Optimization and prediction of the electron–nuclear dipolar and scalar interaction in 1H and 13C liquid state dynamic nuclear polarization

Solution-state dynamic nuclear polarization (DNP) is a powerful tool for hyperpolarization and the study of intermolecular interactions in solution.


Introduction
In dynamic nuclear polarization, the electron-nucleus dipolar and scalar couplings can be described by the Hamiltonian, where h is the Planck constant,Î is the nuclear spin angular momentum operator,Ŝ is the electronic spin angular momentum operator, D is the dipolar coupling tensor, and A is the hyperne coupling tensor (typically in units of MHz). One can compute the dipolar coupling tensor D; however, knowledge of the electron-nucleus dipole-dipole correlation function is required to determine the enhancement factor. 1 Computation of this dipole-dipole correlation function can be achieved with a molecular dynamics simulation. However, such simulations are typically limited to select parameterized systems, and are very computationally intensive. [1][2][3] During the last two decades, signicant advances have been made in the eld of dynamic nuclear polarization (DNP). 4,5 For liquid-state DNP, there has been a resurgence of interest in ameliorating liquid-state high magnetic eld DNP enhancements. [6][7][8][9][10] Liquid state Overhauser effect DNP has been applied for signal enhancement of ow imaging [11][12][13][14] as well as the characterization of local water dynamics in biological systems. [15][16][17][18][19][20][21] More recently, 1 H liquid state DNP measurements of water [22][23][24][25][26] and small organic molecules [27][28][29] at higher magnetic elds have been reported. However, liquid state DNP experiments also provide an excellent approach for understanding and predicting intermolecular solution interactions. The drawbacks for obtaining signicant DNP enhancements (A) in the liquid state are well recognized, since the time-dependent electron-nuclear interaction dominates the Overhauser effect (Oe). [30][31][32][33][34][35] This can be derived from eqn (2)-(4), where g S and g I are the magnetogyric ratios for the electron and nuclear spins, respectively, and the coupling (r) and leakage (f) factors are dened in terms of the nuclear transition probabilities in the presence of a free radical, W D 2 , W D 0 , W D 1 , which represent dipolar relaxation, and W Sc 0 due to scalar relaxation, as well as the transition probability in the absence of a free radical W 10 ( Fig. 1). 35 For molecular liquid systems, the time-dependent dipolar interaction dominates at low magnetic elds and/or short correlation times (s c ) in the extreme narrowing limit u S 2 s c 2 ( 1 (u S electron Larmor frequency). Unfortunately, at the high magnetic elds (3-12 T) commonly employed in NMR, the coupling factor approaches zero (shown in Fig. 2).
Scalar relaxation originates from the coupling of the magnetic moments of electrons and nuclei via the hyperne coupling interaction. 36 Although A in eqn (1) is the isotropic Fermi contact hyperne coupling tensor, henceforth it is labelled as a FC , in order to avoid confusion with the DNP enhancement, A vide infra.
For hydrogen containing molecules, 1 H DNP enhancements are usually dominated by the dipolar relaxation mechanism. If one assumes a rotationally modulated mechanism dominates the electron-nuclear dipolar interaction, the corresponding rotational correlation time (s r ) can be estimated 34,35,37 (see ESI † for detailed derivation). The corresponding DNP coupling factor modulated by exclusive rotational diffusion gives the magnetic Fig. 1 Schematic diagram of energy level and transition probabilities for electron-nuclear ( 13 C) spin systems for benzene/TEMPO (above) and phenylacetylene/TEMPO (below). a S and b S are the spin states of the unpaired nitroxide electron spin, and a I and b I are for nuclear spins. W S represents the electron relaxation; W 0 , W D 1 and W D 2 are zero, single and double quantum transitions, respectively. W 0 is equal to the sum of W Sc 0 and W D 0 in eqn (3) and (4), which are transition rates of scalar and dipolar relaxation, respectively. 13 C DNP enhancement of benzene is mainly due to dipolar relaxation, while scalar relaxation is the dominant mechanism for the b carbon of phenylacetylene.  13 C of chloroform/0.0052 M TEMPO. 44 The relative standard deviation for r is about 15%. The two correlation times were estimated from 1 H DNP coupling factors of benzene in SF CO 2 and normal solvent by a rotational diffusion modulated dipolar interaction mechanism (see ESI † for derivation). eld dependence shown in Fig. 2. More recently, it has been reported that translational diffusion predominantly modulates the dipolar interaction for water 6,38,39 and some small organic molecular systems 29,40 with organic radicals. Using the same correlation times, the eld dependence of the DNP coupling factor modulated by translational diffusion 33,35,41 is also represented by coloured dashed lines in Fig. 2. One notable exception for the 1 H nuclide is a nitroxide-triuoroacetic acid system reported by Bates where the scalar interaction dominates the 1 H DNP enhancement. 42 On the other hand, for the 13 C nuclide, the coupling interaction can be dominated by a strong scalar interaction (W Sc , or by a mixture of scalar and dipolar interactions. As illustrated in Fig. 1, it is well recognized that molecules with a (C-H) group can exhibit weak hydrogen bonding with nitroxides and show modest to large scalar enhancements. 35,44,[46][47][48][49] Griffin and coworkers have pointed out the importance of the scalar interaction for certain other nuclides ( 19 F, 15 N, 31 P) besides 13 C for high-eld liquid-state DNP studies. 50 Unfortunately, it is difficult to estimate the corresponding scalar correlation time s sc . For the case of acetonitrile/ TEMPO, we previously reported 13 C DNP s sc values 2-3 times longer than the dipolar correlation time (s r ). 49 As rst reported by our laboratory, the solid-liquid intermolecular transfer (SLIT) DNP experiment has certain advantages when the radical is not present in the solution. 51,52 In the SLIT DNP experiment, 13 C contact shis and spectral line broadening are avoided in the high eld NMR detection magnet. The SLIT approach also has the advantage of improved low to high magnetic eld transfer efficiencies allowing the transfer of radical free hyperpolarized metabolites for biological uses. 53,54 The use of immobilized radicals for DNP approaches has recently been reconsidered and utilized to generate hyperpolarized water for clinical MRI applications. [11][12][13]55,56 The efficiency of interactions between the radical and nuclei in immobilized radical ow methods can be in fact improved through better design of immobilizing methods, 11,57 as well as the optimum synthesis of new radicals. [58][59][60] In the current study, we demonstrate that 1 H LLIT (liquidliquid intermolecular transfer) and 1 H SLIT DNP with solutes dissolved in supercritical uid (SF) CO 2 result in enhanced electron-nuclear dipolar interactions and exhibit signicant Oe DNP enhancements as a result of reduced correlation times. This is the rst report of SF DNP with supercritical CO 2 except for the earlier 1 H DNP enhancement of supercritical ethylene by Wind and coworkers. 61 It is well recognized that solutes dissolved in supercritical uids exhibit signicantly shorter molecular correlation times. 62 For the case of the 13 C nuclide, we present dipolar dominated 13 C DNP enhancements for the fullerene C 70 , with a trend attributable to the difference in the intermolecular distance for electron-nuclear interaction. In a large number of molecules with acidic C-H groups, signicant scalar interactions and corresponding large positive enhancements are observed in the nitroxide-substrate complex. For example, we show that sp hybridized (H-C) alkyne systems, such as, the phenylacetylene-nitroxide system exhibit very large scalar dominated enhancements. It is also possible to directly compare liquid-liquid intermolecular scalar (Fermi contact) hyperne couplings (a FC ) with experimental scalar DNP data utilizing density functional theory (DFT) modeling. 49 We will subsequently demonstrate that computational predictions of the scalar hyperne coupling constants (HFCs) across a wide set of nitroxide-substrate systems correlate strongly with the DNP enhancements for systems dominated by the scalar interaction.

