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

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 1H-DNP 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.

Dynamic nuclear polarization (DNP) is a class of methods developed to overcome the low sensitivity issue affecting nuclear magnetic resonance (NMR) measurements. They rely on the transfer of the high spin polarization of a polarizing agent (PA) to coupled target nuclei via microwave (MW) irradiation.[1] DNP in liquids at room temperature, often known as Overhauser DNP,[2,3] is a spin relaxation mechanism driven by the time modulation of the hyperfine coupling between an unpaired electron and a target nuclear spin through molecular motions. This technique allows for the direct polarization of target nuclei and therefore has the potential to become a precious tool for routine NMR spectroscopy.[4,5]

In the past decade, DNP in liquids on 1H nuclei has been extensively studied at various magnetic fields.[6−9] In this case, dipolar relaxation modulated by molecular diffusion provides the main mechanism for the polarization transfer.[10−13] However, the efficiency of such a process decreases with rising magnetic field strength and limits the enhancements to ϵ ≲ 102 at 9.4 T on DNP-optimized instruments.[14]

More recently, larger enhancements have been observed for 13C nuclei,[15−17] reaching ϵ > 400 at 9.4 T and ϵ > 20 at 14.1 T. For 13C, the polarization transfer is driven by a mixture of dipolar relaxation and the counteracting scalar relaxation, based on the Fermi contact interaction. The latter is modulated by fast molecular collisions[15,17] (from subpicoseconds to picoseconds) and has been predicted to be the most efficient contribution.[15]

Small nitroxide radicals have often been chosen as PAs for liquid DNP thanks to their efficiency, which is usually attributed to fast diffusion rates and to the localized electron spin density. Other PAs have not been systematically tested, and only a few studies report on them,[18−22] whereas PA optimization is a thriving field in solid-state DNP.[23,24] Recently, we reported 50% larger 13C scalar enhancements when fullerene nitroxides (FNs) are used as PAs in comparison with the TEMPO radical.[17] This unexpected observation still lacks a satisfactory explanation and shows how the current understanding of the scalar relaxation is limited. Therefore, it is still difficult to design a PA whose features are specifically tuned for boosting the DNP efficiency in liquids.

We aim at elucidating the mechanisms contributing to the polarization transfer when the mobility of the PA changes. DNP enhancements on 1H nuclei were measured at low field as a function of the temperature and the size of the PA. In this way, we separately targeted translational diffusion and rotational diffusion, disentangling their impact on the polarization transfer mechanism. DNP enhancements were then measured on 13C nuclei at higher fields. In this case, the polarization transfer is driven by a complex interplay of translational diffusion, rotational diffusion, and the Fermi contact. Semiclassical theory and atomistic simulations were used to investigate how the peculiar differences in the structural dynamics of FN and small nitroxide radicals affect the DNP efficiency.

To analyze the DNP mechanism, it is essential to access the DNP coupling factor, ξ, which describes the efficiency of the relaxation processes driving the polarization transfer.[25] ξ can be calculated from the NMR enhancement ϵ with the Overhauser equation[3]where γe and γn are the electron and the nuclear gyromagnetic ratio, respectively. The leakage factor (f) and the effective saturation factor (seff) were determined independently via nuclear T1 relaxation measurements and ELDOR experiments,[26] respectively (Supporting Information).

1H-DNP experiments were performed at 0.34 T in the temperature range of 200–295 K for toluene and 220–295 K for chloroform, both doped with ∼1 mM of TEMPOL radical (TP). The coupling factor ξ calculated from eq decreases monotonically for decreasing temperatures for both toluene and chloroform, and it is positive over the whole temperature range (Figure a,b). Because ξ > 0, the polarization transfer is dominated by dipolar relaxation, whereas the scalar contribution for 1H-DNP is negligible.[10,22] Employing semiclassical relaxation theory,[10] the coupling factor for dipolar relaxation can be calculated considering both translational diffusion and molecular rotations[10]where ωn is the proton Larmor frequency. R1, is the nuclear relaxation rate, k is the amplitude, and J is the spectral density of the translational diffusion (“D”) and the rotational contribution (“rot”), respectively (Supporting Information). The spectral density JD(ω,τD), where τD is the correlation time, is described by the force-free hard-sphere model (ffHS) for translational diffusion.[27,28] The rotational component can be included phenomenologically with a Lorentzian spectral density Jrot(ωn,τc), with τc as the rotational correlation time.[13,29]

