Category Archives: Theory

Balancing dipolar and exchange coupling in biradicals to maximize cross effect dynamic nuclear polarization #DNPNMR

Equbal, Asif, Kan Tagami, and Songi Han. “Balancing Dipolar and Exchange Coupling in Biradicals to Maximize Cross Effect Dynamic Nuclear Polarization.” Physical Chemistry Chemical Physics 22, no. 24 (2020): 13569–79.

https://doi.org/10.1039/D0CP02051F

Dynamic nuclear polarization (DNP) by the Cross Eect (CE) has become a game changer for solid-state nuclear magnetic resonance (NMR) spectroscopy. The eciency of CE-DNP depends on the strength of the electron-electron coupling in biradical polarizing agents. Hence, the focus lately has been on designing biradicals with a large net exchange (J) and dipolar (D) coupling. In this study, we reveal that the crucial factor for CE-DNP is not the sum, J+D, but rather the relative magnitude of J and D, expressed as the J/D ratio. We show that the mechanistic basis of this interference lies in the isotropic v.s. the anisotropic nature of the J and D couplings, respectively. This interference can lead to a small (eective) electron-electron coupling for many orientations even when J+D is large, resulting in non-adiabatic rotor-events. We find that when 0< jJ/Dj < 1 the CE-DNP eciency is attenuated for the majority of orientations, with greater attenuation observed at higher magnetic elds and faster Magic-Angle Spinning (MAS) frequency. The interference eect of J and D coupling introduced in this study can explain why many biradicals with high or comparable J + D still show signicantly divergent DNP performances. We debut J/D as a consequential criteria for designing ecient biradicals to robustly perform across a large range of B0 elds and MAS frequencies.

Heteronuclear DNP of 1H and 19F nuclei using BDPA as a polarizing agent #DNPNMR

Gennaro, Antonio, Alexander Karabanov, Alexey Potapov, and Walter Köckenberger. “Heteronuclear DNP of 1H and 19F Nuclei Using BDPA as a Polarizing Agent.” Physical Chemistry Chemical Physics 22, no. 15 (2020): 7803–16.

https://doi.org/10.1039/D0CP00892C.

This work explores the dynamic nuclear polarization (DNP) of 1H and 19F nuclei in a sample of 25/75 (% v/v) fluorobenzene/toluene containing the radical 1,3-bisphenylene-2-phenylallyl radical (BDPA) as a polarizing agent. Previously, heteronuclear effects in DNP were studied by analysing the shapes of DNP spectra, or by observing cross-relaxation between nuclei of different types. In this work, we report a rather specific DNP spectrum, where 1H and 19F nuclei obtain polarizations of opposite signs upon microwave (MW) irradiation. In order to explain this observation, we introduce a novel mechanism called heteronuclear thermal mixing (hn-TM). Within this mechanism the spectra of opposite signs can then be explained due to the presence of four-spin systems, involving a pair of dipolar coupled electron spins and hyperfine coupled nuclear spins of 1H and 19F, such that a condition relating their Larmor frequencies |o1e o2e| E oH oF is satisfied. Under this condition, a strong mixing of electron and nuclear states takes place, enabling simultaneous four-spin flip-flops. Irradiation of electron spin transitions with MW followed by such four-spin flip-flops produces non-equilibrium populations of |aHbFi and |bHaFi states, thus leading to the enhancements of opposite signs for 1H and 19F. Signal enhancements, build-up times and DNP-spectra as a function of MW power and polarizing agent concentration, all provide additional support for assigning the observed DNP mechanism as hn-TM and distinguishing it from other possible mechanisms. We also develop a quantum mechanical model of hn-TM based on averaging of spin Hamiltonians. Simulations based on this model show very good qualitative agreement with experimental data. In addition, the system exhibits cross-relaxation between 1H and 19F induced by the presence of BDPA, which was detected by measuring the 19F signal build-up upon saturation of 1H nuclei with a train of radio-frequency pulses. We demonstrate that such cross-relaxation most likely originates due to the same electron and nuclear states mixing in the four-spin systems.