Samples
The production method used to obtain the C 60 and C 70 fullerenes utilized an apparatus similar to the original Krätschmer-Huffman 63 arc-burning method. Cored rods (6 mm diameter) packed with a mixture of graphite and amorphous carbon ( 13 C labelled) were arc-burned in a fullerene generator under a dynamic He atmosphere. Typical electric-arc operating production parameters consist of 20-25 V, 95-115 A, and 180-220 Torr of helium. The fullerenes were extracted by dissolution in CS 2 immediately aer collection of the soot. Following this extraction protocol, the raw extract was ltered over a plug of glass wool. The C 60 and C 70 samples were separated chromatographically utilizing a pentabromobenzyl column, (PBB, 25 cm Â 10 mm i.d., Phenomenex Co., Torrance, California) with CS 2 as the mobile phase. A mass spectrometer for the sample conrmed that the sample was 13 C labelled at a level of approximately 12%. All other reagents and solvents for the LLIT DNP experiments were obtained commercially. C 6 D 6 was purchased from the Isotic Inc, and other chemicals were purchased from Aldrich Chemical Co. and used without further purication. Sample solutions for the LLIT DNP experiments were prepared with TEMPO of varied concentrations from 0.001 to 0.14 M. The immobilized nitroxide materials used for the SLIT DNP experiments were synthesized in our lab by Rossi Gitti. 53 The sample solutions were degassed by bubbling N 2 gas through during DNP experiments.

