Free Submitted: 06 December 2016 Accepted: 23 December 2016 Published Online: 23 January 2017
J. Chem. Phys. 146, 041101 (2017); https://doi.org/10.1063/1.4974358
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• Emmanuelle M. M. Weber
• James G. Kempf
• Daniel Abergel
• Geoffrey Bodenhausen
• Dennis Kurzbach

We report the generation and observation of long-lived spin states in deuterated methyl groups by dissolution DNP. These states are based on population imbalances between manifolds of spin states corresponding to irreducible representations of the C3v point group and feature strongly dampened quadrupolar relaxation. Their lifetime depends on the activation energies of methyl group rotation. With dissolution DNP, we can reduce the deuterium relaxation rate by a factor up to 20, thereby extending the experimentally available time window. The intrinsic limitation of NMR spectroscopy of quadrupolar spins by short relaxation times can thus be alleviated.
Dissolution dynamic nuclear polarization (D-DNP) aims at overcoming the intrinsically low sensitivity of NMR spectroscopy and MRI.1–31. A. S. Kiryutin, H. Zimmermann, A. V. Yurkovskaya, H. M. Vieth, and K. L. Ivanov, J. Magn. Reson. 261, 64 (2015). https://doi.org/10.1016/j.jmr.2015.10.0042. R. Buratto, A. Bornet, J. Milani, D. Mammoli, B. Vuichoud, N. Salvi, M. Singh, A. Laguerre, S. Passemard, S. Gerber-Lemaire, S. Jannin, and G. Bodenhausen, ChemMedChem 9, 2509 (2014). https://doi.org/10.1002/cmdc.2014022143. P. R. Jensen, M. Karlsson, M. H. Lerche, and S. Meier, Chem. - Eur. J. 19, 13288 (2013). https://doi.org/10.1002/chem.201302429 This enables an exciting range of previously inaccessible applications.4–64. J. H. Ardenkjaer-Larsen, B. Fridlund, A. Gram, G. Hansson, L. Hansson, M. H. Lerche, R. Servin, M. Thaning, and K. Golman, Proc. Natl. Acad. Sci. U. S. A. 100, 10158 (2003). https://doi.org/10.1073/pnas.17338351005. J. N. Dumez, J. Milani, B. Vuichoud, A. Bornet, J. Lalande-Martin, I. Tea, M. Yon, M. Maucourt, C. Deborde, A. Moing, L. Frydman, G. Bodenhausen, S. Jannin, and P. Giraudeau, Analyst 140, 5860 (2015). https://doi.org/10.1039/C5AN01203A6. P. R. Vasos, A. Comment, R. Sarkar, P. Ahuja, S. Jannin, J. P. Ansermet, J. A. Konter, P. Hautle, B. van den Brandt, and G. Bodenhausen, Proc. Natl. Acad. Sci. U. S. A. 106, 18469 (2009). https://doi.org/10.1073/pnas.0908123106 D-DNP relies on the coupling between nuclear and electron spins, as well as on the much larger magnitude of the latter’s magnetic moments. By saturating the electron paramagnetic resonance (EPR) transitions of unpaired electrons by microwave (μw) irradiation, the electron polarization is readily transferred to nearby nuclei, most efficiently to protons.77. A. Abragam and M. Goldman, Rep. Prog. Phys. 41, 395 (1978). https://doi.org/10.1088/0034-4885/41/3/002 Other nuclear spins can be enhanced by cross polarization (CP).88. K. Schmidt-Rohr and H. W. Spiess, Multidimensional Solid-State NMR and Polymers (Academic Press, San Diego, CA, 1996). In our laboratory polarizations P(1H) > 90% and P(13C) > 60% can be achieved routinely at cryogenic temperatures of 1.2 K in a magnetic field strength of 6.7 T. The rapid dissolution of the frozen hyperpolarized sample with overheated water and its transfer in 3-6 s to solution-state 800 or 400 MHz NMR systems allows us to achieve signal enhancements by factors up to 104–105 for 13C nuclei.99. B. Vuichoud, J. Milani, A. Bornet, R. Melzi, S. Jannin, and G. Bodenhausen, J. Phys. Chem. B 118, 1411 (2014). https://doi.org/10.1021/jp4118776 The process is schematically depicted in Fig. 1.