Study of electron spectral diffusion process under DNP conditions by ELDOR spectroscopy focusing on the 14N Solid Effect #DNPNMR

Ramirez Cohen, Marie, Akiva Feintuch, Daniella Goldfarb, and Shimon Vega. “Study of Electron Spectral Diffusion Process under DNP Conditions by ELDOR Spectroscopy Focusing on the 14N Solid Effect.” Magnetic Resonance Discussions, February 24, 2020, 1–26.

https://doi.org/10.5194/mr-2020-3

Electron spectral diffusion (eSD) plays an important role in solid state, static DNP with polarizers having in-homogeneously 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 <sup>14</sup>N Solid Effect (SE) has not yet been taken into account in this theoretical framework and is the subject of the present work. The <sup>14</sup>N SE depolarization was studied using W-band ELDOR of a 0.5&thinsp;mM TEMPOL solution, where eSD is negligible, taking into account the hyperfine interaction of both <sup>14</sup>N and <sup>1</sup>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&thinsp;mM TEMPOL solutions, where eSD is significant using the eSD model and the SE contributions were added ad-hoc employing the <sup>1</sup>H and <sup>14</sup>N frequencies and their combinations, as found from the analysis of the 0.5&thinsp;mM sample. This approach worked well for the 20&thinsp;mM solution where a good fit for all ELDOR spectra recorded along the EPR spectrum was obtained and the inclusion of the <sup>14</sup>N SE mechanism improved the agreement with the experimental spectra. For the 10&thinsp;mM solution, simulations of the ELDOR spectra recorded along the gz position gave a lower quality fit than for spectra recorded in the center of the EPR spectrum, suggesting that the simple approach used to the SE of the <sup>14</sup>N contribution, when its contribution is high, is lacking as the anisotropy of its magnetic interactions has not been considered explicitly.

Nitroxide Derivatives for Dynamic Nuclear Polarization in Liquids: The Role of Rotational Diffusion #DNPNMR

Levien, M., M. Hiller, I. Tkach, M. Bennati, and T. Orlando. “Nitroxide Derivatives for Dynamic Nuclear Polarization in Liquids: The Role of Rotational Diffusion.” The Journal of Physical Chemistry Letters 11, no. 5 (March 5, 2020): 1629–35.

https://doi.org/10.1021/acs.jpclett.0c00270

Polarization transfer efficiency in liquid-state dynamic nuclear polarization (DNP) depends on the interaction between polarizing agents (PAs) and target nuclei modulated by molecular motions. We show how translational and rotational diffusion differently affect the DNP efficiency. These contributions were disentangled by measuring 1HDNP enhancements of toluene and chloroform doped with nitroxide derivatives at 0.34 T as a function of either the temperature or the size of the PA. The results were employed to analyze 13C-DNP data at higher fields, where the polarization transfer is also driven by the Fermi contact interaction. In this case, bulky nitroxide PAs perform better than the small TEMPONE radical due to structural fluctuations of the ring conformation. These findings will help in designing PAs with features specifically optimized for liquid-state DNP at various magnetic fields.

Relaxation Mechanisms #DNPNMR #EPR

This is an excellent review and summary on different relaxation mechanisms observed in EPR spectroscopy. Understanding EPR relaxation is crucial to understand the DNP process.

Eaton, Sandra S., and Gareth R. Eaton. “Relaxation Mechanisms.” In EMagRes, edited by Robin K. Harris and Roderick L. Wasylishen, 1543–56. Chichester, UK: John Wiley & Sons, Ltd, 2016.

https://doi.org/10.1002/9780470034590.emrstm1507

After a paramagnetic species absorbs energy, there are various relaxation processes by which the excitation energy is lost to the surroundings thereby enabling return to the ground state. The focus of this article is on relaxation of species with S= 1∕2 in magnetically dilute samples. The relative importance of various spin–lattice relaxation processes for each paramagnetic species is strongly dependent on temperature, electronic, and molecular structure. The Raman and local-mode processes make significant contributions to T 1 relaxation in rigid and semirigid lattices for a wide range of species at temperature above about 10 K. The Orbach process requires a low-lying excited state. The thermally activated process is significant when a stochastic process averages inequivalent environments on a timescale comparable to the Larmor frequency, as occurs by rotation of methyl groups or hopping of a hydrogen-bonded proton. Spin-echo dephasing at low temperatures is dominated by nuclear spin diffusion. It is enhanced by dynamic processes that average inequivalently coupled nuclei on the time scale of the hyperfine interaction and by motions that average g and A anisotropy. Analysis of the processes that contribute to relaxation as a function of temperature is shown for triarylmethyl radicals, semiquinones, nitroxides, Cu2+ complexes, iron–sulfur complexes, and radicals in irradiated solids. In fluid solution, motion provides additional relaxation mechanisms. Analysis of T2 in solution is a powerful tool to elucidate motion. Experiments as a function of both temperature and resonance frequency are key to distinguishing between relaxation mechanisms.