Dynamic nuclear polarization instrument
The instrument used for the LLIT DNP experiments was described previously. 44 The ow transfer DNP apparatus for normal liquids and supercritical uid CO 2 is shown in Fig. 4, where SF CO 2 can be used as the owing solvent. For ow 1 H DNP performed under supercritical uid conditions, N 2 degassed neat liquid benzene containing free radical TEMPO (0.1 M-0.01 M) originates at the HPLC pump and ows at a rate of 0.1 mL min À1 . The typical sample volumes inside the low eld microwave cavity and high eld NMR detector are 160 and 60 mL, respectively, and the volume of the transfer region is 80 mL. CO 2 is pumped from a syringe pump of a Suprex SFC/200A Multipurpose Unit and equilibrated to a ow rate of 1.01 mL min À1 and 165 atm. The liquid sample is introduced into the CO 2 ow, and at a total ow rate of 1.11 mL min À1 the sample solution enters the SFC oven where it is heated to 40 C. The ow rate maintains the liquid sample concentration ensuring the liquid solutes solubility and also keeps optimum condition based on transfer and residence times for the ow 1 H DNP apparatus.
The instruments for the SLIT DNP performed in normal liquids and SF CO 2 were reported in our previous studies. [51][52][53][54] The immobilized nitroxide radical is contained in a ow cell and located in the 0.33 T low eld cavity, where electron spins are polarized. The experimental procedure of SLIT 1 H DNP is similar to that of LLIT 1 H DNP. The rate of liquid ow containing the sample was adjusted accordingly to obtain preferred concentrations in normal liquids or SF CO 2 as the owing solvent.

Determination of experimental parameters
The determination of the leakage factor f and the electron spin saturation factor s is described previously for the DNP owing system. 44 In ref. 44, we reported a theoretical model for determining the absolute enhancement for the low to high magnetic eld transfer experiments, which is scaled according to the observed enhancement considering relaxation losses during the transfer. This model is restated in ESI. † For most systems reported in this study, the DNP data were processed based on this model, and the absolute DNP enhancements were calculated using the method we applied previously. 53,64,65 For benzaldehyde, nitrobenzene, toluene, diphenylmethane, triphenylmethane, benzonitrile, anisole, phenylamine and acetone systems, the absolute enhancements of 13 C LLIT DNP were obtained utilizing a ratio method 66-68 using the 13 C enhancement of cyclohexane as the reference compound, with detailed procedures illustrated in the ESI. † Enhancements of ethyl acetoacetate and diethyl malonate were determined by the ratio method using 13 C of benzene as the reference. The DNP enhancements of C 70 were also determined using the ratio method using C 60 as the reference. Compared to the former model, the ratio method does not require extrapolation from observed enhancements at varied liquid ow rates and microwave powers. The applicability of the ratio method was carefully evaluated utilizing the adamantane/TEMPO system, where the DNP enhancement was validated by this method using different microwave power levels (Table S1 †). A detailed discussion is included in the ESI. † However, the ratio method does lead to low-to-high magnetic eld transfer efficiency errors when the substrate molecules of interest contain quaternary carbons with signicantly longer T 1 relaxation times. For the electron spin saturation parameter s, we employed relatively high radical concentrations (0.1 M and higher) for DNP experiments in normal solvents in this work, in order to saturate a single EPR line and also have leakage factors approaching unity. For the benzene/SF CO 2 studies a low nitroxide radical concentration (0.001 M) was employed since fast Heisenberg electron-electron exchange led to a single broad EPR line for this system.

Theory: geometry optimization, solvation, and thermochemistry
Geometry optimizations were performed for all species at the unrestricted M06-L 69 level of density functional theory. The def2-SVP basis set 70 was used for all atoms during optimization. The nature of stationary points was assessed in all cases by computation of analytic vibrational frequencies, which were also used to compute the molecular partition functions necessary to predict 298.15 K thermochemical quantities using the conventional ideal-gas, rigid-rotator, quantum-mechanical quasi-harmonic-oscillator 71 approximation. 72 Improved electronic energies were computed with the M06-2X density functional 73 and the SMD continuum solvation model 74 to account for the effects of the solvation environment, as single-point calculations, using the def2-TZVPP basis set 70 on all atoms. Benzene was used for SMD solvent parameters on nitroxide/ benzene and nitroxide/phenylacetylene systems; whereas cyclohexane SMD solvent parameters were specied for nitroxide/benzaldehyde and nitroxide/nitrobenzene systems.

Theory: isotropic hyperne coupling
The 13 C hyperne coupling constants were computed in the gas phase at the unrestricted B3LYP level of DFT employing the EPR-III basis 75 for C, N, H, O. We chose to use the B3LYP functional 76 based on previously demonstrated good EPR performance for a nitroxide in aqueous solution. 1 Hyperne coupling constants were computed using the spin-orbit mean-eld approximation SOMF(1X). 77 For all substrate/TEMPO systems, Boltzmann weighted isotropic HFCs for nucleus j, a iso j , are determined from low-energy intermolecular congurations, c i , as computed from eqn (5). a iso j,ci is the isotropic HFC for nucleus j in geometrical conguration c i , DG ci is the relative free  energy of geometrical conguration c i , R is the universal gas constant, and T is the temperature (taken to be 298.15 K). Symmetry equivalent atoms are averaged together.

