Maximizing NMR signal per unit time by facilitating the e-e-n cross effect DNP rate

Dipolar Order Induced Electron Spin Hyperpolarization

The structure of coupled electron spin systems is of fundamental interest to many applications, including dynamic nuclear polarization (DNP), enhanced nuclear magnetic resonance (NMR), the generation of electron spin qubits for quantum information science (QIS), and quantitative studies of paramagnetic systems by electron paramagnetic resonance (EPR). However, the characterization of electron spin coupling networks is nontrivial, especially at high magnetic fields. This study focuses on a system containing high concentrations of trityl radicals that give rise to a DNP enhancement profile of 1H NMR characteristic of the presence of electron spin clusters. When this system is subject to selective microwave saturation through pump-probe ELectron DOuble Resonance (ELDOR) experiments, electron spin hyperpolarization is observed. We show that the generation of an out-of-equilibrium longitudinal dipolar order is responsible for the transient hyperpolarization of electron spins. Notably, the coupled electron spin system needs to form an AX-like system (where the difference in the Zeeman interactions of two spins is larger than their coupling interaction) such that selective microwave irradiation can generate signatures of electron spin hyperpolarization. We show that the extent of dipolar order, as manifested in the extent of electron spin hyperpolarization generated, can be altered by tuning the pump or probe pulse length, or the interpulse delay in ELDOR experiments that change the efficiency to generate or readout longitudinal dipolar order. Pump-probe ELDOR with selective saturation is an effective means for characterizing coupled electron spins forming AX-type spin systems that are foundational for DNP and quantum sensing.

Relaxation enhancement by microwave irradiation may limit dynamic nuclear polarization

Dynamic nuclear polarization enables the hyperpolarization of nuclear spins beyond the thermal-equilibrium Boltzmann distribution. However, it is often unclear why the experimentally measured hyperpolarization is below the theoretically achievable maximum polarization. We report a (near-) resonant relaxation enhancement by microwave (MW) irradiation, leading to a significant increase in the nuclear polarization decay compared to measurements without MW irradiation. For example, the increased nuclear relaxation limits the achievable polarization levels to around 35% instead of hypothetical 60%, measured in the DNP material TEMPO in 1H glassy matrices at 3.3 K and 7 T. Applying rate-equation models to published build-up and decay data indicates that such relaxation enhancement is a common issue in many samples when using different radicals at low sample temperatures and high Boltzmann polarizations of the electrons. Accordingly, quantification and a better understanding of the relaxation processes under MW irradiation might help to design samples and processes towards achieving higher nuclear hyperpolarization levels.

Electron-to-nuclear spectral mapping via dynamic nuclear polarization

We report on a strategy to indirectly read out the spectrum of an electronic spin via polarization transfer to nuclear spins in its local environment. The nuclear spins are far more abundant and have longer lifetimes, allowing for repeated polarization accumulation in them. Subsequent nuclear interrogation can reveal information about the electronic spectral density of states. We experimentally demonstrate the method by reading out the ESR spectrum of nitrogen vacancy center electrons in diamond via readout of lattice 13C nuclei. Spin-lock control on the 13C nuclei yields a significantly enhanced signal-to-noise ratio for the nuclear readout. Spectrally mapped readout presents operational advantages in being background-free and immune to crystal orientation and optical scattering. We harness these advantages to demonstrate applications in underwater magnetometry. The physical basis for the "one-to-many" spectral map is itself intriguing. To uncover its origin, we develop a theoretical model that maps the system dynamics, involving traversal of a cascaded structure of Landau-Zener anti-crossings, to the operation of a tilted "Galton board." This work points to new opportunities for "ESR-via-NMR" in dilute electronic systems and in hybrid electron-nuclear quantum memories and sensors.

