Diastereoisomers of l-proline-linked trityl-nitroxide biradicals: synthesis and effect of chiral configurations on exchange interactions

The chiral configuration of the two radical parts is a crucial factor controlling the exchange interactions and DNP properties of trityl-nitroxide biradicals.


Introduction
Exchange-coupled biradicals have recently attracted tremendous interest owing to their unique physiochemical properties and potential applications in high-frequency dynamic nuclear polarization (DNP), 1,2 molecule-based magnetism, [3][4][5] and molecular charge transfer 6-8 as well as molecular sensing. 9,10 A key point in the design of new biradicals is to control the magnitude and sign of the spin-spin exchange interaction that determines their physiochemical properties and potential applications. The intramolecular exchange interaction of biradicals strongly depends on the number of chemical bonds in the linkage between the two spins, the linker conformation, and the s/p contributions to the bonding as well as the environment (e.g., temperature and solvent). This exchange interaction can be through-bond and/or through-space, and its value varies by many orders of magnitude due to different linkers between the two radical moieties. 11,12 In general, for the biradicals with pconjugated backbones, the exchange interaction is mediated more effectively via through-bond mechanisms. The large exchange interactions have been achieved by enhancing the degree of p-orbital overlap between the spacer and two radical moieties through a conformational constraint to enforce their coplanarity. [13][14][15][16] Using donor-bridge-acceptor biradical systems, the dependence of magnetic exchange interaction on the degree of p-orbital overlap and torsional rotations between different parts has been well demonstrated. [17][18][19] Comparatively, the exchange interactions in the biradicals with nonconjugated spacers are much weaker and can be through-bond and/or through-space, depending on the exibility of the spacers. Recently, weakly coupled nitroxide biradicals have attracted intense attention as high-eld DNP polarizing agents which boost the sensitivity of solid-state nuclear magnetic resonance spectroscopy. [20][21][22][23][24][25][26][27] Nonconjugated linkers were applied in these biradicals and the rigidity and conformation of the linkers were well tailored in order to optimize the through-bond exchange and dipolar interactions and simultaneously realize the matching conditions of the EPR frequency. In addition, the supramolecular interaction with host molecules has been an effective approach to modulate the exchange interaction in nitroxide biradicals. [28][29][30][31] Despite these extensive studies, to the best of our knowledge, there is no related study on the chiral effect of the linker and radical moieties on the exchange interaction of biradicals.
In the past few years, we have developed trityl-nitroxide (TN) biradicals which combine two different radical properties into unique molecules. [32][33][34][35][36] Similar to other biradicals, the exchange interaction of TN biradicals is a key factor for their applications. We have ne-tuned the exchange interactions of TN biradicals by structural modication of the linkers 37 as well as by supramolecular interaction with cyclodextrins. 38 The largest DNP enhancement at a high magnetic eld (18.8 T) has been achieved by using these TN biradicals as polarizing agents, 35,36 in part due to the lack of nuclear depolarization. 39 In the present work, we utilize the chiral effect of the linker and two radical parts to modulate the spin-spin exchange interaction of TN biradicals. The trityl radical has a propeller conguration which affords the right-handed (P) and le-handed (M) helices. Due to the large steric bulk of three aryl groups, the interconversion between the two enantiomeric helices is slow and they are separable at room temperature. 40,41 Thus, the conjugation of the trityl radical CT-03 with the racemic mixture of the nitroxide APO through L-proline leads to four enantiomerically pure diastereoisomers (TNT 1 , TNT 2 , TNL 1 and TNL 2 , Scheme 1) which were separated by reversed-phase (TNT 1 and TNT 2 ) or chiral (TNL 1 and TNL 2 ) HPLC. The congurations of these diastereoisomers were determined by the comparison of experimental and calculated electronic circular dichroism (ECD) spectra. The effect of the congurations of the trityl and nitroxide radicals on the exchange interactions was investigated by EPR at different temperatures and solvents. Moreover, the DNP properties of TNT 1,2 and TNL 1,2 were also studied at a high eld (18.8 T).