Soware
All optimization, thermochemistry, and solvation computations were accomplished using the Gaussian09 Rev D.01 suite of electronic structure programs. 78 All EPR computations were accomplished in the gas phase using the ORCA 3.0.2 suite 79 of electronic structure programs.  Fig. 2). An important difference of nitroxides dissolved in normal liquids versus supercritical uids is the higher Heisenberg exchange rates in the latter case. Batchelor, 89 as well as Randolph and Carlier 90 suggest a large increase in Heisenberg electron-electron exchange rates and hence the increased line widths of nitroxides in SF's may be due to critical clustering between solute and solvent molecules. Thus, the EPR signal for TEMPO collapses to a single broad line in SF CO 2 (see Fig. S2 †). Also, the values of the saturation factor s are smaller in SF CO 2 compared with normal liquids (see Table S2 † and saturation curves Fig. S3 and S4 †). Han et al. 91 and Bennati et al. 6 have presented new models and alternative methods for quantifying the Overhauser DNP saturation factor especially for the case of low radical concentrations ($0.001 M). However, their results suggest that at nitroxide concentrations of 0.01-0.02 M the errors in determining the saturation factor are not as signicant. Thus, we have presented data in liquid C 6 D 6 determined at both 0.001 M and 0.01 M of TEMPO concentrations as illustrated in Table 1 for comparison with the SF CO 2 data. The increased 1 H DNP enhancement of benzene in SF CO 2 in comparison with benzene in liquid C 6 D 6 is attributed to increased mobility of benzene provided by the supercritical uid. There is an approximately 2-3 fold increase in the DNP enhancement of SF CO 2 compared with liquid C 6 D 6 , which is in agreement with the decreased factor of molecular correlation times of small molecules in SF CO 2 . 62,92,93 Assuming a rotationally dominated mechanism, predicts correlation times of 10 and 42 ps, respectively for SF CO 2 and liquid C 6 D 6 . 43 Furthermore, within experimental error the absolute enhancement of 9% benzene in SF CO 2 with 0.001 M TEMPO approaches the dipolar limiting value of À330 corresponding to a coupling factor r ¼ 0.5, leading to nearly the highest possible dipolardominant enhancement in the 1 H DNP experiment (point A in Fig. 2). This indicates that fast molecular motion of benzene in SF CO 2 satises the extreme narrowing limit u S 2 s c 2 ( 1 shown as the at region at the low magnetic eld strength in Fig. 2, for the pure dipolar relaxation models at 0.33 T. Based on discussion in the introduction for cases where the enhancement is induced by mixed scalar and dipolar relaxation, it is clear that by conducting ow transfer 1 H DNP using SF CO 2 , both dipolar and scalar relaxation can result in substantial DNP Oe enhancements.

SLIT 1 H DNP experiments in supercritical uid (SF) CO 2
The solid-liquid intermolecular transfer (SLIT) 1 H DNP experiment has the advantage of the radical not being present in the liquid or uid. We have obtained SLIT 1 H DNP results for benzene in supercritical CO 2 with two immobilized radicals that have been previously reported. 53 Table 2 presents the SLIT 1 H DNP absolute enhancements of benzene dissolved in deuterated benzene and SF CO 2 using the immobilized nitroxides 43 (I)  and (II) as illustrated in Fig. 3. The absolute enhancements were obtained by estimating a transfer efficiency of $80% (the efficiency with which the polarized sample bolus is transferred from the low to high eld strength magnet). 43 For I and II, a 3 to 4 fold increase is observed for the 1 H SLIT DNP enhancement for SF CO 2 , in comparison with liquid C 6 D 6 , which is due to an increase in molecular motion of the immobilized nitroxide/ benzene complex in SF CO 2 . The absolute DNP enhancement from nitroxide II is slightly higher (A ¼ À246) in comparison with radical I (A ¼ À205) presumably due to the increased mobility (shorter correlation time s c ) of the radical attached to a longer exible chain off the surface of the silica gel for nitroxide II.