Large cross-effect dynamic nuclear polarisation enhancements with kilowatt inverting chirped pulses at 94 GHz

Dynamic nuclear polarisation (DNP) is a process that transfers electron spin polarisation to nuclei by applying resonant microwave radiation, and has been widely used to improve the sensitivity of nuclear magnetic resonance (NMR). Here we demonstrate new levels of performance for static cross-effect proton DNP using high peak power chirped inversion pulses at 94 GHz to create a strong polarisation gradient across the inhomogeneously broadened line of the mono-radical 4-amino TEMPO. Enhancements of up to 340 are achieved at an average power of a few hundred mW, with fast build-up times (3 s). Experiments are performed using a home-built wideband kW pulsed electron paramagnetic resonance (EPR) spectrometer operating at 94 GHz, integrated with an NMR detection system. Simultaneous DNP and EPR characterisation of other mono-radicals and biradicals, as a function of temperature, leads to additional insights into limiting relaxation mechanisms and give further motivation for the development of wideband pulsed amplifiers for DNP at higher frequencies.

Modelling and correcting the impact of RF pulses for continuous monitoring of hyperpolarized NMR

Monitoring the build-up or decay of hyperpolarization in nuclear magnetic resonance requires radio-frequency (RF) pulses to generate observable nuclear magnetization. However, the pulses also lead to a depletion of the polarization and, thus, alter the spin dynamics. To simulate the effects of RF pulses on the polarization build-up and decay, we propose a first-order rate-equation model describing the dynamics of the hyperpolarization process through a single source and a relaxation term. The model offers a direct interpretation of the measured steady-state polarization and build-up time constant. Furthermore, the rate-equation model is used to study three different methods to correct the errors introduced by RF pulses: (i) a 1 / cos⁡ n - 1 θ correction (θ denoting the RF pulse flip angle), which is only applicable to decays; (ii) an analytical model introduced previously in the literature; and (iii) an iterative correction approach proposed here. The three correction methods are compared using simulated data for a range of RF flip angles and RF repetition times. The correction methods are also tested on experimental data obtained with dynamic nuclear polarization (DNP) using 4-oxo-TEMPO in 1 H glassy matrices. It is demonstrated that the analytical and iterative corrections allow us to obtain accurate build-up times and steady-state polarizations (enhancements) for RF flip angles of up to 25∘ during the polarization build-up process within ± 10  % error when compared to data acquired with small RF flip angles (< 3 ∘ ). For polarization decay experiments, corrections are shown to be accurate for RF flip angles of up to 12∘ . In conclusion, the proposed iterative correction allows us to compensate for the impact of RF pulses offering an accurate estimation of polarization levels, build-up and decay time constants in hyperpolarization experiments.

Design of a cryogen-free high field dual EPR and DNP probe

We present the design and construction of a cryogen free, dual electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR) probe for novel dynamic nuclear polarization (DNP) experiments and concurrent "in situ" analysis of DNP mechanisms. We focus on the probe design that meets the balance between EPR, NMR, and low temperature performance, while maintaining a high degree of versatility: allowing multi-nuclear NMR detection as well as broadband DNP/EPR excitation/detection. To accomplish high NMR/EPR performance, we implement a novel inductively coupled double resonance NMR circuit (¹H-¹³C) in a solid state probe operating at cryogenic temperatures. The components of the circuit were custom built to provide maximum NMR performance, and the physical layout of this circuit was numerically optimized via magnetic field simulations to allow maximum microwave transmission to the sample for optimal EPR performance. Furthermore this probe is based around a cryogen free gas exchange cryostat and has been designed to allow unlimited experiment times down to 8.5 Kelvin with minimal cost. The affordability of EPR/DNP experiment is an extremely important aspect for broader impact with magnetic resonance measurements. The purpose of this article is to provide as complete information as we have available for others with interest in building a dual DNP/EPR instrument based around a cryogen-free cryostat.