Results and discussion
Synthesis of the four enantiomerically pure diastereoisomers Scheme 1 shows the synthetic procedure of the four biradical diastereoisomers. The racemic mixture of the nitroxide APO was rstly coupled with N-Boc-L-proline to afford the nitroxide diastereoisomers NP 1 (yield, 42%) and NP 2 (yield, 44%) which were easily separated using column chromatography on silica gel. Then NP 1 and NP 2 underwent deprotection by TFA, followed by conjugation with the trityl radical CT-03 to give the biradicals TNT 1,2 and TNL 1,2 , respectively. TNT 1,2 displayed two close peaks (11.34 and 11.58 min) with an area ratio of 1 : 1 on reversed-phase high performance liquid chromatography (RP-HPLC, Fig. S1 †) due to the P/M propeller congurations of the trityl part. 40,41 Therefore, it is possible to separate the two enantiomerically pure diastereoisomers of TNT 1,2 by semipreparative RP-HPLC and $2 mg of both diastereoisomers (TNT 1 and TNT 2 ) were obtained. In contrast, only one peak was observed in the RP-HPLC chromatogram of TNL 1,2 under the same conditions (Fig. S1 †). Attempts to separate the two diastereoisomers of TNL 1,2 by optimizing the RP-HPLC conditions failed. In addition, attempts to obtain the pure diastereoisomers of TNL 1,2 through their esterication using chiral agents such as S-(À)-1,1 0 -binaphthyl-2,2 0 -diol were unsuccessful. As Scheme 1 Synthesis of the four enantiomerically pure diastereoisomers of TN biradicals. M/P represents the helices of the trityl radical, while R/S indicates the configurations of L-proline and the nitroxide APO.
such, the separation of TNL 1 and TNL 2 was achieved by analytical HPLC with a chiral stationary phase (Fig. S3 †) and this separation procedure was repeated $50 times to afford $0.4 mg of TNL 1 and $0.4 mg of TNL 2 . The amounts obtained for the four diastereoisomers are sufficient for subsequent ECD and EPR experiments.