LLIT 13 C DNP experiments for molecular fullerene-nitroxide systems
For the case of molecules containing the 13 C nuclide, the Overhauser enhancement is usually a prole of both scalar and dipolar interactions. However, for molecules with quaternary sp 2 hybridized carbon atoms, a dipolar enhancement usually dominates. Our laboratory previously reported LLIT and SLIT 13 C DNP results for the fullerene C 60 /TEMPO system and observed dipolar dominated enhancements in both experiments. 65 In contrast, the fullerene C 70 with ellipsoidal D 5h symmetry is very different in comparison with C 60 , with 5 different non-equivalent carbon sites on the fullerene cage surface with signicant differences in surface curvature as illustrated in Fig. 6. Johnson and coworkers have previously unambiguously assigned the ve different carbons by 2D 13 C NMR techniques. 94 A surprising feature of the 13 C DNP enhancements for the C 70 /TEMPO system is the signicantly higher dipolar enhancements (A ¼ À281) observed at the polar cap carbons C 1 in comparison with the equatorial belt carbons C 5 , A ¼ À160. Moreover, there is a trend of decreasing enhancement values from the polar carbons (C 1 ) to the carbons at the equatorial position (C 5 ). The dipolar dominated 13 C DNP enhancement value A ¼ À250 for C 60 as well as the values for C 70 are remarkably large when compared with small aromatic molecules (e.g. benzene, A ¼ À220, discussed in the next section). The relatively large dipolar 13 C DNP enhancements can be partially attributed to the high I h and D 5h symmetry of C 60 and C 70 with corresponding relatively short rotational correlation times. However, a model of mixed rotational and translational diffusion cannot be excluded for the electron-nuclear interaction of both systems. It is well recognized that 13 C paramagnetic NMR shis are a sensitive probe for the electron-nuclear hyperne (scalar) interaction without the time-dependence noted above for dipolar interaction. The contact shis of both fullerenes (Table S4 †) indicate a very minor scalar contribution. Moreover, the T 1 relaxation times and corresponding similar f factors for these carbon sites exclude the inuence of leakage factor f on the determination of absolute enhancements in the C 70 carbon sites (see Table S3 † for relaxation data and leakage factor).
One possible origin of the enhancement differences of C 70 carbons is the variation of intermolecular distance between TEMPO and C 70 carbon from the polar to equatorial sites. Haddon has demonstrated the importance of expressing the curvature of a surface of sp 2 carbon atoms in terms of the porbital axis vector (POAV) to analyse local strain of fullerenes. 95 The local curvature of the C 70 carbons is assessed with the pyramidalization angle (q sp À 90), where q sp is the angle between the carbon s orbital and the p orbital as shown in Fig. 7. 95 The curvature/POAV angle is related to the interaction distance between nitroxide radicals and the carbons of C 60 and C 70 . The C 70 carbons with a larger pyramidalization angle are more accessible to the nitroxide radical in the weak intermolecular collisional complex, therefore resulting in a larger dipolar interaction. The correlation between the coupling factor   Table S3 †). r and the pyramidalization angle shown in Fig. 8 provides evidence for the dependence of the dipolar interaction on local curvature of the C 70 carbons.

LLIT 13 C DNP experiments of other molecular substratenitroxide systems and density functional theory computations: background
It is well recognized that molecules with C-H groups readily form weak complexes with nitroxides provide 13 C DNP interactions ranging from modest dipolar to strong scalar interaction(s) dependent on the hydrocarbon acidity. 44,46,50 For the case of molecules with sp 3 hybridized carbons (C-H) that are not bound to electronegative elements, the 13 C DNP presents modest dipolar enhancements as illustrated for the case of cyclohexane (A ¼ À270) and adamantane (A ¼ À254 and À209) ( Table 6). It is well recognized that there is increasing acidity for the sp 3 hybridized carbon (-C-H X ) group in progressing from toluene (pK a ¼ 41.2) to diphenylmethane (pK a ¼ 33.4), and triphenylmethane (pK a ¼ 31.4). This trend results in a signicant change in the DNP enhancement originating from a modest dipolar (A ¼ À209) to scalar interaction (A ¼ +129) for 13 CH X (X ¼ 1-3) (Fig. 9). The aromatic ortho, meta and para carbons reect nearly the same dipolar to scalar trend as the sp 3 hybridized (-C-H X ) group. This trend is especially relevant in view of the change in the molecular size (and corresponding correlation time) in progressing from toluene to triphenylmethane. Clearly, spin delocalization from the sp 3 hybridized (-C-H X ) group to the aromatic pi system is an important factor dictating this trend. A second factor is the expected longer scalar correlation time for the nitroxide/triphenylmethane complex in comparison with the toluene complex, which results in a larger scalar component in the overall coupling factor. However, the sp 2 aromatic ipso carbons exhibit dipolar enhancements (see Fig. S7 †). The absolute enhancement trend in these cases could have a larger error because of signicantly longer T 1 relaxation times than the corresponding molecules with attached hydrogens (-C-H X groups). On the other hand, for the case of sp 3 hybridized carbons attached to electron withdrawing groups (X-C-H X ), these weakly acidic hydrocarbons lead to very signicant scalar enhancements as represented by chloroform (HCCl 3 ) example with A ¼ +2200, which is close to the scalar limit. In addition, there are numerous other examples of large scalar enhancements for electron withdrawing sp 3 hybridized carbon (X-C-H X ) groups including nitromethane, diethyl malonate, ethylacetoacetate, and acetonitrile as illustrated in Fig. 10 and Table 6. All of these examples have acidic (C-H) groups with pK a acidities ranging from 10 to 25. Thus, sp 3 hybridized carbon hydrocarbons exhibit a wide range of DNP enhancements ranging from those with pK a s 40-50 (e.g., toluene, cyclohexane) that exhibit modest dipolar  Coupling factor derived from 13 C LLIT DNP absolute enhancements of the indicated carbon (i.e. 13 CH X , X ¼ 1-3, 13 C-ortho, 13 C-meta, and 13 C-para) for the series of toluene (red diamond), diphenylmethane (blue circle), and triphenylmethane (green triangle) (Ph Y CH X , X ¼ 1-3, Y ¼ 4-X). 66 Dashed lines illustrate motif trends for different molecules. The relative standard deviation for r is about 15%. interactions, to hydrocarbons with C-H groups exhibiting pK a acidities between 10 and 30 with large scalar enhancements (A ¼ +400 to +2200). Even molecules with weakly acidic (C-H) sites exhibit signicant scalar enhancements, for example, the C 1 carbon in 1-chlorobutane (A ¼ +460), when the remaining nonacidic (C-H) sites (C 2 -C 4 ) exhibit dipolar enhancements ( Table  6). The ability of nitroxide radicals to probe the weak acidity of C-H groups in more complex molecular systems is a unique application of solution state DNP.