Here we highlight a curious and potentially valuable side-effect of hyperpolarisation by D-DNP: the creation of non-equilibrium population distributions in symmetrical deuterated spin systems. The utility of this finding lies in the long-lived nature of these population imbalances, which exhibit lifetimes that can be 20 times longer than the spin-lattice relaxation time T1(Dz) of the Zeeman polarization Dz of deuterium nuclei (henceforth denoted by D = 2H) that often relaxes too quickly (typically 0.5 < T1(Dz) < 2 s) considering the time required to transfer a hyperpolarized solution to an NMR spectrometer or to an MRI system for spectroscopy or imaging (Fig. 1).
Several related phenomena have been reported in the context of D-DNP: multiplet asymmetries that can be exploited for spin polarimetry (SPY),1010. B. Vuichoud, J. Milani, Q. Chappuis, A. Bornet, G. Bodenhausen, and S. Jannin, J. Magn. Reson. 260, 127 (2015). https://doi.org/10.1016/j.jmr.2015.09.006 an imbalance between symmetric and non-symmetric spin states (A/E imbalance) in 13CH3 groups has been discussed by Levitt, Dumez and co-workers,11,1211. M. C. Tayler, I. Marco-Rius, M. I. Kettunen, K. M. Brindle, M. H. Levitt, and G. Pileio, J. Am. Chem. Soc. 134, 7668 (2012). https://doi.org/10.1021/ja302814e12. J. N. Dumez, P. Hakansson, S. Mamone, B. Meier, G. Stevanato, J. T. Hill-Cousins, S. S. Roy, R. C. Brown, G. Pileio, and M. H. Levitt, J. Chem. Phys. 142, 044506 (2015). https://doi.org/10.1063/1.4906273 a triplet-singlet imbalance (TSI) has been observed in 13CH2 groups1313. D. Mammoli, B. Vuichoud, A. Bornet, J. Milani, J. N. Dumez, S. Jannin, and G. Bodenhausen, J. Phys. Chem. B 119, 4048 (2015). https://doi.org/10.1021/jp512128c and a sextet-triplet imbalance (STI) in 13CD2 groups.1414. D. Kurzbach, E. M. M. Weber, A. Jhajharia, S. F. Cousin, A. Sadet, S. Marhabaie, E. Canet, N. Birlirakis, J. Milani, S. Jannin, D. Eshchenko, A. Hassan, R. Melzi, S. Luetolf, M. Sacher, M. Rossire, J. Kempf, J. A. B. Lohman, M. Weller, G. Bodenhausen, and D. Abergel, J. Chem. Phys. 135, 194203 (2016). https://doi.org/10.1063/1.4967402
Here, we report the observation of a spin-state imbalance (SSI) in deuterated methyl groups CD3. The lifetime TSSI(D3) provides a new way to access of the activation energy of the rotation of methyl groups.
A 13CD3 group comprises an SI3 system with nuclear spins S = 1/2 and I = 1. To understand relaxation in 13CD3 groups, it is important to consider the C3v point group symmetry of the time-averaged Hamiltonian by using the symmetry-adapted eigenbasis described by Bernatowicz et al.1515. P. Bernatowicz, J. Kowalewski, D. Kruk, and L. G. Werbelow, J. Phys. Chem. A 108, 9018 (2004). https://doi.org/10.1021/jp049854m Each of the 27 symmetrized eigenstates of the D3 subsystem belongs to one of the four manifolds (irreducible representations) A, E1, E2, and B of the C3v point group. Various relaxation pathways between these eigenstates can be identified.
The principal components of the quadrupolar tensors of the three deuterons are aligned along the C—D bonds as shown in Fig. 2. The tensors are assumed to have cylindrical symmetry $( η = 0 )$. Fast 120° jumps of the CD3 group around its C3v symmetry axis lead to averaging of the quadrupolar tensors so that the three deuterons are no longer distinguishable with respect to quadrupolar relaxation.