Conguration of the four biradical diastereoisomers
In order to determine the absolute congurations of the four biradical diastereoisomers, the experimental electronic circular dichroism (ECD) spectra of NP 1 /NP 2 and the four diastereoisomers were recorded in methanol. Meanwhile, the theoretical ECD spectra of NP 1 , TNT 2 and TNL 2 were also calculated using quantum chemical methods. All calculated ECD spectra with the TD-DFT method show an acceptable tting with the corresponding experimental spectra in terms of the spectral pattern and sign of the bands with respect to the wavelength. As illustrated in Fig. 1A, NP 1 exhibits a relatively strong ECD signal with a negative Cotton effect at 217 nm and a broad signal with a positive Cotton effect at 420 nm. Good agreement between the experimental and calculated ECD spectral patterns of NP 1 conrms the S absolute conguration of the nitroxide part. Accordingly, the absolute conguration of the nitroxide part of NP 2 is assigned as R.
Based on the absolute conguration of the nitroxide part, the absolute congurations of the four biradical diastereoisomers were further determined. The ECD spectrum of TNT 1 is characteristic of the trityl radical with two strong positive Cotton effects at 384 nm and 467 nm and two relatively weak negative Cotton effects at 324 and 352 nm. 42 Interestingly, the ECD spectra of TNT 1 and TNT 2 are mirror images most likely because the ECD signals of the nitroxide part in these biradical diastereoisomers are very weak and negligible as compared to the signals of the trityl part. Using TD-DFT calculations, the absolute congurations of TNT 1 and TNT 2 were assigned as (M, S, S) and (P, S, S), respectively. Likewise, the congurations of TNL 1 and TNL 2 were assigned as (M, S, R) and (P, S, R), respectively (Fig. S10 †). Fig. 2 shows the EPR spectra of the four diastereoisomers in aqueous solutions at room temperature. Both TNT 1 and TNT 2 in phosphate buffer (PB, 20 mM, pH 7.4) exhibit well-resolved triplets with line separations of $8.2 G, about half the 14 N hyperne splitting (a N , 16.0 G) of APO. This spectral feature is characteristic of strong intramolecular exchange interaction between the two spins. 37 Of note is that this EPR triplet pattern was only observed for the directly linked TN biradicals in previous studies. [32][33][34]37 Therefore, the strong exchange interactions for TNT 1 and TNT 2 are unexpected given that there are multiple s bonds (proline linker) between the two radical moieties. In contrast to TNT 1,2 , TNL 1,2 had much more complicated and less symmetric EPR spectra with an intense central line surrounded by multiple weak peaks (TNL 1 ) or one broad peak (TNL 2 ) at both sides. The broad EPR peak of TNL 2 at the le side indicates that it has a wide conformational distribution possibly due to the relatively high exibility of the linker. 37 Since the anisotropic hyperne and dipolar interactions of TN biradicals are averaged out in the liquid state, the exchange interactions (J) can be estimated from their EPR spectra in aqueous solution. Using the well-established simulation program, 43 the J values of TNL 1 and TNL 2 at room temperature are estimated to be 14 G and 32 G (Table 1), respectively. As expected, TNT 1 (252 G) and TNT 2 (128 G) have much higher J values than TNT 1,2 . Interestingly, the b and g relaxation parameters in the line width formula of the nitrogen hyperne pattern obtained for TNL 1,2 are larger than those of TNT 1,2 , indicating that the molecular rotation of TNL 1,2 is slower than that of TNT 1,2 . The slow molecular rotation further demonstrates that TNL 1,2 has loose geometries where the effective rotational radius is rather large and the two radical moieties are far away from each other. This spatial separation of the two radical moieties in TNL 1,2 may further explain why they have small J values as compared to TNT 1,2 . Taken together, the much stronger exchange interaction of TNT 1,2 than TNL 1,2 suggests that the R/S congurations of the nitroxide part play more important roles in modulating their exchange interactions than the M/P helices of the trityl part. This is unsurprising since the molecular structure of the trityl radical has high symmetry. Thus, it can also be deduced that the relative geometric conformation between the trityl part and the proline linker is similar for TNT 1 /TNT 2 or TNL 1 /TNL 2 . To verify this hypothesis, the four diastereoisomers of TN biradicals were reduced with ascorbate to the corresponding trityl monoradicals and their EPR spectra were recorded. As shown in Fig. S5, † the four trityl monoradicals had almost identical and partially overlapped triplet signals under anaerobic conditions due to the hyperne splitting (a N , 0.18 G) of the nitrogen from the proline linker. The identical a N value conrms that the relative geometric conformation between the trityl part and the proline linker is the same for the four monoradicals and the M/P helices of the trityl part have a minor effect on their exchange interactions.

Effect of temperature on the exchange interactions
The through-space exchange interaction of the biradicals with exible linkers can be enhanced at high temperature due to the rapid rotation of the chemical bonds in the linkers which increases the collisional frequencies of the two radical parts. As mentioned above, TNL 2 has a exible linker as evidenced by its broad EPR low-eld peak. To further investigate the effect of the linker exibility of the four diastereoisomers on their exchange interactions, their EPR spectra were recorded at high temperatures in the range of 305 K to 355 K. As shown in Fig. 3A, the EPR spectra of TNL 2 exhibited outstanding changes with temperature with two relatively stronger peaks at both sides than the central peak at high temperature. Similar results were also observed for TNL 1 . However, the EPR spectra of the two diastereoisomers TNT 1,2 at 355 K did not exhibit a signicant change except for slightly narrow linewidths (Fig. S8 †). Spectral simulation revealed that the J values of TNL 1 and TNL 2 increased with temperature from 17 G (305 K) to 93 G (355 K) and 53 G (305 K) to 149 G (355 K), respectively. The positive response of J values with temperature for TNL 1,2 can be explained by their exible linkers which allow for fast rotation of the chemical bonds in the linker, increase the collisional frequencies of the two radical moieties and further enhance the through-space exchange interactions. 44 In contrast, the EPR spectra of TNT 1,2 had no noticeable changes at different temperatures and their J values kept constant throughout the temperature range studied, implying that these two biradical diastereoisomers have rigid linkers (Fig. S8 †). Therefore, the conguration of the nitroxide part plays a critical role in modulating the exibility of the linkers and further the dependence of the exchange interactions on temperature.