A calibration-based approach to real-time in-vivo monitoring of pyruvate C1 and C2 polarization using the J_CC spectral asymmetry #DNPNMR

To measure the degree of polarization induced by the DNP process, one possibility is to calculate the ratio of the microwave OFF signal to microwave ON signal (neglecting depolarization under MAS conditions). While the ON signal is easy to measure since it typically a much better signal-to-noise ratio, measuring the OFF signal can often be challenging and the quality of the OFF signal will determine the error.

Measuring the NMR signal intensities of strongly coupled spin systems is a direct measure that does not require measuring the off signal. And a very elegant way is described in this paper from 2013:

Lau, Justin Y. C., Albert P. Chen, Yi-Ping Gu, and Charles H. Cunningham. “A Calibration-Based Approach to Real-Time in-Vivo Monitoring of Pyruvate C1 and C2 Polarization Using the J_CC Spectral Asymmetry #DNPNMR.” NMR in Biomedicine 26, no. 10 (October 2013): 1233–41. 

https://doi.org/10.1002/nbm.2942

A calibration-based technique for real-time measurement of pyruvate polarization by partial integral analysis of the doublet from the neighbouring J-coupled carbon is presented. In vitro calibration data relating the C2 and C1 asymmetries to the instantaneous C1 and C2 polarizations, respectively, were acquired in blood. The feasibility of using the in vitro calibration data to determine the instantaneous in vivo C1 and C2 polarizations was demonstrated in the analysis of rat kidney and pig heart spectral data. An approach for incorporating this technique into in vivo protocols is proposed.

A similar approach was used later by Vuichoud et al. analyzing the asymmetry of signal intensities of 2H Pake patterns. The same technique has been used in the Polarized Target Community to measure absolute target polarizations as initially described by Hamada et al.

Jain, Sheetal K., Guinevere Mathies, and Robert G. Griffin. “Off-Resonance NOVEL.” The Journal of Chemical Physics 147, no. 16 (October 28, 2017): 164201.

https://doi.org/10.1063/1.5000528

Dynamic nuclear polarization (DNP) is theoretically able to enhance the signal in nuclear magnetic resonance (NMR) experiments by a factor gamma_e/gamma_n, where gamma’s are the gyromagnetic ratios of an electron and a nuclear spin. However, DNP enhancements currently achieved in high-field, high-resolution biomolecular magic-angle spinningNMRare well below this limit because the continuous-wave DNP mechanisms employed in these experiments scale as w0^(-n) where n ~  1–2. In pulsed DNP methods, such as nuclear orientation via electron spin-locking (NOVEL), the DNP efficiency is independent of the strength of the main magnetic field. Hence, these methods represent a viable alternative approach for enhancing nuclear signals. At 0.35 T, the NOVEL scheme was demonstrated to be efficient in samples doped with stable radicals, generating 1H NMR enhancements of 430. However, an impediment in the implementation of NOVEL at high fields is the requirement of sufficient microwave power to fulfill the on-resonance matching condition, omega_0I = omega_1S, where omega_0I and omega_1S are the nuclear Larmor and electron Rabi frequencies, respectively. Here, we exploit a generalized matching condition, which states that the effective Rabi frequency, omega_1Seff, matches omega_0I . By using this generalized off-resonance matching condition, we generate 1H NMR signal enhancement factors of 266 (70% of the onresonanceNOVEL

enhancement) with omega_1S/2pi = 5 MHz.We investigate experimentally the conditions for optimal transfer of polarization from electrons to 1H both for the NOVEL mechanism and the solid-effect mechanism and provide a unified theoretical description for these two historically distinct forms of DNP.