Benzene/TEMPO
For the case of hydrocarbons with sp 2 hybridization, benzene has been an archetypal system for many previous solution state DNP studies. In addition, earlier NMR contact shi studies have clearly established a small scalar contribution to the dipolar dominated DNP enhancement for the benzene/TEMPO system, A ¼ À220. 44,68,96,97 Electron withdrawing groups attached to sp 2 hybridized quaternary carbons dramatically increase this dipolar interaction. For example, the aromatic ipso (quaternary) sp 2 carbons ( 13 C-X) of monosubstituted benzenes such as benzonitrile, phenylamine, benzaldehyde, anisole, and nitrobenzene exhibit dipolar enhancements with both electron donating and electron withdrawing substitutents (X) (see Fig. S5 †). A similar trend is observed for sp 2 hybridized carbonyl carbons with electronegative oxygens directly attached (Fig. S5 †). The highest dipolar enhancement in this trend is for the carbonyl carbon of acetone with a dipolar enhancement of A ¼ À744 representing a coupling factor of $55% of the dipolar limit at 0.33 T for this small molecule. For comparison, the signicantly larger fullerene C 60 molecule with sp 2 hybridized quaternary carbons exhibits a solution state enhancement of A ¼ À250 and does not have a signicant scalar component vide supra. 65 These results suggest that substrate molecules (100-700 Daltons) with sp 2 hybridized carbons that do not have a signicant scalar contribution exhibit dipolar enhancements with TEMPO ranging from 25 to 50% of the dipolar limit at 0.33 T. As previously noted, at the lower end of this range, the benzene/TEMPO system represents a small molecule with both dipolar and scalar 13 C interactions. We have previously reported based on DFT calculations that the formation of weak hydrogen bonding between C-H bond of substrate molecules and nitroxides results in unpaired spin density at the substrate carbon nuclei and results in non-trivial scalar contributions to the 13 C DNP enhancements for acetonitrile/TEMPO and acetamide/ TEMPO. 49 It is of considerable interest to establish the important orientation and interaction site(s) for the electron-nuclear interaction for the case of the benzene/TEMPO system. We have obtained the Boltzmann weighted 13 C a FC ¼ 0.80 MHz via DFT computations using eqn (5) by considering the four lowestenergy molecular congurations (see S6-S9 and Table S5 † for optimized orientations and their parameters). The two important conformations with the largest contributions to the hyperne coupling are shown in Fig. 11 and 12. It is important to note that in both conformations the nitroxide N-O bond vector is either orthogonal to one C-H bond vector or orthogonal between (T shape) two C-H bond vectors with interaction distances of 0.230 and 0.239 nm, respectively. This orthogonal approach of the N-O and C-H bond is also consistent for the lowest energy conformations found below for other monosubstituted benzene/TEMPO complexes vide infra. The computational average a FC value (a FC ¼ 0.80 MHz) indicates a nontrivial scalar contribution to the 13 C DNP NMR signal of benzene. For the comparison of benzene and monosubstituted benzenes, their comparable molecular size and lack of signicant conformational differences allow the assumption of relatively small changes in the correlation times.