Solvent effect on the exchange interactions
Solvents have an important inuence on the exchange interaction of biradicals by changing the population of the conformations or collisional frequencies of their two radical parts. Thus, the solvent effect on the exchange interactions of the four biradical diastereoisomers was also investigated in seven solvents (PB, MeOH, DMF, acetonitrile, acetone, THF and dioxane) at room temperature. EPR spectra were recorded

Solid-state EPR studies and spectral simulation
It has been demonstrated that the magnitudes of both dipolar and exchange interactions are very critical for the applications of biradicals in DNP which is carried out at low temperature. For this reason, the estimation of these two parameters from the frozen-solution spectra was attempted. Fig. 4 shows the EPR spectra of the four diastereoisomeric biradicals in a 60 : 40 (v/v) glycerol/H 2 O glass-forming solution at low temperature ($220 K). At the rst glimpse, the two diastereoisomers of TNT 1,2 have strong exchange interactions as reected from small overall separations between the outermost lines (i.e., 52 G for TNT 1 and 51 G for TNT 2 ) in their EPR spectra which are much smaller than 2Azz ($70 G) of the nitroxide radical. Comparatively, the exchange interactions of the two diastereoisomers of TNL 1,2 are identical and quite weak since there is a large overall separation of 73 G between the outermost lines in their EPR spectra. In order to reliably determine D and J values from the frozen solution spectra, especially when the J coupling is smaller than the dipolar and hyperne interactions, we modied our previous EPR simulation program (ROKI/EPR) 37 by taking into account the anisotropic dipolar interaction besides g and hyperne tensors. Note that this new program (called ROKI/DNP) enables the precise measurement of D and J values even determining the sign of J. Furthermore, it can also determine two polar angles which dene the orientation of the linker in the principal direction of the nitroxide moiety. If the spectra are recorded at a high resonance frequency, the three Euler angles can be estimated giving the relative orientation of the principal axes of g and hyperne tensors between the nitroxide and the trityl moieties (see more details in the Experimental section). As shown in Table 1, the order of the J values for the four biradical diastereoisomers in the frozen state is TNT 1 (196 G) $ TNT 2 (172 G) >> TNL 2 (6.3 G) $ TNL 1 (5.4 G). This trend is similar to the results obtained at room temperature. As mentioned above, the exible linkers in TNL 1,2 allow for the spatial proximity of the two radical parts and their exchange interactions are mostly based on a though-space mechanism above room temperature. In the frozen state, their molecular conformations were immobilized and their throughspace exchange interactions were inhibited. Thus, the very weak exchange interactions observed for TNL 1,2 in the frozen state are most likely due to the through-bond mechanism. The close J values of TNL 1 and TNL 2 indicate that they have similar preferential conformation(s) at low temperature. The similar conformations of TNL 1,2 in the frozen state were further conrmed by their identical dipolar interactions (D ¼ 8 G) which indicate the same distances between the two spins in TNL 1,2 . Comparatively, the exchange interactions of TNT 1,2 did not signicantly vary with temperature and had similar J values at $220 K and room temperature. These temperature-insensitive exchange interactions are due to the rigid linkers in TNT 1,2 which prevent the rotation of the chemical bonds in the linker and solidify their molecular conformations.

