Dynamic nuclear polarization of (1)H, (13)C, and (59)Co in a tris(ethylenediamine)cobalt(III) crystalline lattice doped with Cr(III).

The study of inorganic crystalline materials by solid-state NMR spectroscopy is often complicated by the low sensitivity of heavy nuclei. However, these materials often contain or can be prepared with paramagnetic dopants without significantly affecting the structure of the crystalline host. Dynamic nuclear polarization (DNP) is generally capable of enhancing NMR signals by transferring the magnetization of unpaired electrons to the nuclei. Therefore, the NMR sensitivity in these paramagnetically doped crystals might be increased by DNP. In this paper we demonstrate the possibility of efficient DNP transfer in polycrystalline samples of [Co(en)3Cl3]2·NaCl·6H2O (en = ethylenediamine, C2H8N2) doped with Cr(III) in varying concentrations between 0.1 and 3 mol %. We demonstrate that (1)H, (13)C, and (59)Co can be polarized by irradiation of Cr(III) with 140 GHz microwaves at a magnetic field of 5 T. We further explain our findings on the basis of electron paramagnetic resonance spectroscopy of the Cr(III) site and analysis of its temperature-dependent zero-field splitting, as well as the dependence of the DNP enhancement factor on the external magnetic field and microwave power. This first demonstration of DNP transfer from one paramagnetic metal ion to its diamagnetic host metal ion will pave the way for future applications of DNP in paramagnetically doped materials or metalloproteins.

Introduction

The number and variety of applications of high-field dynamic nuclear polarization (DNP) have inn class="Chemical">creased significantly during the past few years,[1] primarily because microwave-driven DNP is widely applicable and capable of enhancing NMR signals by several orders of magnitude. Microwave-driven DNP therefore dramatically reduces the acquisition times of many lengthy experiments.[2,3] Accordingly, high-field magic-angle spinning (MAS) DNP has been used by many groups to examine samples where the analyte and a stable paramagnetic polarizing agent, usually a g ≈ 2 organic radical, are dissolved in a glass-forming mixture (typically 60/40 v/v glycerol/water).[4−12] The spin system is then irradiated with high-frequency microwaves, which enables the transfer of electron polarization to nuclear spins, leading to an enhanced NMR signal. With this approach, the best overall results have been achieved when the analyte is homogeneously dispersed within the glass (e.g., membrane proteins, amyloid fibrils, or microcrystals).[13−25]

The appearance of commercially available high-field n class="Chemical">DNP instrumentation has also stimulated the development of additional approaches to produce suitable paramagnetic samples.[13,17,21,24,26−28] Many of these studies have focused on the cross effect (CE) as well as approaches required to optimize the enhancements. In addition, mechanistic studies have renewed interest in the solid effect (SE)[29−31] and demonstrated that high-power microwave (mw) sources can increase the enhancement of the SE to the point where it is competitive with the CE.[32] In parallel, new and improved polarizing agents for both the SE and CE have appeared.[33−42]

The introduction of paramagnetic transition-metal and rare-earth ions as polarizing agents for the n class="Chemical">SE[42] and for the Overhauser effect (OE) in solution[43] demonstrated the possibility of applying DNP to a variety of samples that contain intrinsic paramagnetic metal sites or can be easily doped with those species. This approach is applicable to a large collection of paramagnetic metalloproteins and enzymes, and also to a group of crystalline (inorganic) materials containing paramagnetic dopants or defects. These materials often occur naturally (e.g., ruby, Al2O3:Cr3+), or can be synthesized by substituting a diamagnetic host ion with a paramagnetic analogue (i.e., a d- or f-block metal center);[44] additionally, unpaired electrons can be found in F centers (i.e., Farbzentren or color centers, anionic vacancies in the lattice that are occupied by electrons)[45−47] or other defects where dopants substitute a host site with a mismatch in the number of valence electrons, such as diamond NV centers, which feature interesting spin properties.[48−50] Doping with paramagnetic species often does not significantly alter the physical properties of the host material if the host ion and the dopant have similar properties (i.e., charge and ionic size), and therefore, it is an ideal tool to study the properties of the pristine (diamagnetic) materials using paramagnetic techniques.