Spin Hyperpolarization in Modern Magnetic Resonance

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

A unified description for polarization-transfer mechanisms in magnetic resonance in static solids: Cross polarization and DNP

Polarization transfers are crucial building blocks in magnetic resonance experiments, i.e., they can be used to polarize insensitive nuclei and correlate nuclear spins in multidimensional nuclear magnetic resonance (NMR) spectroscopy. The polarization can be transferred either across different nuclear spin species or from electron spins to the relatively low-polarized nuclear spins. The former route occurring in solid-state NMR can be performed via cross polarization (CP), while the latter route is known as dynamic nuclear polarization (DNP). Despite having different operating conditions, we opinionate that both mechanisms are theoretically similar processes in ideal conditions, i.e., the electron is merely another spin-1/2 particle with a much higher gyromagnetic ratio. Here, we show that the CP and DNP processes can be described using a unified theory based on average Hamiltonian theory combined with fictitious operators. The intuitive and unified approach has allowed new insights into the cross-effect DNP mechanism, leading to better design of DNP polarizing agents and extending the applications beyond just hyperpolarization. We explore the possibility of exploiting theoretically predicted DNP transients for electron–nucleus distance measurements—such as routine dipolar-recoupling experiments in solid-state NMR.

Rotaxane-branched radical dendrimers with TEMPO termini

The precise synthesis of novel rotaxane-branched radical dendrimers Gn-TEMPO (n = 1-3) with up to 24 TEMPO radicals as termini was successfully achieved, from which nanoparticles with a good longitudinal relaxivity were further prepared, thus making them potential candidates as promising contrast agents for magnetic resonance imaging.

Solid-state MAS NMR at ultra low temperature of hydrated alanine doped with DNP radicals

Magic angle spinning (MAS) nuclear magnetic resonance (NMR) experiments at ultra low temperature (ULT) (≪ 100 K) have demonstrated clear benefits for obtaining large signal sensitivity gain and probing spin dynamics phenomena at ULT. ULT NMR is furthermore a highly promising platform for solid-state dynamic nuclear polarization (DNP). However, ULT NMR is not widely used, given limited availability of such instrumentation from commercial sources. In this paper, we present a comprehensive study of hydrated [U-¹³C]alanine, a standard bio-solid sample, from the first commercial 14.1 Tesla NMR spectrometer equipped with a closed-cycle helium ULT-MAS system. The closed-cycle helium MAS system provides precise temperature control from 25 K to 100 K and stable MAS from 1.5 kHz to 12 kHz. The ¹³C CP-MAS NMR of [U-¹³C]alanine showed 400% signal gain at 28 K compared with at 100 K. The large sensitivity gain results from the Boltzmann factor, radio frequency circuitry quality factor improvement, and the suppression of its methyl group rotation at ULT. We further observed that the addition of organic biradicals widely used for solid-state DNP significantly shortens the ¹H T₁ spin lattice relaxation time at ULT, without further broadening the ¹³C spectral linewidth compared to at 90 K. The mechanism of ¹H T₁ shortening is dominated by the two-electron-one-nucleus triple flip transition underlying the Cross Effect mechanism, widely relied upon to drive solid-state DNP. Our experimental observations suggest that the prospects of MAS NMR and DNP under ULT conditions established with a closed-cycle helium MAS system are bright.

Biomolecular Perturbations in In-Cell Dynamic Nuclear Polarization Experiments

In-cell DNP is a growing application of NMR to the study of biomolecular structure and function within intact cells. An important unresolved question for in-cell DNP spectroscopy is the integrity of cellular samples under the cryogenic conditions of DNP. Despite the rich literature around cryopreservation of cells in the fields of stem cell/embryonic cell therapeutics, cell line preservation and in cryo-EM applications, the effect of cryopreservation procedures on DNP parameters is unclear. In this report we investigate cell survival and apoptosis in the presence of cryopreserving agents and DNP radicals. We also assess the effects of these reagents on cellular enhancements. We show that the DNP radical AMUPol has no effect on membrane permeability and does not induce apoptosis. Furthermore, the standard aqueous glass forming reagent, comprised of 60/30/10 d₈-glycerol/D₂O/H₂O (DNP juice), rapidly dehydrates cells and induces apoptosis prior to freezing, reducing structural integrity of the sample prior to DNP analysis. Preservation with d₆-DMSO at 10% v/v provided similar DNP enhancements per √unit time compared to glycerol preservation with superior maintenance of cell size and membrane integrity prior to freezing. DMSO preservation also greatly enhanced post-thaw survival of cells slow-frozen at 1°C/min. We therefore demonstrate that in-cell DNP-NMR studies should be done with d₆-DMSO as cryoprotectant and raise important considerations for the progression of in-cell DNP-NMR towards the goal of high quality structural studies.