Figure 1

(a,b) 1H coupling factor ξ for toluene and chloroform doped with TP as a function of temperature. The values at room temperature agree with the predictions from molecular dynamics calculations.[11,30] Fits (solid lines) were performed with eq , where krot ≈ 0. (c,d) Self-diffusion coefficient of solvent (Ds) and TP in the solvent (DTP,s) as a function of temperature for toluene and chloroform. Lines are fits performed with a Speedy–Angell power law (toluene) and the Arrhenius function (chloroform) (Supporting Information).

As previously predicted for water[10,31] and observed in organic solvents,[32] the coupling factor ξ at room temperature for small organic radicals is mainly dependent on translational diffusion, and including a rotational contribution introduces an overparameterization.[33,34] Therefore, as a first approximation, we assume krot = 0 for TP, leaving only the translational diffusion component in eq . The correlation time is defined as τD = rD2/(Ds + Dr,s), where rD is the distance of the closest approach and Ds and Dr,s are the self-diffusion coefficients of the solvent and of the radical in the solvent, respectively. Therefore, it is necessary to determine Ds and Dr,s over a wide range of temperatures.

Figure c,d shows Ds and Dr,s of the investigated solvents as a function of temperature. DTP,tol, DCHCl, and DTP,CHCl were measured with pulsed-field gradient NMR (Supporting Information), whereas Dtol is reproduced from the literature.[35]

With Ds and Dr,s, the fit of the coupling factor ξ to eq requires only one free parameter, which is the distance of closest approach, rD, that is, the average distance over the different directions of approach between the PA and the target molecule.[10] The fits are in good agreement with the experimental data (Figure ) and confirm that a slower translational diffusion reduces the coupling factor ξ. The best-fit parameters are rDring = 3.5 Å and rDmethyl = 3.9 Å for toluene and rD = 3.65 Å for chloroform, respectively. The trend ξring > ξmethyl that is experimentally observed for toluene over the whole temperature range implies rDring < rDmethyl. Interestingly, the geometries of the TP–toluene complexes optimized via density functional theory (DFT) calculations reflect the same relation (Supporting Information).

Besides the translational diffusion, we aimed to selectively target the influence of molecular rotation by testing a series of bulkier nitroxide derivatives as PAs in both chloroform and toluene. They consist of 3β-doxyl-5α-cholestane (TP-CLST) and FNs, that is, nitroxide radicals functionalized with fullerene C60, having additional side chains (up to three) that improve the solubility and increase the rotational correlation time[22] (Figure a). All selected nitroxide derivatives have the spin density localized on the NO group. Therefore, the hyperfine coupling that drives the polarization transfer is not different from the TP radical. However, their increasing molecular size affects the rotational correlation time of the PA in the solvent, which ranges from τcEPR ≈ 6 ps for the TP radical to τcEPR ≈ 450 ps for larger FNs, as obtained from continuous-wave electron paramagnetic resonance (CW-EPR) measurements at 9 GHz (Table and Supporting Information).

Figure 2

(a) Structure of nitroxide radical and nitroxide derivatives used as PAs. (b,c, bottom) Coupling factor ξ of toluene[22] and chloroform doped with nitroxide derivatives plotted as a function of the rotational correlation time τcEPR of the PA. Radical concentration was c ≈ 1.5 mM for toluene and c ≈ 1 mM for chloroform. ξ was simulated with eq without (dashed lines) and with the rotational contribution (solid lines). (b,c, top) Relaxation rates for translational diffusion (R1,D) and rotation (R1,rot) as a function of τc.