Paramagnetically doped inorganic systems have been investigated extensively with electron paramagnetic resonance (EPR) spectroscopy, but their characterization by NMR spectrosn class="Chemical">copy remains a challenge,[51−57] as the target diamagnetic metals may have nonfavorable nuclear properties, including a quadrupolar interaction (I > 1/2, i.e., quadrupolar broadening), or suffer from low natural abundance and/or low gyromagnetic ratio. These properties reduce the overall sensitivity and when combined often require complicated experimental methods and extended acquisition times.[58,59] The presence of paramagnetic doping in these systems makes them appealing for applications of DNP, which offers the ability to boost the nuclear polarization and reduce the experiment time. However, in these cases both the polarization source (paramagnetic dopant) and the target (diamagnetic host ion) are often considered nonideal systems for DNP spectroscopy. Typically, organic S = 1/2 radicals for the SE (e.g., trityl,[60] BDPA[34,61]) or specifically tailored biradicals for the CE (e.g., TOTAPOL,[62] AMUPol[63]) as well as I = 1/2 nuclei (e.g., 1H, 13C, 15N, 29Si) are seen as being “ideal” for mechanistic studies and have been used successfully in DNP experiments. However, systems having electron and nuclear spins greater than 1/2 are much more abundant than systems with S = 1/2 and I = 1/2 and therefore are of particular interest, especially in materials science and inorganic chemistry. Additionally, quadrupolar nuclei are sensitive probes of their environment as a result of the coupling between the inherent quadrupole moment and the electric field gradient generated by its surroundings—the magnitude of the coupling will be observed within the spectrum accompanied by a specific shape characteristic of local symmetry. In the case of heavy transition metals, further spectral effects from a considerable chemical shift anisotropy (CSA) can be observed, which are extremely sensitive to the local electronic environment.[64] These couplings often lead to broad NMR powder patterns, with increasing complexity when both anisotropic interactions are present.[65−70] However, this information on couplings and shifts is often difficult to obtain because of typically low gyromagnetic ratios and subsequently low spectral sensitivities.[71−75] In order for DNP-enhanced NMR spectroscopy to become a more generally applicable method, it is important to examine these “nonideal” but more practical cases, even if the enhancements are lower than those achieved in “ideal” systems. Therefore, investigating the feasibility of DNP experiments involving direct polarization transfer from an S > 1/2 metal site to another diamagnetic nucleus at an S = 0, I > 1/2 metal site in a doped polycrystalline system is of considerable interest.

Despite the fact that many metals have paramagnetic oxidation states, they often have prohibitively broad EPR lines due to the large spin–orbit n class="Chemical">coupling and fast electronic relaxation from low-lying excited states, making them unsuitable for DNP.[76] Gd3+ and Mn2+, which have S-term (L = 0) ground states and zero first-order spin–orbit coupling, stand out as valid polarizing agents for high-field DNP NMR spectroscopy.[42] A similar situation is encountered for Cr(III) in an octahedral ligand field, where the three d-shell electrons form a 4A2 ground state with vanishing orbital momentum and spin–orbit coupling. This makes Cr(III) complexes with near-octahedral symmetry ideal targets for investigation as DNP polarizing agents in this study.

Besides these can class="Chemical">ses with vanishing spin–orbit coupling, Cr(V) complexes, obtained in situ from Cr(VI) salts in the presence of diols, have been successfully polarized when used at low magnetic fields and low temperature (i.e., liquid helium temperature).[77−83] Hence, it can be foreseen that their analogous VO2+ and Mo(V) complexes could accomplish this task despite their nonzero spin–orbit coupling because these metal ions have a d1 configuration, resulting in a nondegenerate ground state (in the presence of Jahn–Teller distortion and/or low-symmetry components).