Role of electron spin dynamics and coupling network in designing dynamic nuclear polarization

Dynamic nuclear polarization (DNP) has emerged as a powerful sensitivity booster of nuclear magnetic resonance (NMR) spectroscopy for the characterization of biological solids, catalysts and other functional materials, but is yet to reach its full potential. DNP transfers the high polarization of electron spins to nuclear spins using microwave irradiation as a perturbation. A major focus in DNP research is to improve its efficiency at conditions germane to solid-state NMR, at high magnetic fields and fast magic-angle spinning. In this review, we highlight three key strategies towards designing DNP experiments: time-domain "smart" microwave manipulation to optimize and/or modulate electron spin polarization, EPR detection under operational DNP conditions to decipher the underlying electron spin dynamics, and quantum mechanical simulations of coupled electron spins to gain microscopic insights into the DNP mechanism. These strategies are aimed at understanding and modeling the properties of the electron spin dynamics and coupling network. The outcome of these strategies is expected to be key to developing next-generation polarizing agents and DNP methods.

High-field solution state DNP using cross-correlations

At the magnetic fields of common NMR instruments, electron Zeeman frequencies are too high for efficient electron-nuclear dipolar cross-relaxation to occur in solution. The rate of that process fades with the electron Zeeman frequency as ω^-2 - in the absence of isotropic hyperfine couplings, liquid state dynamic nuclear polarisation (DNP) in high-field magnets is therefore impractical. However, contact coupling and dipolar cross-relaxation are not the only mechanisms that can move electron magnetisation to nuclei in liquids: multiple cross-correlated (CC) relaxation processes also exist, involving various combinations of interaction tensor anisotropies. The rates of some of those processes have more favourable high-field behaviour than dipolar cross-relaxation, but due to the difficulty of their numerical - and particularly analytical - treatment, they remain largely uncharted. In this communication, we report analytical evaluation of every rotationally driven relaxation process in liquid state for 1e1n and 2e1n spin systems, as well as numerical optimisations of the steady-state DNP with respect to spin Hamiltonian parameters. A previously unreported cross-correlated DNP (CCDNP) mechanism was identified for the 2e1n system, involving multiple relaxation interference effects and inter-electron exchange coupling. Using simulations, we found realistic spin Hamiltonian parameters that yield stronger nuclear polarisation at high magnetic fields than dipolar cross-relaxation.

Scaling analyses for hyperpolarization transfer across a spin-diffusion barrier and into bulk solid media

By analogy to heat and mass transfer film theory, a general approach is introduced for determining hyperpolarization transfer rates between dilute electron spins and a surrounding nuclear ensemble. These analyses provide new quantitative relationships for understanding, predicting, and optimizing the effectiveness of hyperpolarization protocols, such as Dynamic Nuclear Polarization (DNP) under magic-angle spinning conditions. An empirical DNP polarization-transfer coefficient is measured as a function of the bulk matrix 1H spin density and indicates the presence of two distinct kinetic regimes associated with different rate-limiting polarization transfer phenomena. Dimensional property relationships are derived and used to evaluate the competitive rates of spin polarization generation, propagation, and dissipation that govern hyperpolarization transfer between large coupled spin ensembles. The quantitative analyses agree closely with experimental measurements for the accumulation, propagation, and dissipation of hyperpolarization in solids and provide evidence for kinetically-limited transfer associated with a spin-diffusion barrier. The results and classical approach yield general design criteria for analyzing and optimizing polarization transfer processes involving complex interfaces and composite media for applications in materials science, physical chemistry and nuclear spintronics.