Under these conditions a peculiar phenomenon arises: any imbalance generated between the populations that belong to different irreducible representations (A, E1, E2, or B) will persist since its return to thermal Boltzmann equilibrium is inhibited. This is because the flow of populations between these eigenstates is forbidden to first order.
Quantum states that feature an imbalance between populations belonging to different symmetry manifolds13,1613. D. Mammoli, B. Vuichoud, A. Bornet, J. Milani, J. N. Dumez, S. Jannin, and G. Bodenhausen, J. Phys. Chem. B 119, 4048 (2015). https://doi.org/10.1021/jp512128c16. M. Carravetta and M. H. Levitt, J. Chem. Phys. 122, 214505 (2005). https://doi.org/10.1063/1.1893983 vanish in thermal equilibrium. Here, using both hyperpolarization and a novel type of coherence transfer under radiofrequency pulses, we generated such imbalances in the CD3 groups of DMSO-d6 and acetone-d6 at cryogenic temperatures. Evidence of their existence was then observed in liquid-state 13C NMR spectra after dissolution. In thermal equilibrium, the 13C multiplets feature a symmetric 1:3:6:7:6:3:1 septet pattern due to the scalar couplings 1J(D,13C) = 18 Hz to the three equivalent neighboring deuterons with I = 1. However, in our experiments, an imbalance between the different symmetry manifolds is produced, which results in an asymmetric septet. The lifetime TSSI of the non-equilibrium deuterium spin state imbalance was obtained by monitoring the decay of this asymmetry.1,17–191. A. S. Kiryutin, H. Zimmermann, A. V. Yurkovskaya, H. M. Vieth, and K. L. Ivanov, J. Magn. Reson. 261, 64 (2015). https://doi.org/10.1016/j.jmr.2015.10.00417. Y. Feng, R. M. Davis, and W. S. Warren, Nat. Phys. 8, 831 (2012). https://doi.org/10.1038/nphys242518. G. Pileio, M. Carravetta, and M. H. Levitt, Proc. Natl. Acad. Sci. U. S. A. 107, 17135 (2010). https://doi.org/10.1073/pnas.101057010719. G. Pileio and M. H. Levitt, J. Chem. Phys. 130, 214501 (2009). https://doi.org/10.1063/1.3139064
In recent work,1414. D. Kurzbach, E. M. M. Weber, A. Jhajharia, S. F. Cousin, A. Sadet, S. Marhabaie, E. Canet, N. Birlirakis, J. Milani, S. Jannin, D. Eshchenko, A. Hassan, R. Melzi, S. Luetolf, M. Sacher, M. Rossire, J. Kempf, J. A. B. Lohman, M. Weller, G. Bodenhausen, and D. Abergel, J. Chem. Phys. 135, 194203 (2016). https://doi.org/10.1063/1.4967402 we described how the hyperpolarization of 13C nuclei in a 13CD2 group can be transferred to the attached deuterium nuclei via multispin order terms like CzDz, etc., through side-effects of non-ideal cross-polarization (CP) from protons to 13C. Similar principles apply to 13CD3 groups. During the CP-driven buildup of 13C polarization from the DNP-polarized protons of the frozen solvent, the relatively weak CP irradiation of 13C is insufficient to decouple its dipolar interactions with nearby deuterons. Consequently, 1H-13C CP leads to multispin carbon-deuterium coherences of the form n1CzDz, n2CzDzDz′ and n3CzDzDz′Dz″(with norms n1 = 3−1, n2 = 6−1/2, and n3 = 2−1) and permutations thereof. After dissolution, these operators project onto long-lived spin state imbalances states that are in antiphase with respect to 13C.1414. D. Kurzbach, E. M. M. Weber, A. Jhajharia, S. F. Cousin, A. Sadet, S. Marhabaie, E. Canet, N. Birlirakis, J. Milani, S. Jannin, D. Eshchenko, A. Hassan, R. Melzi, S. Luetolf, M. Sacher, M. Rossire, J. Kempf, J. A. B. Lohman, M. Weller, G. Bodenhausen, and D. Abergel, J. Chem. Phys. 135, 194203 (2016). https://doi.org/10.1063/1.4967402