Table 1

Correlation Times (in ps) for Translational Diffusion (τD) and Rotation (τcEPR) in Toluene and Chloroform Doped with TP and Nitroxide Derivatives

toluene with TEMPOL					chloroform with TEMPOL
T (K)	τDring	τDmethyl	τcEPR	τD/τcEPR	T (K)	τD	τcEPR	τD/τcEPR
200	344	427	16.2	>21	220	256	30	8.5
240	108	134	10.4	>10	240	142	14	10
270	59	74	7.4	>7.9	270	69	7.3	9.5
297	38	47	6.4	>5.9	297	40	4.6	8.7

Error on τcEPR is ∼10%. Error on τD is < 15%. Data from Enkin et al., 2015.[22]

The coupling factor ξ of chloroform doped with nitroxide derivatives (c ≈ 1 mM) was measured at 0.34 T at room temperature, whereas the values for toluene at the same field were previously reported.[22] As shown in Figure , ξ decreases for larger τcEPR and so does the DNP efficiency. The rationale for describing the polarization transfer requires an interplay of translational diffusion, governed by τD, and rotational motion, characterized by the rotational correlation time, τc. The translational diffusion of solvent molecules nearby the NO group of the PA remains almost unchanged compared with free TP because the accessibility to the radical is not hampered.[21] Therefore, the distance of closest approach, rD, in the ffHS model is considered to be independent of the particular derivative under study. However, because of the larger molecular size, the diffusion coefficient of nitroxide derivatives in the solvent (Dr,s) is expected to be much smaller than DTP,s. A reasonable approximation consists of choosing Dr,s ≈ 0 for nitroxide derivatives, which leads to τD ≈ rD2/Ds (Table ). The rotational contribution of the dipolar relaxation becomes larger for slower rotations, as previously observed in high-viscosity liquids.[29,36] This is the case in FN-na (where n is the number of adducts), with rotational correlation times τcEPR larger than τD (Table ). The rotational dynamics of the solvent molecules are much faster, being τc < 2 ps for both toluene[37] and chloroform,[38] meaning that their contribution can be neglected at this magnetic field (τcωn ≪ 1). Therefore, the spectral density Jrot(ω,τc)  =  2τc/(1 + τc2ω2) can be calculated assuming τc ≈ τcEPR.

The data in Figure were fitted to eq , where the sole free parameter is the amplitude of the rotational contribution krot, whereas kD is determined by τD and the radical concentration c (Supporting Information). The model fits the experimental data (Figure ) when krot = 0.8 × 108 for toluene and krot = 0.5 × 108 for chloroform. krot is similar for the two investigated solvents, and thus a bound state due to secondary interactions, such as π-stacking or halogen-bond-like interactions between the PA and the target molecule, is unlikely. Therefore, the rotational contribution is determined mainly by the choice of the PA. In particular, we note that in the limit of either fast rotating PAs (τc < 20 × 10–12 s) or immobilized PAs (τc > 10–5 s), this contribution is ineffective (Supplementary Figure S10).

The effect of bulkier nitroxide derivatives used as PAs in liquid-state DNP was also investigated for 13C as target nuclei. In this case, the scalar relaxation effectively contributes to the polarization transfer. Nitroxide derivatives TP-CLST, FN-1a, and FN-2a were tested as PAs in 13CCl4 and 13CHCl3 (c ≈ 10–20 mM), whereas FN and FN-3a showed instability in those solvents. DNP on 13C nuclei was performed at 1.2 T rather than at 0.34 T due to better NMR sensitivity. The experimental ξ values are reported in Figure and show an increase in absolute value with the molecular size. This translates into higher DNP efficiency for larger PAs: Specifically, up to 50% larger 13C enhancements were observed for FN-2a in comparison with the nitroxide radical TEMPONE (TN).[17] However, the dependency of the dipolar contribution on τcEPR does not account for such an effect, as discussed in the following paragraph.