Electron spin relaxation of P1 centers in synthetic diamonds with potential as B1 standards for DNP enhanced NMR

The microwave magnetic field, B₁, in the non-resonant structures typically used for DNP-enhanced NMR is relatively small, so calibration via continuous wave (CW) power saturation requires a sample with longer spin lattice relaxation times than the samples used as CW standards in X-band cavities. HPHT diamonds have strong, easily observed EPR signals from P1 centers (nitrogen defects), and are indefinitely stable. This makes HPHT diamonds attractive as secondary standards for calibration of electron B₁ field strength in a variety of experimental arrangements. The concentrations of P1 centers is also typically in the 30-200 ppm range, or equivalently 10-60 mM, and therefore the EPR relaxation observed is relevant to DNP enhanced NMR employing free radical polarizing agents at similar concentrations. Pulsed and CW saturation relaxation measurements T₁ and T₂ are compared at X-band. Under CW conditions the relevant T₁T₂ product of time constants in our samples at room temperature is found to be dominated by electron-electron spin diffusion, and the product is large enough that saturation will be possible with the B₁ of typical DNP systems. The similarity of T₁ and T₂ values obtained by pulse measurements at X-band and Q-band suggests that the X-band results can be extrapolated to the higher EPR frequencies used for DNP experiments. The electron spin dynamics observed here in HPHT diamond samples identify them as useful model systems to better delineate the interplay of electron spin relaxation, magic angle spinning, and inhomogeneous microwave irradiation as they affect DNP enhancement.

Dynamic Nuclear Polarization Enhancement of 200 at 21.15 T Enabled by 65 kHz Magic Angle Spinning

Solid-state nuclear magnetic resonance under magic angle spinning (MAS) enhanced with dynamic nuclear polarization (DNP) is a powerful approach to characterize many important classes of materials, allowing access to previously inaccessible structural and dynamic parameters. Here, we present the first DNP MAS experiments using a 0.7 mm MAS probe, which allows us to reach spinning frequencies of 65 kHz, with microwave irradiation, at 100 K. At the highest magnetic field available for DNP today (21.1 T), we find that the polarizing agent HyTEK2 provides DNP enhancements as high as 200 at a spinning rate of 65 kHz at 100 K, and BDPA yields an enhancement of 106 under the same conditions. Fast spinning rates enable excellent DNP performance, but they also yield unprecedented ¹H resolution under DNP conditions. We report well-resolved ¹H-detected ¹H-¹³C and ¹H-¹⁵N correlation spectra of microcrystalline histidine·HCl·H₂O.

Synthesis, structural characterization and electrochemical and magnetic studies of M(hfac)2 (M = CuII, CoII) and Nd(hfac)3 complexes of 4-amino-TEMPO

Three mononuclear complexes [M(hfac)x(ATEMPO)y], where M = Cu (11) and Co (12), x = y = 2; M = Nd (13), x = 4, y = 1, and two polynuclear complexes [{Cu(hfac)2(ATEMPO)}n], where n = 2 (14) and 4 (15), were obtained by the reaction of M(hfac)x (M = CuII, CoII, NdIII; x = 2, 3) with 4-amino-TEMPO (4-amino-2,2,6,6-tetramethylpiperidin-N-oxyl) in good yields and their structural, electrochemical and magnetic properties were examined. In all cases, the radical is coordinated to the metal through the amino group, except 15, and the metal ions have an octahedral geometry, except 13. Different coordination architectures of the copper complexes were obtained as a function of the stoichiometry and solvents used. In complexes 11 and 12 the radicals show an equatorial-equatorial and axial-equatorial arrangement, respectively, giving rise to two distinct 2D supramolecular systems through intermolecular interactions. Compound 13 is the first example of a lanthanide complex of the ATEMPO radical. The NdIII ion adopts a rare nine-coordination via binding to four hfac ligands and the radical. The dinuclear complex 14 shows a (Cu-O)2 core in which the CuII ions are bridged by the oxygen atoms from the hfac ligands. In compound 15 the ATEMPO radical acts as a bidentate ligand through the amino and nitroxyl groups leading to an unprecedented tetranuclear square-shaped framework. Cyclic voltammetry showed redox processes associated with the copper and TEMPO moieties. Electrochemical impedance spectroscopy revealed the temperature dependence of the conductivity for compound 15 with a maximum of 2.09 × 10-5 S cm-1 at 408 K. The magnetic behavior of complexes 11-15 is determined by metal-radical interactions. Ferromagnetic interaction has been observed for complex 11 due to the existence of two different exchange pathways arising from the conformational arrangement of the radicals around the metal center, whereas the single conformation of the radical in complex 14 resulted in a weak antiferromagnetic coupling. In complex 15 both O-Cu and N-Cu contacts are present giving rise to ferromagnetic and antiferromagnetic interactions, respectively.