In the present paper, we demonstrate that it is possible to utilize n class="Chemical">DNP to polarize a host crystalline lattice via paramagnetic transition-metal dopants. We are able to observe 1H (indirect) and 13C (direct) DNP-enhanced NMR spectra from the bidentate ethylenediamine ligands, including the ability to directly polarize the 59Co nucleus of the diamagnetic transition-metal host within the crystalline lattice. This method paves the way for numerous applications of DNP to paramagnetically doped crystalline materials and potentially to (partially) paramagnetic biosolids.

Figure 1 illustrates the (a, b) molecular and (c) long-range packing of the diamagnetic host complex, [n class="Chemical">Co(en)3Cl3]2·NaCl·6H2O (en = ethylenediamine, C2H8N2). The Co atom is six-coordinate, surrounded by three bidentate ethylenediamine ligands coordinated through the electron lone pair on the nitrogen atoms. The symmetry of the free Co(en3)3+ molecular cation would appear to be D3d, but it decreases to C3 point symmetry within the trigonal P3 space group.[84] Cr(III)-doped [Co(en)3Cl3]2·NaCl·6H2O is an ideal system for DNP studies in crystalline environments for several reasons: Co(III) can be substituted by the equally charged Cr(III) without significant distortion of the lattice parameters or symmetry because of the rather similar crystal ionic radii (i.e., 0.545 Å for low-spin Co3+ vs 0.615 Å for Cr3+).[85] While Co(III) is in a low-spin (S = 0) 3d6 electronic state in the strong octahedral crystal field, Cr(III) exists in a 3d3 configuration and is therefore strictly paramagnetic (S = 3/2). Despite the high-spin state and subsequent occurrence of electron quadrupole coupling [i.e., zero-field splitting (ZFS)], the half-integer spin quantum number results in a narrow EPR m = −1/2 ↔ +1/2 central transition (CT) suitable for DNP. Furthermore, the variable doping ratio permits tuning of the electron–electron interactions. While the natural isotopic mixture of chromium comprises four different isotopes (4.3% 50Cr, 83.8% 52Cr, 9.5% 53Cr, and 2.4% 54Cr), only the minority isotope 53Cr is magnetically active, with a nuclear spin of I = 3/2; additionally, the corresponding hyperfine coupling is rather small (about 45 MHz) and does not significantly contribute to the observed line width of the CT. Among Cr complexes, Cr(en3)3+ embedded in [Co(en)3Cl3]2·NaCl·6H2O is found to have a small and axially symmetric ZFS.[44,84,86] Cobalt is an isotopically pure element. The 59Co nucleus has a gyromagnetic ratio close to that of 13C and can therefore be detected with conventional NMR probes with minor adjustments to the 13C channel. It has a nuclear spin of I = 7/2, and a large quadrupole moment of Q = 0.42 barns,[87] although the nuclear quadrupole coupling is small for this complex with C3 symmetry; the CT (1/2 ↔ −1/2) does not suffer from a second-order quadrupolar broadening at rather low magnetic fields of ≥5 T.[88] However, 59Co does have an extremely sensitive nuclear magnetic shielding that is very sensitive to the polarizability and local chemical bonding environment. Hence, CSA can be a sensitive tool to probe changes in both temperature and chemical structure, as it leads to a large chemical shift range (e.g., a 59Co chemical shift range of >15 000 ppm; at a field of 5 T, this spans >0.8 MHz).[65,88−91] Besides the metal nuclei (i.e., Na+, Cr3+, and Co3+), the sample contains the usual complement of 1H, 13C, 14N, 15N, and 17O spins in the organic ligands as well as the counterions (Cl–).