These forms of antiphase spin state imbalance feature much longer relaxation times than one would expect, considering the quadrupolar interactions involved. A pictorial representation of the relaxation matrix, ΓQ, that describes the flow of populations between states of the D3 subsystem under the influence of quadrupolar couplings is shown in Fig. 3. Each of the 27 symmetry-adapted eigenstates $| 1 ⟩$ to $| 27 ⟩$ belongs to one of the four symmetry manifolds, A, E1, E2, and B. States belonging to different irreducible representations are not connected by any off-diagonal matrix elements if methyl group rotation is infinitely fast. This implies that the return to thermal equilibrium of a spin state imbalance between different symmetry manifolds cannot occur via quadrupolar relaxation. The relaxation time of the SSI can be found by evaluating the corresponding matrix elements. The relaxation rates shown in the matrix in Figure 3 were evaluated taking into account the entire Liouville space. This leads to the following expression for the lifetime of the longest-lived spin state imbalance in deuterated methyl groups:
 $T S S I ( D 3 ) = ( τ R τ R + τ C ω Q 2 + 2 τ R τ R + 4 τ C ω Q 2 ) − 1 ,$ (1)
here τR denotes the correlation time for rotation around the C3v symmetry axis, while τC refers to the overall tumbling. The lifetime TSSI(D3) would thus be infinite for infinitely fast methyl group rotation, since τR would become zero. TSSI(D3) thus provides a measure of the frequency of methyl group rotation and will be short if the activation energy for jumps around the C3v axis is high. However, for infinitely fast rotation around the C3v axis, chemical shift anisotropy (CSA) relaxation of the SSI could still occur in a manner that is analogous to the case described by Dumez et al. for protonated methyl groups.1212. J. N. Dumez, P. Hakansson, S. Mamone, B. Meier, G. Stevanato, J. T. Hill-Cousins, S. S. Roy, R. C. Brown, G. Pileio, and M. H. Levitt, J. Chem. Phys. 142, 044506 (2015). https://doi.org/10.1063/1.4906273
The multiplet of the 13C spins of the 13CD3 groups in DMSO-d6 at different times after dissolution and transfer to a conventional 400 MHz spectrometer is depicted in Fig. 4. They consist of seven lines numbered L1-L7. Deuterium populations that are not stored in the form of an imbalance have relaxed to thermal equilibrium. Then, in the first acquired spectrum (at time t = 0), the 13C multiplet of the hyperpolarized sample displays a significant asymmetry due to the presence of non-equilibrium deuterium populations that gradually disappears as the multiplet returns to its equilibrium distribution. There are two contributions: on the one hand, the central line L4 is attenuated, whilst the outer lines L1 and L7 are enhanced. On the other hand, antiphase terms of the form n1CxDz, n2CxDzDz′, and n3CxDzDz′Dz″ give rise to the observed tilt of the multiplet in Fig. 4. Simulations with SpinDynamica confirm that the spectra can be reproduced by a superposition of antiphase terms, spin state imbalances, and Cx magnetization.