Figure 3

ξ from 13C-DNP at 1.2 T on 13CCl4 and 13CHCl3 doped with nitroxide derivatives. The prediction (dashed-dotted line) has been calculated with eq considering the contributions to the relaxation rates from the translational diffusion (R1,D), the contact scalar interaction (R1,cont1), and the rotation (R1,rot).

The coupling factors ξ for TN in CCl4 and CHCl3 were modeled using a combination of relaxation rates driven by the translational diffusion (R1,D from the ffHS model) and the scalar relaxation arising from the Fermi contact (R1,cont), as reported in previous studies.[15,17]R1,cont is described by the Pulse model for random molecular collisions,[39] which comprises different types i of contact, each one characterized by a duration, 2τ, and a collision frequency, 1/τp,where F = ⟨A⟩2/(ℏ2τp,), and ⟨A⟩2 is the mean- square amplitude over time of the scalar interaction. For CCl4 and CHCl3, the scalar coupling is modulated mainly by fast molecular collisions with a duration of τ1 ≈ 0.5 ps.[15,17] The scalar contribution is included in eq as follows[10]where R1 = R1,D + R1,rot + R1,cont. Equation can be used to predict ξ for nitroxide derivatives at 1.2 T. The component R1,D was previously parametrized for the TN radical[17] and has now been rescaled for the diffusion of larger PAs (Supplementary Table S.IX). R1,cont was modeled as in ref (17). The amplitude of the rotational component was fixed to krot = 5 × 108 for both solvents, as determined from the low-field analysis of chloroform, and rescaled for c ≈10 mM. However, the prediction of ξ calculated with eq does not fit the experimental data, as shown in Figure . This implies that for nitroxide derivatives, the Fermi contact hyperfine coupling between the NO group and the target molecule could be subject to additional modulations with time scales different from the one of random molecular collisions.

To quantitatively access the time scales at which the hyperfine coupling is modulated, we also analyzed ξ values reported in a previous study[17] for different magnetic fields (1.2, 9.4, and 14.1 T). FN-2a in CCl4 was chosen as a study system due to its good DNP performance at low fields. Whereas the efficiency of FN-2a as a PA is higher than that of TN in a low field (|ξFN2a| > |ξTN|), the situation is reversed at high fields (|ξFN2a| ≪ |ξTN|), where the enhancements in 13CCl4 at 9.4 T are ϵ ≈ 10 and 430 for FN-2a and TN,[17] respectively. ξFN2a was simulated with eq with the components R1,D, R1,rot, and R1,cont (Table ), where now the scalar part considers not only one but rather two types of collisions (R1,cont = R1,cont1 + R1,cont2). Despite the few experimental data points, the correlation time τ2 of the additional contribution R1,cont2 can be reasonably estimated due to its large impact on the shape of ξ as a function of the magnetic field (Supplementary Figure S11 and ref (17)), whereas the amplitude F2 acts as a scaling factor. From this analysis, we obtained τ2 = 2.0–6.0 ps, where τ̅2 = 3.0 ps is the best-fit parameter, with an amplitude F2 accounting for ∼40% of the total scalar contribution (Table and Figure a).

Table 2

Correlation Times and Amplitudes of the Relaxation Contributions Used for Simulating ξTN (from Ref (17)) and ξFN2a as a Function of the Magnetic Field

		rotation		contact 1		contact 2
solvent	radical	krot	τc (ps)		τ1 (ps)		τ̅2 (ps)c
CCl4	TN		7.7b	1.25 × 1012	0.5
CCl4	FN-2a	5 × 108	637	1.25 × 1012	0.5	1.2 × 1012	3.0
CHCl3a	TN		4.8	1.25 × 1012	0.5
CHCl3a	FN-2a	5 × 108	385	1.25 × 1012	0.5	0.8 × 1012	3.0

For CHCl3, an additional Fermi contact component R1,cont1,H arises from hydrogen-bond-like collisions mediated by the H atom: The parameters are = 0.5 × 1012 rad/s, τ1,H = 12 ps, as reported in ref (17).