Figure 1

Molecular and long-range crystal packing of [Co(en)3Cl3]2·NaCl·6H2O (en = ethylenediamine, C2H8N2). (a) Molecular unit without hydrogen atoms. (b) Molecular unit with hydrogen atoms. (c) 2D rendering of the crystal structure with the c axis perpendicular to the page. Color scheme: Co, blue; N, light blue; C, gray; Cl, green; Na, purple; O, red. Hydrogen atoms have been removed for clarity. (d) Select interatomic distances determined by X-ray diffraction.[84]

Molecular and long-range crystal packing of [n class="Chemical">Co(en)3Cl3]2·NaCl·6H2O (en = ethylenediamine, C2H8N2). (a) Molecular unit without hydrogen atoms. (b) Molecular unit with hydrogen atoms. (c) 2D rendering of the crystal structure with the c axis perpendicular to the page. Color scheme: Co, blue; N, light blue; C, gray; Cl, green; Na, purple; O, red. Hydrogen atoms have been removed for clarity. (d) Select interatomic distances determined by X-ray diffraction.[84]

Experimental Section

Synthesis

[M(en)3Cl3]2·NaCl·6n class="Chemical">H2O (M = Co, Cr) were prepared according to the protocol of McGarvey[86] by dissolving Co(en)3Cl3·2H2O (Sigma-Aldrich) or Cr(en)3Cl3·3.5H2O (Strem Chemicals) together with 2.5 g of NaCl per 1 g of complex salt in deionized H2O. The quantity of H2O was chosen so that the NaCl concentration was slightly below saturation. For the preparation of Cr(III)-doped [Co(en)3Cl3]2·NaCl·6H2O with molar doping ratios of 0.1, 0.3, 1, and 3%, portions of the Cr(en)3Cl3 and Co(en)3Cl3 solutions were mixed in the appropriate molar ratios. Crystals were obtained by slow evaporation from each of the six solutions (i.e., with 0.1, 0.3, 1, and 3% Cr(III) as well as the 0% and 100% controls). After ∼50% of the solution had evaporated, the crystals were collected using a Büchner funnel with a suction pump and washed with the supernatant. The red-to-orange elongated, needle-shaped crystals with sizes up to several millimeters were then air-dried and ground to a fine powder using an agate mortar and pestle. Crystal structure details for [Co(en)3Cl3]2·NaCl·6H2O are summarized in Table S1 in the Supporting Information.

EPR Spectroscopy

X-Band (9 GHz) EPR experiments were performed using a Bruker ElexSys E580 spectrometer with a Bruker ER 4118X-MD5 dielectric ring resonator employing a cylindrical TE011 mode. Sample temperature control was achieved using a Bruker ER 4118CF-O flow n class="Chemical">cryostat with liquid helium or liquid nitrogen as the cryogen and an Oxford Instruments ITC 503S temperature controller. A custom-built spectrometer was used for 140 GHz EPR experiments.[92]

NMR Spectroscopy

13C{n class="Chemical">1H} cross-polarization (CP) experiments for line width analysis were performed using an 11.7 T (500 MHz, 1H) home-built spectrometer (courtesy of D. Ruben, MIT-FBML) with a Chemagnetics (Fort Collins, CO) triple-resonance (1H/13C/15N) MAS probe equipped with a 4.0 mm Kel-F stator housing. The spinning frequency was set to 10 kHz and regulated with a Bruker (Billerica, MA) MAS controller, and the temperature was maintained at 298 K. The spin lock on 13C during CP was optimized to match the Hartmann–Hahn condition[96] under MAS with γB1/2π = 50 kHz on protons during a contact time of 1.2 ms, which was maintained constant for all samples. Proton pulses and two-pulse phase modulation (TPPM) decoupling[97] were optimized for γB1/2π = 83 kHz. All of the spectra were recorded using 512 averaged transients and a recycle delay of 10 s and were referenced externally to adamantane (40.49 ppm with respect to 4,4-dimethyl-4-silapentane-1-sulfonic acid).