Dynamic nuclear polarization studies
Since TN biradicals are very promising DNP polarizing agents especially at a high eld, 35  and TNL 1,2 were also evaluated on an 800 MHz/527 GHz DNP/ MAS solid-state NMR system. 45 The enhancements of 13 C NMR signals of 13 C-15 N proline were measured using TNT 1,2 and TNL 1,2 as polarizing agents. As shown in Fig. 5, TNL 1,2 exhibits an over 40-fold signal enhancement, whereas TNT 1,2 has only a 7-fold enhancement. The distinct enhancements imply that the nitroxide chirality and thus the amplitude of the exchange interactions signicantly inuence the DNP properties of TNT 1,2 and TNL 1,2 . Our present study experimentally veried the adverse effect of the too strong exchange interactions of TNT 1,2 on its DNP enhancement although a similar result was theoretically suggested in a previous study. 46 In addition, the exchange interaction may affect the electron spin relaxation of biradicals 47 that has been shown to be a crucial factor controlling the DNP properties of nitroxide biradicals. 48,49 Thus, the effect of the exchange interaction is multiple. Detailed theoretical simulations may quantitatively describe the effect of the exchange interactions on the DNP properties of TN biradicals. 39,50 On the other hand, the 40-fold signal enhancement of TNL 1,2 is somewhat lower than that previously seen for TEMTriPol-1 (3 ¼ 65 for 13 C-urea) which differs from TNL 1,2 only by the linker and has an exchange coupling of 17 G determined by the new simulation program, which was reported to be 26 G in a previous paper. 36 Since TNL 1,2 (J $ 6 G) has weaker exchange interaction than TEMTriPol-1 (J ¼ 17 G), an optimal J value for TN biradicals may exist that is large enough for highly efficient polarization transfer but is so small as not to interfere with the frequency matching required for DNP. 51

Conclusions
We synthesized four enantiomerically pure diastereoisomers (TNT 1 , TNT 2 , TNL 1 and TNL 2 ) of TN biradicals with different chiral congurations in the nitroxide and trityl parts. The chiral conguration of the nitroxide part plays important roles in modulating the exchange interactions of these diastereoisomers and their dependence on temperature and solvents due to the different exibilities of the linkers. The diastereoisomeric mixture TNL 1,2 with a small and similar J value ($6 G) has  a much higher DNP enhancement (3 ¼ 40) than TNT 1,2 (J > 190 G, 3 ¼ 7), accounting for the adverse effect of too strong exchange interactions on the DNP enhancement. 36 This study demonstrates that the chiral conguration of the radical part is an effective factor modulating the exchange interaction of TN biradicals and this strategy can be used to develop new biradicals with improved DNP properties.

General information
All reactions were carried out under an argon atmosphere. Dichloromethane (CH 2 Cl 2 ) was redistilled with CaH 2 and dimethylformamide (DMF) were passed through a column of molecular sieves. Boc-L-proline, 1-hydroxybenzotriazole (HOBt), (benzotriazol-1-yloxy)tris(dimethylamino)phosphoniumhexauoro-phosphate (BOP), N,N-diisopropylethyl-amine (DIPEA), 2,2,5,5-tetramethyl-3-amino-pyrrolidine-1-oxyl free radical (APO) and ascorbic acid were purchased and used without purication. CT-03 was prepared according to a previously reported method. 52 Thin layer chromatography was performed on 0.25 mm silica gel plates. Flash column chromatography was employed using silica gel with a 200-300 mesh. Thin layer chromatography plates were visualized by exposure to UV light. High-resolution mass spectrometry was carried out in methanol employing electrospray ionization (ESI) methods. High resolution mass spectrometry (HRMS) analyses were performed on a LCMS-IT-TOF Shimadzu liquid chromatograph mass spectrometer. EPR measurements were carried out on a Bruker EMX-plus X-band spectrometer. ECD spectra were recorded on a Jasco J715 spectropolarimeter (Jasco Corporation, Tokyo, Japan). Analytical HPLC was carried out on an Agilent 1100 equipped with a G1315B DAD detector and G1311A pump. Semipreparative HPLC was carried out on an SSI 1500 equipped with a UV/vis detector and versa pump.