Nitrobenzene/TEMPO
For the case of nitrobenzene/TEMPO (NMR and DNP spectra shown by Fig. 14), the introduction of the strong electron withdrawing nitro group on the aromatic ring leads to a lowest energy conformation with an orthogonal approach of the N-O and C-H bond vectors between the ortho and meta carbons (Fig. 13). The weighted Boltzmann averaging of HFC for the ortho carbon (a FC ¼ 1.424) is in strong agreement with the large scalar enhancement, A ¼ +587 observed for this site ( Table 3). The large 13 C-para and 13 C-meta contribution appears to originate from a slightly higher energy conguration (Fig. S23 †)   Fig. 11 The electronic spin density distribution of the largest 13 C-H HFC contributing orientation between benzene and TEMPO where two C-H moieties bite the TEMPO N-O group. Dashed lines are given as guides for intermolecular distances, which are 2.39Å for O/H (of C-H moiety with closest approach to TEMPO oxygen) and 2.86Å for N/H (of C-H with closest approach to TEMPO nitrogen). Fig. 12 The electronic spin density distribution of the second largest 13 C-H HFC contributing orientation between benzene and TEMPO where one C-H moiety points at N-O group. Dashed line is given as a guide for intermolecular distance, which is 2.30Å between the oxygen atom of TEMPO and the hydrogen atom of benzene C-H moiety.
where the para C-H bond vector is orthogonal to the nitroxide, N-O bond vector. However, delocalization of polarized spin from the dominant ortho conformation to the meta and para sites can not be excluded. It is interesting to note in this regard that the strong electron withdrawing nitro group leads to scalar enhancements, whereas, electron donating groups such as the amino group of phenylamine leads to dipolar enhancements at all ortho, meta, and para carbon positions (Table S10 †).

Benzaldehyde/TEMPO
In contrast with benzene and nitrobenzene, the benzaldehyde/ TEMPO system provides a system where two different weak sp 2 hybridized C-H bonds can complex with TEMPO ( Fig. 15 and Table 4). The weighted Boltzmann averaging of hyperne couplings continues to show strong agreement with the scalar enhancements measured by DNP (see Table S7 † for details). In this case the ortho aromatic C-H bond and the aldehyde, O]C-H bonds both contribute as a "dual complexation site" with TEMPO for the lowest energy conformation. In addition, this conformation is similar to the orthogonal bond vector conformations found for benzene and nitrobenzene. However, the more acidic aldehyde O]C-H site exhibits a larger hyper-ne coupling (a FC ¼ 1.155) and corresponding larger scalar enhancement (A ¼ +373) in comparison with the modest hyperne coupling and DNP enhancement found for ortho C-H site, a FC ¼ 0.442 and A ¼ +131, respectively. It is also interesting     to note that the modest electron withdrawing aldehyde group leads to modest scalar enhancements at all ortho, meta, and para carbon positions (Table 4).

Phenylacetylene/TEMPO
For the case of sp hybridized carbons there is a paucity of data for the complexation of alkynes with nitroxides. For cyano sp hybridized carbons modest 13 C dipolar DNP enhancements have been reported for benzonitrile and acetonitrile (Table 6 and Table S16 †). However, for the acidic sp hybridized C-H carbons there is a paucity of examples reported. In one notable early NMR shi study, a transient hydrogen bonding between phenylacetylene and di-tert-butyl nitroxide was proposed, 68 since the former is a good proton donor with a pK a of 21 (Fig. 1).
It should be noted that alkynes are key components in the widely employed "click" reaction extensively employed in organic, polymer, and biomedical functionalization studies. 98 Phenylacetylene has an acetylenic proton of relatively high acidity (pK a of 21) 99 compared with benzene as shown in Fig. 1. The DFT and DNP results for phenylacetylene/TEMPO are shown in Fig. 17 and Table 5. As predicted, the phenylacetylene/ TEMPO exhibits a large hyperne coupling, a FC ¼ 3.28 and corresponding large scalar dominated enhancement (A ¼ +1400) for the sp hybridized C-H b carbon (shown in Table 5). Moreover, the b carbon exhibits the largest scalar-dominant DNP enhancement observed to date for a molecule not containing halogens, corresponding to a DNP coupling factor of À0.53 (point D in Fig. 2). In analogous fashion to the previous examples above, the lowest energy conformation has the N-O bond vector orthogonal to the sp hybridized C-H bond vector (Fig. 17), but the interaction distance is considerably shorter (0.203 nm) than the previous examples, vide supra. It is also interesting to note that the a sp hybridized carbon exhibits a notable scalar enhancement (A ¼ +290) as well, also consistent with the relatively large computationally derived hyperne coupling (a FC ¼ 0.871). The ortho, meta, and para carbons on the benzene ring of phenylacetylene show very small dipolardominated (negative) enhancements that are nearly zero.  Clearly there is a large difference in the spin-lattice T 1 relaxation time of the scalar dominated b carbon relative to the o, m, and p carbons of the aromatic ring. At low radical (TEMPO) concentrations (0.01 M), the b carbon polarization is notably enhanced, but the other carbon atoms are barely observable. For the ring carbons having dipolar-dominated interactions, whereas, at higher radical concentrations (0.14 M) dipolar enhancements become observable, but the b carbon is barely observed because of the very short nuclear relaxation times at this concentration which limits the transfer efficiency from the low (0.33 T) to the high observable magnetic eld (4.7 T). However, the lower radical concentration used (0.01 M) may diminish the observed DNP enhancements for the b carbon and other carbons because of a lower leakage factor and three-spin effects 100 (Fig. 16b). These results suggest that for molecules having specic strong scalar complexation sites, it is possible to independently detect enhancements contributed by the scalar and dipolar interactions by varying the radical concentration.