DNP Experiments

The 211 MHz/140 GHz DNP NMR experiments were performed using a custom-built NMR spectrometer (n class="Chemical">courtesy of D. Ruben, MIT-FBML) in combination with a custom-built MAS DNP NMR probe featuring a triple-channel radiofrequency circuit and a 140 GHz microwave guide. The probe employs a cryogenic sample exchange and corrugated overmoded waveguide technology to minimize microwave mode conversion and Ohmic losses.[93] The 140 GHz microwaves were generated by a gyrotron oscillator, which provided ∼3–10 W of power at the probe entrance.[94] Sample cooling to 80 K was provided by the cold MAS N2 gas using a custom-built liquid N2 heat exchanger. The temperature was monitored on the outside stator surface by fiber-optic thermometers (Neoptix, Québec, Canada). The field position was swept with a ±750 G superconducting sweep coil and determined with a 1H field sweep/lock system.[95]

Powdered samples were packed into 4 mm o.d. sapphire rotors for all of the DNP experiments. The magnetic field was first n class="Chemical">set to the expected theoretical SE DNP matching condition for each nucleus. DNP enhancements were obtained as the ratio of the NMR signal intensities with microwaves (mw on) and without microwaves (mw off) measured under identical experimental conditions. The magnetic field position was then optimized in order to maximize the enhancement factor.

DNP-enhanced and nonenhanced NMR signal amplitudes were ren class="Chemical">corded using a 13C{1H} CP experiment in the case of 1H DNP, a direct polarization Bloch decay for 13C, and a rotor-synchronized Hahn echo (or solid echo) for 59Co DNP. The spin lock on 13C during CP was optimized to match the Hartmann–Hahn condition (96) under MAS with γB1/2π = 100 kHz on protons during a contact time of 1.5 ms. TPPM 1H decoupling (γB1/2π = 100 kHz) was used during acquisition, the transverse magnetization evolution, and refocusing periods. Relaxation and buildup time constants were then obtained by least-squares fitting of the data with a single-exponential function. The nuclear spin–lattice relaxation time constant (T1) and the DNP buildup constant (TB) were measured by applying a presaturation pulse train consisting of 16 pulses with a flip angle of 108° and γ B1/2π = 50 kHz (phase alternating along +x and +y) separated by 5 ms on the 1H/13C/59Co channel. This was followed by a variable recovery time during which the longitudinal magnetization was allowed to build up. The polarization was then read out using a Bloch decay (for 13C and 59Co) or 13C{1H} CP (for 1H). A time period of typically 1.3 × T1 (TB) was allowed for polarization to build up prior to the read-out pulses (Table S2 in the Supporting Information). (98)

Data Processing

59Co NMR parameters were simulated using the WSOLIDS software package.[99] Crystalline figures were made with Mercury[100] and the UCSF Chimera package.[101] EPR spectra were simulated using the Easyspin package.[102]

Results and Discussion

The pulsed 140 GHz EPR spectrum at 80 K (the same temperature as in the n class="Chemical">DNP experiments) of 0.1% Cr(III)-doped [Co(en)3Cl3]2·NaCl·6H2O is shown in Figure 2. The shape of the spectrum can be explained using a spin Hamiltonian including the electron Zeeman interaction and the zero-field splitting of the S = 3/2 system:where g is the (isotropic) electronic g factor; μB is the Bohr magneton; ℏ is the reduced Planck constant; Ŝ is the electron spin vector operator, constituted of the operator matrices according to ŜT = (Ŝ, Ŝ, Ŝ); and D is the traceless ZFS tensor, typically expressed by its characteristic parameters D = 3/2D and E = 1/2(D – D). The latter parameter can be omitted in eq 1 because the corresponding term is active only in tensor symmetries lower than axial. Since chromium in its natural isotopic composition features the magnetically active nucleus 53Cr with 9.5% abundance, a second spin system with the same terms as above but with an additional hyperfine coupling term ĤHFI = a(53Cr)Ŝ·Î has to be simulated and added to eq 1 with the appropriate weight. In the above term, a(53Cr) is the isotropic hyperfine coupling to 53Cr while Î is the nuclear spin vector operator, constituted of the operator matrices according to ÎT = (Î, Î, Î).