Data from Liu et al., 2017.[15]

τ̅2 is the best-fit value within the range τ2 = 2.0 to 6.0 ps (Supplementary Figure S11).

Figure 4

(a) ξFN2a in CCl4 and CHCl3 as a function of the magnetic field: experimental data (squares) and fits with eq (solid lines). The relaxation contributions calculated with the values in Table and normalized are shown in the top panel. Calculations for ξTN (dotted lines) are shown for comparison.[17] (b) Time trace of the C–C distance of the methyl groups on one side of the nitroxide ring obtained from MD runs for TN and FN-2a in chloroform (total time = 10 ns, T = 300 K, integration step = 2 fs). Dark lines are smoothed data (11 pt moving average). (c) Structural variation observed with the measured distance indicated in orange in FN-2a as extracted from the MD simulation.

To shine light onto the origin of this collision on a longer time scale, the behavior of nitroxide derivatives was explored by a computational approach combining DFT calculations and molecular dynamics (MD) simulations. Specifically, we focused on possible structural rearrangements of the nitroxide groups capable of modulating the hyperfine interaction. The conformational space of TN and FN-2a was explored by DFT calculations to identify structures corresponding to true energetic minima (Supporting Information). As already known for TN, a chairlike conformation constitutes the energetic minimum, whereas a twist structure is higher in energy (∼2.9 kJ/mol) yet still accessible at T = 300 K. For FN-2a, the asymmetry of the linker increases the number of possible conformations, but only one chairlike conformation was identified as the most favorable. In contrast with TN, other arrangements, such as the “boat” and, higher in energy, the twist, are inaccessible for FN-2a at room temperature.

The dynamics of both PAs were probed by MD simulations in CHCl3 using GROMACS 2018.4[40] and a set of previously reported parameters for the nitroxide radicals.[41] The results are summarized in Figure b, where the C–C distance of the methyl groups on one side of the nitroxide ring is used as a descriptor of the corresponding ring conformation. For TN, the expected interchange of chair conformations via twist intermediates is observed (Figure b). In contrast, FN-2a shows a stable chair conformation that remains unchanged at the simulation temperature in the investigated time frame, in agreement with DFT predictions. However, a different type of structural variation is observable for FN-2a, best described as the transformation of a chair to a half-chair conformation of the six-membered ring (Figure c). With respect to the DFT results, this corresponds to a transition state between the two conformers of lowest energy, that is, a chair and a “boat” (Supporting Information). Notably, this structural fluctuation happens on a time scale of few picoseconds (Figure b), which correlates well with the one extracted from the ξ experimental data (collision duration 2·τ2 = 4.0–12.0 ps). This suggests that the rearrangement of the methyl groups could effectively contribute to the modulation of the Fermi contact between the NO group and the target molecule, thus affecting the DNP efficiency.

In conclusion, we have explored how the mobility of the PA affects the efficiency of DNP in liquids. Translational diffusion and rotational diffusion can be disentangled by independently manipulating the temperature and the molecular size of the PA, respectively. In the case of 1H-DNP, where the polarization transfer is mainly driven by dipolar relaxation, fast rotating small molecules or immobilized radicals are the best choices as PAs. The situation is more complex for DNP on 13C nuclei when FNs are used as PAs. The Fermi contact interaction between the target molecule and the PA is modulated at least on two different time scales (2τ1 ≈ 1 ps and 2τ2 ≈ 6 ps), which are determined by the molecular collision and, as suggested here, by conformational changes of the PA. Our findings show how rotational diffusion and structural reorientations affect the DNP performances at specific magnetic fields. We foresee that these results will help in designing optimal PAs/target systems for efficient DNP in liquids and eventually boost new applications of NMR spectroscopy.