Crossover from a Solid Effect to Thermal Mixing 1H Dynamic Nuclear Polarization with Trityl-OX063

Trityl-OX063 is a narrow-line, water-soluble, and biocompatible polarizing agent, widely used for dynamic nuclear polarization (DNP) amplified NMR of ¹³C, but not of the abundant ¹H nuclear spin, for which the ineffective solid effect (SE) is expected to be operational. Surprisingly, we observed a crossover from SE to thermal mixing (TM) DNP of ¹H with increasing Trityl-OX063 concentration at 7 T. We experimentally ascertained diagnostic signatures of TM-DNP that have only been theoretically predicted: (i) an electron paramagnetic resonance (EPR) spectrum that maintains an asymmetrically broadened EPR line from strong e-e couplings and (ii) hyperpolarization, i.e., cooling of select electron-spin populations, manifested in a characteristic pump-probe electron double-resonance spectrum under DNP conditions. Low microwave power requirements, high polarization transfer rates, and efficient DNP at high magnetic fields are the key benefits of TM-DNP.

Study of electron spectral diffusion process under DNP conditions by ELDOR spectroscopy focusing on the 14N solid effect

Electron spectral diffusion (eSD) plays an important role in solid-state, static dynamic nuclear polarization (DNP) with polarizers that have inhomogeneously broadened EPR spectra, such as nitroxide radicals. It affects the electron spin polarization gradient within the EPR spectrum during microwave irradiation and thereby determines the effectiveness of the DNP process via the so-called indirect cross-effect (iCE) mechanism. The electron depolarization profile can be measured by electron-electron double resonance (ELDOR) experiments, and a theoretical framework for deriving eSD parameters from ELDOR spectra and employing them to calculate DNP profiles has been developed. The inclusion of electron depolarization arising from the 14 N solid effect (SE) has not yet been taken into account in this theoretical framework and is the subject of the present work. The 14 N SE depolarization was studied using W-band ELDOR of a 0.5 mM TEMPOL solution, where eSD is negligible, taking into account the hyperfine interaction of both 14 N and 1 H nuclei, the long microwave irradiation applied under DNP conditions, and electron and nuclear relaxation. The results of this analysis were then used in simulations of ELDOR spectra of 10 and 20 mM TEMPOL solutions, where eSD is significant using the eSD model and the SE contributions were added ad hoc employing the 1 H and 14 N frequencies and their combinations, as found from the analysis of the 0.5 mM sample. This approach worked well for the 20 mM solution, where a good fit for all ELDOR spectra recorded along the EPR spectrum was obtained and the inclusion of the 14 N SE mechanism improved the agreement with the experimental spectra. For the 10 mM solution, simulations of the ELDOR spectra recorded along the g z position gave a lower-quality fit than for spectra recorded in the center of the EPR spectrum. This indicates that the simple approach we used to describe the 14 N SE is limited when its contribution is relatively high as the anisotropy of its magnetic interactions was not considered explicitly.