Figure 2

140 GHz EPR spectrum of 0.1% Cr(III)-doped [Co(en)3Cl3]2·NaCl·6H2O. The spectrum was recorded by detecting the Hahn echo intensity as a function of the external magnetic field at a temperature of 80 K. The pulse sequence (π/2–τ–π) was 13–200–26 ns, and 400 shots were recorded with a four-step phase cycle over 701 field points during a single field sweep. The dashed line shows a 10× vertical magnification to emphasize the anistropically broadened m = ±3/2 ↔ ±1/2 transitions.

140 GHz EPR spectrum of 0.1% Cr(III)-doped [n class="Chemical">Co(en)3Cl3]2·NaCl·6H2O. The spectrum was recorded by detecting the Hahn echo intensity as a function of the external magnetic field at a temperature of 80 K. The pulse sequence (π/2–τ–π) was 13–200–26 ns, and 400 shots were recorded with a four-step phase cycle over 701 field points during a single field sweep. The dashed line shows a 10× vertical magnification to emphasize the anistropically broadened m = ±3/2 ↔ ±1/2 transitions.

The spectrum is dominated by the m = −1/2 ↔ +1/2 CT of the Cr3+ ion, but the anisotropically broadened m = ±3/2 ↔ ±1/2 transitions are visible as a Pake pattern centered around the CT. Spectral simulation using the EasySpin package[102] allowed us to determine g = 1.98712 and D = +740 MHz (E = 0 MHz); the sign of the ZFS n class="Chemical">constant D is unambiguously defined on the basis of the slight asymmetry of the Pake pattern caused by the ∼15% Boltzmann population difference of the respective transitions and was confirmed by spectral simulation (Figure S1 in the Supporting Information). Although the occurrence of a significant ZFS may not be expected for the case of ideal hexagonal symmetry, distortion of the trigonal-antiprismatic ligand field is frequently observed in similar systems such as ruby; additionally, spin–orbit coupling generates an admixture of mainly the 4T2 excited state to the 4A2 electronic ground state, leading to the observed shift in g with respect to that of a free electron and a nonvanishing ZFS.[103]

While the g value is in relatively good agreement with the value of 1.9874 reported by McGarvey[86] (especially considering the low field of ∼340 mT where the previous experiments were performed), in our 80 K experiment D is n class="Chemical">considerably larger than at room temperature (740 vs 148 MHz). Experiments performed at 9.7 GHz and 80 K confirmed our findings and also emphasized the significantly higher accuracy in the g value determination provided by our high-field measurements (see Figure 3). The higher accuracy is attributed not only to the larger Zeeman splitting but also to the reduction in the second-order ZFS broadening of the CT at higher magnetic fields. In the 140 GHz spectrum it is also easy to observe the outermost peaks of the hyperfine splitting quartet [a(53Cr) = 45 MHz] of the ∼10% abundant 53Cr nucleus, while those peaks are completely masked by the second-order ZFS at 9.7 GHz (Figure 3).

Figure 3

140 GHz (top, green) and 9.7 GHz (bottom, red) EPR spectra of 0.1% Cr(III)-doped [Co(en)3Cl3]2·NaCl·6H2O at a temperature of 80 K. The 140 GHz spectrum was obtained from the pulsed spectrum shown in Figure 2 by a mathematical pseudofield-modulation derivation (using EasySpin’s fieldmod function[102]) with a pseudomodulation amplitude of 0.05 mT. The 9.7 GHz spectrum was recorded using CW EPR at a microwave power of 20 μW with field modulation of 0.2 mT in amplitude and 100 kHz in frequency; 2048 points were recorded with a time constant of 40.96 ms and a conversion time of 81.92 ms in a single sweep. The thin lines show 10× vertical magnifications to emphasize weak spectral features. The five equidistant dashed lines represent the positions of the prominent ZFS features and serve only as guides to the eyes.