Reduction of the four biradical diastereoisomers by ascorbic acid
Each diastereoisomer (50 mM) was mixed with ascorbic acid (2 mM) in PBS (20 mM, pH 7.4). Aer the reaction was completed, the resulting solution was transferred into a capillary tube and EPR spectra were recorded using the following EPR parameters: microwave power, 0.5 mW; modulation amplitude, 0.03 G.

EPR spectroscopy
EPR measurements were carried out on a Bruker EMX-plus Xband spectrometer at room temperature (298 K) or low temperature ($220 K). General instrumental settings were as follows: modulation frequency, 100 kHz; microwave power, 10 mW; and modulation amplitude, 1 G for room temperature and 2 G for low temperature. Measurements were performed in 50 mL capillary tubes. Spectral simulation was performed by using the program developed by Professor Rockenbauer. 43 In this study, the exchange, dipolar and hyperne couplings are given in Gauss units which can be converted into cm À1 by multiplying with g Â 4.6686 Â 10 À5 , where g is the respective Zeeman factor. EPR measurements under anaerobic conditions were carried out using a gas-permeable Teon tube (i.d. ¼ 0.8 mm). Briey, the sample solution was transferred to the tube which was then sealed at both ends. The sealed sample was placed inside a quartz EPR tube with open ends. Argon gas was allowed to bleed into the EPR tube, and then an EPR spectrum was recorded.