Succinyl-DOTOPA: An effective triradical dopant for low-temperature dynamic nuclear polarization with high solubility in aqueous solvent mixtures at neutral pH

We report the synthesis of the nitroxide-based triradical compound succinyl-DOTOPA and the characterization of its performance as a dopant for dynamic nuclear polarization (DNP) experiments in frozen solutions at low temperatures. Compared with previously described DOTOPA derivatives, succinyl-DOTOPA has substantially greater solubility in glycerol/water mixtures with pH > 4 and therefore has wider applicability. Solid state nuclear magnetic resonance (ssNMR) measurements at 9.39 T and 25 K, with magic-angle spinning at 7.00 kHz, show that build-up times of DNP-enhanced, cross-polarized ¹³C ssNMR signals are shorter and that signal amplitudes are larger for glycerol/water solutions of L-proline containing succinyl-DOTOPA than for solutions containing the biradical AMUPol, with electron spin concentrations of 15 mM or 30 mM, resulting in greater net sensitivity gains from DNP. In similar measurements at 90 K, AMUPol yields greater net sensitivity, apparently due to its longer electron spin-lattice and spin-spin relaxation times. One- and two-dimensional ¹³C ssNMR measurements at 25 K on the complex of the 27-residue peptide M13 with the calcium-sensing protein calmodulin, in glycerol/water with 10 mM succinyl-DOTOPA, demonstrate the utility of this compound in DNP-enhanced ssNMR studies of biomolecular systems.

Cross-Effect Dynamic Nuclear Polarization Explained: Polarization, Depolarization, and Oversaturation

The scope of this Perspective is to analytically describe NMR hyperpolarization by the three-spin cross effect (CE) dynamic nuclear polarization (DNP) using an effective Hamiltonian concept. We apply, for the first time, the bimodal operator-based Floquet theory in the Zeeman-interaction frame for two and three coupled spins to derive the known interaction Hamiltonian for CE-DNP. With a unified understanding of CE-DNP, and supported by empirical observation of the state of electron spin polarization under the given experimental conditions, we explain diverse manifestations of CE from oversaturation, enhanced hyperpolarization by broad-band saturation, to nuclear spin depolarization under magic-angle spinning.

Dynamic nuclear polarization via the cross effect and thermal mixing: B. Energy transport

The fundamental process of dynamic nuclear polarization (DNP) via the cross effect (CE) and thermal mixing (TM) is a triple spin flip, in which two interacting electron spins and a nuclear spin interacting with one of these electron spins flip together. In the previous article (Wenckebach, 2018) these triple spin flips were treated by first determining the eigenstates of the two interacting electron spins exactly and next investigating transitions involving these exact eigenstates and the nuclear spin states. It was found that two previously developed approaches-the scrambled states approach and the fluctuating field approach-are just two distinct limiting cases of this more general approach. It was also shown that triple spin flips constitute a single process causing two flows of energy: a flow originating in the electron Zeeman energy and a flow originating in the mutual interactions between the electron spins. In order to render their definitions more precise, the former flow was denoted as the CE and the latter as TM. In this article the treatment is extended to a glass containing N_I equivalent nuclear spins I=12 and N_S randomly distributed and oriented electron spins S=12. Rate equations are derived for the two flows of energy to the nuclear spins. The flow originating in the electron Zeeman energy-i.e. the CE-is found to lead to the same stationary state as was previously predicted by the scrambled states approach, though the rate may be smaller due to limitations imposed by conservation of energy. The flow originating in the mutual interactions between the electron spins-i.e. TM-is found to involve the full spectrum of the mutual interactions between the electron spins, while the fluctuating field approach only accounts for the component of this spectrum at the nuclear magnetic resonance (NMR) frequency. Still, TM is found to induce equal spin temperature for different nuclear spin species during nuclear spin-lattice relaxation and, at least in some cases also during polarization. It is also confirmed that TM couples local nuclear spins near the electron spins so strongly to the mutual interactions between electron spins, that they may constitute a single energy reservoir (Cox et al., 1973). Hence such local nuclear spins may have to be included in treatments of the dynamics of the electron spins.