Slice selection in low-temperature, DNP-enhanced magnetic resonance imaging by Lee-Goldburg spin-locking and phase modulation #DNPNMR

Chen, Hsueh-Ying, and Robert Tycko. “Slice Selection in Low-Temperature, DNP-Enhanced Magnetic Resonance Imaging by Lee-Goldburg Spin-Locking and Phase Modulation.” Journal of Magnetic Resonance 313 (April 2020): 106715.

https://doi.org/10.1016/j.jmr.2020.106715

Large enhancements in nuclear magnetic resonance (NMR) signals provided by dynamic nuclear polarization (DNP) at low temperatures have the potential to enable inductively-detected 1H magnetic resonance imaging (MRI) with isotropic spatial resolution on the order of one micron, especially when low temperatures and DNP are combined with microcoils, three-dimensional (3D) phase encoding of image information, pulsed spin locking during NMR signal detection, and homonuclear dipolar decoupling by Lee-Goldburg (LG) irradiation or similar methods. However, the relatively slow build-up of nuclear magnetization under DNP leads to very long acquisition times for high-resolution 3D images unless the sample volume or field of view (FOV) is restricted. We have therefore developed a method for slice selection in low-temperature, DNP-enhanced MRI that limits the FOV to about 50 m in one or more dimensions. This method uses small-amplitude phase modulation of LG irradiation in the presence of a strong magnetic field gradient to invert spin-locked 1H magnetization in the selected slice. Experimental results are reported, including effects of radio-frequency field inhomogeneity, variations in the amplitude of phase modulation, and shaped phase modulation.

Pulse-Shaped Dynamic Nuclear Polarization under Magic-Angle Spinning #DNPNMR

Equbal, Asif, Kan Tagami, and Songi Han. “Pulse-Shaped Dynamic Nuclear Polarization under Magic-Angle Spinning.” The Journal of Physical Chemistry Letters 10, no. 24 (December 19, 2019): 7781–88.

https://doi.org/10.1021/acs.jpclett.9b03070

Dynamic nuclear polarization (DNP) under magic-angle spinning (MAS) is transforming the scope of solid-state NMR by enormous signal amplification through transfer of polarization from electron spins to nuclear spins. Contemporary MAS-DNP exclusively relies on monochromatic continuous-wave (CW) irradiation of the electron spin resonance. This limits control on electron spin dynamics, which renders the DNP process inefficient, especially at higher magnetic fields and non cryogenic temperatures. Pulse-shaped microwave irradiation of the electron spins is predicted to overcome these challenges but hitherto has never been implemented under MAS. Here, we debut pulse-shaped microwave irradiation using arbitrary-waveform generation (AWG) which allows controlled recruitment of a greater number of electron spins per unit time, favorable for MAS-DNP. Experiments and quantum mechanical simulations demonstrate that pulse-shaped DNP is superior to CW-DNP for mixed radical system, especially when the electron spin resonance is heterogeneously broadened and/or when its spin−lattice relaxation is fast compared to the MAS rotor period, opening new prospects for MAS-DNP.

Prediction of flow effects in quantitative NMR measurements #DNPNMR

Friebel, Anne, Thomas Specht, Erik von Harbou, Kerstin Münnemann, and Hans Hasse. “Prediction of Flow Effects in Quantitative NMR Measurements.” Journal of Magnetic Resonance 312 (March 2020): 106683.

https://doi.org/10.1016/j.jmr.2020.106683.

A method for the prediction of the magnetization in flow NMR experiments is presented, which can be applied to mixtures. It enables a quantitative evaluation of NMR spectra of flowing liquid samples even in cases in which the magnetization is limited by the flow. A transport model of the nuclei’s magnetization, which is based on the Bloch-equations, is introduced into a computational fluid dynamics (CFD) code. This code predicts the velocity field and relative magnetization of different nuclei for any chosen flow cell geometry, fluid and flow rate. The prediction of relative magnetization is used to correct the observed reduction of signal intensity caused by incomplete premagnetization in fast flowing liquids. By means of the model, quantitative NMR measurements at high flow rates are possible. The method is predictive and enables calculating correction factors for any flow cell design and operating condition based on simple static T1 time measurements. This makes time-consuming calibration measurements for assessing the influence of flow effects obsolete, which otherwise would have to be carried out for each studied condition. The new method is especially interesting for flow measurements with compact medium field NMR spectrometers, which have small premagnetization volumes. In the present work, experiments with three different flow cells in a medium field NMR spectrometer were carried out. Acetonitrile, water, and mixtures of these components were used as model fluids. The experimental results for the magnetization were compared to the predictions from the CFD model and good agreement was observed.

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