a simple methodology to ensure the solution is saturated with predetermined concentrations of oxygen gas prior to measurements of the singlet lifetime. Singlet lifetimes were measured by using the spin-lock induced crossing pulse sequence. We present a linear relationship between the amount of oxygen dissolved in solution and the singlet relaxation rate constant. Singlet relaxation was found to be ∼2.7 times less sensitive to relaxation induced by paramagnetic oxygen compared with longitudinal relaxation. The relaxation behaviour is described by using a model of correlated fluctuating fields. We additionally examine the extension of singlet lifetimes by doping solutions with the chelating agent sodium ascorbate, which scavenges oxygen radicals in solution.