EPR simulation
The EPR spectra are computed by using a perturbation solution of the biradical spin Hamiltonian: The computations are carried out in three different frames: (1) The (x, y, z) reference frame is chosen as the principal axis of theĝ 1 Zeeman andÂ 1 hyperne tensor of the nitroxide moiety. The orientation of the magnetic eld is given by the q and f polar angles and dened in the above frame.
The slightly anisotropicĝ 2 tensor and a smallÂ 2 hyperne tensor of the trityl are dened in the (x 0 , y 0 , z 0 ) frame. The relative orientation of the two frames is characterized by the three Euler angles a, b and g:ĝ The same transformation denes the relationship of the hyperne tensorsÂ 1 andÂ 2 .
(3) The dipolar interaction D 00 is dened in a third frame, where the z 00 axis shows the direction of the linker and its orientation is given by two polar angles x and z. A perturbation procedure is applied in the case when the Zeeman term is large compared to the exchange, dipolar and hyperne interactions.
Then in the Zeeman and hyperne terms, only the z component of the electron and nuclear spin remains: Here the g-factor is gðq; fÞ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi g xx 2 sin 2 q cos 2 f þ g yy 2 sin 2 q sin 2 f þ g zz 2 cos 2 q q The angular dependence of the hyperne constant is The angle dependence of the dipolar interaction is given as The d angle between the magnetic eld and the z 00 axis can be expressed by the polar angles x and z: The biradicals have four energy levels that can be assigned to the S ¼ 1 triplet and S ¼ 0 singlet state. Both the exchange and dipolar terms can mix the M S ¼ 0 states of the S ¼ 1 triplet and S ¼ 0 singlet: The diagonal elements in the |S, M S i basis are while the off-diagonal elements are zero.
The Zeeman and hyperne interactions have only diagonal elements in the |S, M S , M I1 , M I2 i basis if M S ¼ 1 or À1: For the M S ¼ 0 state, these interactions give zero diagonal elements, but in this case the off-diagonal elements can be nonzero: Aðq; fÞ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi g xx 2 A xx 2 sin 2 q cos 2 f þ g yy 2 A yy 2 sin 2 q sin 2 f þ g zz 2 A zz 2 cos 2 q q g 1 ðq; fÞ h1, 0|H Z + H HF |0, 0i Since the |1, 1i and |1, À1i triplet states are well separated from the central states, the eigenvalues can be obtained directly from the diagonal elements. We introduce the indices i ¼ 1 and 4 for the highest |1, 1i and lowest |1, À1i states, respectively. Furthermore i ¼ 2 and 3 denote the two central states with M S ¼ 0.
The mixing of |1, 0i and |0, 0i states can be obtained by the solution of the secular equation: The mixing coefficients can be expressed by the factor R: It is worth noting that the transition probability and energy depend on the relative sign of D and J, which offers a possibility to decide from the frozen solution EPR spectra whether the Heisenberg exchange is ferro-or anti-ferromagnetic. Then, the energy expressions for the central states are Due to the triplet-singlet mixing, four transitions can take place in the whole M I1 , M I2 subspace. The two resonances have the transition probability The respective frequency is The above resonances can be called "allowed", since their intensities are larger than 1.0 and the line separations are smaller than J. The other pair of resonances has the transition probability This transition can be considered as "forbidden" due to the smaller transition probability: 2p 2 2 < 1.0 and the frequency spread can be extended in a broad range comparable with the value of J: ħu 13 or 34 ¼ 1/2(g 1 + g 2 )m B H 0 + 1/2(A 1 M I1 + A 2 M I2 ) AE (J/2 + D + R/2) For a xed u EPR microwave frequency the above relationships allow the determination of the corresponding four resonance elds H i,M I1 ,M I2 (q, f), where the i index denotes the four transitions.
The ROKI/DNP program can use either Lorentzian or Gaussian, or mixed line shapes f(H) and the powder pattern can be obtained by integrating over the angles q and f: All parameters can be optimized to achieve the best t of the experimental spectra; the method of optimization is the same as that described in the ROKI/EPR program. 43 Due to the large number of optimized parameters ambiguity can occur. This problem can be reduced by recording the frozen solution spectra at different resonance frequencies. In X band spectra the determination of the three Euler angles is rather problematic due to the small g anisotropy of the trityl moiety. The polar angles, however, are more reliable since the nitroxide part has a large Zeeman and hyperne anisotropy.
DNP/ssNMR spectroscopy of the diastereoisomeric mixtures TNT 1,2 and TNL 1,2 DNP experiments were performed on frozen solutions of 10 mM biradical in d8-glycerol : D 2 O : H 2 O 60 : 30 : 10 v/v/v with 0.25 M U-13 C-15 N proline. DNP experiments at 800 MHz were performed on a Bruker BioSpin 527 GHz solid-state NMR DNP spectrometer. This spectrometer is equipped with a Bruker 800 WB/RS Plus magnet with a sweep coil, an Avance III NMR console, and a low-temperature 3.2 mm triple-resonance DNP MAS NMR probe. 45 A gyrotron microwave source emits microwaves at a frequency of 527.043 GHz. In the DNP experiments the nuclear polarization is measured through the spectrum of 13 C-15 N proline, which is observed via 13 C-1 H cross-polarization (CP). A CP spin-locking eld of 50 kHz is applied on 13 C, while the spin-locking eld on 1 H is ramped from 36 to 45 kHz. The contact time was set to 2 ms. During the acquisition SPINAL-64 decoupling 53 was used at 83 kHz. Each CP acquisition was preceded by a presaturation sequence consisting of 300 90 1 H pulses 20 ms apart at an RF power of 100 kHz, followed by a period of polarization build-up, which was set to 1.26T 1 for optimal sensitivity. Each spectrum was acquired with a 4-step phase cycle and acquired three times to conrm stability and reproducibility. The MAS frequency was set to 8 kHz and the sample temperature was kept at 103 K, unless noted otherwise. The enhancement, 3, was obtained from comparison of the 13 C signal amplitude with and without microwaves. T 1 (microwaves off) and T B (microwaves on) were measured via a saturation recovery experiment. T 2 was determined from the decay of the echo intensity during a rotor-synchronized Hahn echo sequence. To obtain the CE DNP enhancement eld proles the magnetic eld is swept and at each eld position the nuclear polarization is measured via the cross-polarization experiment as described above.

Conflicts of interest
There are no conicts to declare.