The observed deviation of the multiplet from equilibrium provides a direct measure of the magnitude of the spin state imbalance between different symmetry manifolds. The asymmetry A can be quantified via the intensities of the individual multiplet components
 $A = ( L 1 + L 2 + L 3 − L 5 − L 6 − L 7 ) / L 4 .$ (2)
Note that only fast rotation about the C3v axis can average the three quadrupolar tensors in the CD3 group. Thus, the faster the rotation of the CD3 group, the better the separation of the four symmetry manifolds. Hence, a long lifetime TSSI(D3) of the asymmetry constitutes an indirect measure of the frequency of rotation of deuterated methyl groups. A similar behaviour has been shown by Levitt and co-workers for CH3 groups.12,2012. J. N. Dumez, P. Hakansson, S. Mamone, B. Meier, G. Stevanato, J. T. Hill-Cousins, S. S. Roy, R. C. Brown, G. Pileio, and M. H. Levitt, J. Chem. Phys. 142, 044506 (2015). https://doi.org/10.1063/1.490627320. B. Meier, J. N. Dumez, G. Stevanato, J. T. Hill-Cousins, S. S. Roy, P. Hakansson, S. Mamone, R. C. Brown, G. Pileio, and M. H. Levitt, J. Am. Chem. Soc. 135, 18746 (2013). https://doi.org/10.1021/ja410432f Werbelow and Grant have given a theoretical treatment of the effects of methyl group rotation on 13C NMR spectra.2121. L. G. Werbelow and D. M. Grant, Can. J. Chem. 55, 1558 (1977). https://doi.org/10.1139/v77-216
Importantly, no asymmetry of the 13C multiplet was observed in direct polarization experiments (without CP), which confirms that that the antiphase terms in the solid state that project on spin state imbalances only arise when employing CP.
Fig. 5 shows the experimental asymmetry A defined in Eq. (2) in DMSO-d6 and acetone-d6. The characteristic lifetimes of the multiplet asymmetry, denoted TSSI(D3), were found to be 6.8 s in DMSO-d6 and 12.8 s in acetone-d6. The S—O bond in DMSO tends to adopt a zwitterionic character (S+O), in contrast to the neutral double bond (C=O) in acetone. Because of the polarity of the CO moiety is lower than in SO, the methyl group rotation in acetone is expected to be faster than in DMSO. The oxygen atom of the carbonyl group constitutes a greater hindrance for the rotation of the deuterons in DMSO than in acetone, thus explaining the differences in TSSI(D3).2222. S. E. McLain, A. K. Soper, and A. Luzar, J. Chem. Phys. 124, 74502 (2006). https://doi.org/10.1063/1.2170077
It is obvious from Eq. (1) that lower energy barriers for methyl group rotation result in shorter τR, therefore leading to increased lifetimes and longer TSSI(D3). An increased negative charge on the neighboring oxygen, resulting in stronger interactions with the deuterons of the CD3 moiety and a larger rotational energy barrier, will thus lead to reduced lifetimes TSSI(D3). These lifetimes therefore provide an indirect measure of the activation energy of rotational jumps in deuterated methyl groups.
As longitudinal relaxation times of deuterons are typically on the order of a few seconds, the long lifetime of the here reported spin-state imbalance prolonging the experimental time window significantly, thus extending the scope of quadrupolar NMR.
The 13C spectra of DMSO-d6 in natural isotopic 1.1% abundance were observed in a mixture of ethanol:DMSO-d6:glycerol-d8 (v:v:v=1:2:1). Acetone-d6 containing samples were prepared in analogy to the DMSO samples. All samples were doped with 50 mM TEMPOL (4-hydroxy-2,2,6,6 tetramethylpiperidine-1-oxyl). Dissolution DNP and NMR experiments are explained in detail in Ref. 1414. D. Kurzbach, E. M. M. Weber, A. Jhajharia, S. F. Cousin, A. Sadet, S. Marhabaie, E. Canet, N. Birlirakis, J. Milani, S. Jannin, D. Eshchenko, A. Hassan, R. Melzi, S. Luetolf, M. Sacher, M. Rossire, J. Kempf, J. A. B. Lohman, M. Weller, G. Bodenhausen, and D. Abergel, J. Chem. Phys. 135, 194203 (2016). https://doi.org/10.1063/1.4967402.
The authors wish to thank Bruker BioSpin for providing a prototype for D-DNP. This work was supported by the French CNRS, the ENS, and the European Research Council (ERC contract “Dilute para-water”). The SpinDynamica code for Mathematica was programmed by Malcolm H. Levitt, with contributions from Jyrki Rantaharju, Andreas Brinkmann, and Soumya Singha Roy, available at www.SpinDynamica.soton.ac.uk.
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