Conclusions
In summary, we have found that for 1 H DNP, supercritical uids provide a convenient approach for decreasing the correlation time for solutes and provide an alternative approach for improving dipolar enhancements at high magnetic elds without the need for polarization at low temperatures ($4 K).
For the system SF CO 2 /benzene/TEMPO, the DNP enhancement approaches the dipolar limiting value of À330 (r ¼ 0.5) at 0.33 T. For biomedical applications, there has been considerable interest in the DNP enhancement of water as reviewed by Günther. 8 For example, Bennati and coworkers have experimentally reported an Oe dipolar DNP enhancement A ¼ À170 for the water/TEMPONE-D- 15 N system at 9.7 GHz (0.33 T). 22 For 13 C DNP at 0.33 T, we have found that molecules (100-700 Daltons) dissolved in liquids containing carbon sites without a signicant scalar contribution (e.g., carbonyls) exhibit dipolar enhancements ranging from, A ¼ À250 to À740 with TEMPO vide supra. It is easy to predict that 13 C DNP for these carbon sites could also exhibit 13 C DNP enhancements 2 to 3 times greater if conducted in SF CO 2 . For the biomedical metabolites, the enhancement in SF CO 2 followed by rapid dissolution in water or saline solutions and transfer to high magnetic elds could be a viable approach for NMR nuclides with long T 1 relaxation times for both NMR and MRI applications. Furthermore, other SF uids, such as, supercritical water and nitrous oxide represent alternative uids for decreasing correlation times at higher magnetic elds for DNP at high elds. For the case the C 70 /TEMPO system, we have reported signicantly higher dipolar enhancements at the polar cap carbons with greater sp 2 curvature in comparison with the equatorial belt carbons. For the case of 13 C DNP where both dipolar and scalar interactions are important, the correlation between experimental scalar DNP enhancements (A) and the Boltzmann weighted hyperne coupling constants (a FC ) calculated using the DFT methods provides a predictive tool for any substrate systems exhibiting a non-trivial scalar interaction as illustrated in Fig. 18. A cautionary note of these predictions is the importance of the scalar and/or dipolar correlation time(s) that is not included in the current computational approach. For this work, we assume similar correlation times for the monosubstituted benzenes employed in this study. Finally, of critical importance, molecules with sp hybridized C-H groups, such as, the b carbon of phenylacetylene deserve further study because of the large scalar enhancements observed for this system. The short intermolecular distance between the hydrogen attached to the b C-H group and the orthogonal O-N bond of the nitroxide in TEMPO is about 2.0Å (see Fig. 17). The shorter intermolecular distance is an indication of stronger hydrogen bonding between the acetylene group and the radical, and hence has a greater effect on the scalar interaction, compared with other sp 3 and sp 2 hybridized carbon systems. Furthermore, compared with sp 2 carbons such as the aldehyde carbon of benzaldehyde, the phenylacetylene b carbon has a greater s character of the bonding carbon hybrid orbital caused by sp hybridization. The hyperne coupling constant (a FC ) is directly proportional to the unpaired electron spin density at the investigating carbon nucleus, hence the increased HFC value of phenylacetylene b carbon indicates the contribution of increased s character and corresponding greater spin density transfer from the radical to the sp carbon nucleus, |j(0)| 2 . This conclusion is consistent with the observation of experimental and computed increasing s character for 13 C-1 H coupling constants (J CH ) which increases markedly as a result of Fermi contact contributions 104 with the trend, 159 Hz for benzene, 105 173.7 Hz for the carbonyl group in benzaldehyde, 106 (C 6 H 5 13 C 1 HO) and 251 Hz for the sp b carbon in phenylacetylene 107 (C 6 H 5 C 13 C 1 H). In conclusion, solution state DNP provides a unique approach for studying intermolecular weak bonding interactions of solutes in normal liquids and SF uids.