140 GHz (top, green) and 9.7 GHz (bottom, red) EPR spectra of 0.1% Cr(III)-doped [n class="Chemical">Co(en)3Cl3]2·NaCl·6H2O at a temperature of 80 K. The 140 GHz spectrum was obtained from the pulsed spectrum shown in Figure 2 by a mathematical pseudofield-modulation derivation (using EasySpin’s fieldmod function[102]) with a pseudomodulation amplitude of 0.05 mT. The 9.7 GHz spectrum was recorded using CW EPR at a microwave power of 20 μW with field modulation of 0.2 mT in amplitude and 100 kHz in frequency; 2048 points were recorded with a time constant of 40.96 ms and a conversion time of 81.92 ms in a single sweep. The thin lines show 10× vertical magnifications to emphasize weak spectral features. The five equidistant dashed lines represent the positions of the prominent ZFS features and serve only as guides to the eyes.

In Figure 4 we illustrate that variation of the Cr(III) doping ratio has no impact on either the g value or the D value, indicating that both the n class="Chemical">crystal structure and properties are preserved and that the Cr(III) sites are not affected by an increase in the molar ratio of the paramagnetic dopant to 3%. Besides a gradual increase in mostly homogeneous line width due to stronger electron–electron interactions between different Cr(III) doping sites with increasing doping ratio, distinct shoulders emerge only in the EPR spectrum of the sample with a 3% doping ratio. These shoulders (marked with asterisks) show an offset of ∼250 MHz with respect to the CT, being in reasonable agreement with nearest-neighbor electron–electron coupling to a Cr(III) dopant at an adjacent complex site.

Figure 4

CW X-band EPR spectra of Cr(III)-doped [Co(en)3Cl3]2·NaCl·6H2O with doping ratios of 0.1% (blue), 0.3% (green), 1.0% (orange), and 3.0% (red) recorded at sample temperatures of 298 K (left series) and 80 K (middle and right series). The series to the right depicts an enlarged region of the CT of the S = 3/2 spin system at 80 K to visualize the features introduced by second-order ZFS. Thin lines show 7.5× amplifications to emphasize the weaker spectral features. The five equidistant dashed lines represent the positions of the prominent ZFS features and serve only as guides to the eyes. The 80 K (298 K) data were recorded using a microwave power of 0.2 μW (0.63 mW) and field modulation of 0.2 mT (0.1 mT) in amplitude and 100 kHz in frequency; 2048 (1024) points were recorded with a time constant of 40.96 (20.48) ms and a conversion time of 81.92 (40.96) ms in 1 to 24 scans depending on the doping ratio and temperature. Asterisks mark shoulders of the 3% Cr-doped complex that indicate nearest-neighbor electron–electron coupling.

CW X-band EPR spectra of Cr(III)-doped [n class="Chemical">Co(en)3Cl3]2·NaCl·6H2O with doping ratios of 0.1% (blue), 0.3% (green), 1.0% (orange), and 3.0% (red) recorded at sample temperatures of 298 K (left series) and 80 K (middle and right series). The series to the right depicts an enlarged region of the CT of the S = 3/2 spin system at 80 K to visualize the features introduced by second-order ZFS. Thin lines show 7.5× amplifications to emphasize the weaker spectral features. The five equidistant dashed lines represent the positions of the prominent ZFS features and serve only as guides to the eyes. The 80 K (298 K) data were recorded using a microwave power of 0.2 μW (0.63 mW) and field modulation of 0.2 mT (0.1 mT) in amplitude and 100 kHz in frequency; 2048 (1024) points were recorded with a time constant of 40.96 (20.48) ms and a conversion time of 81.92 (40.96) ms in 1 to 24 scans depending on the doping ratio and temperature. Asterisks mark shoulders of the 3% Cr-doped complex that indicate nearest-neighbor electron–electron coupling.

Variable-temperature continuous-wave (CW) EPR spectra obtained from the 0.1% n class="Chemical">Cr(III)-doped sample (Figure 5) reveal a strong temperature dependence of the ZFS. Spectral simulation using the EasySpin package allowed us to extract the ZFS constant D as a function of sample temperature (Figure 6). While D reaches a plateau value of 840 MHz at temperatures below 20 K, its magnitude decreases almost linearly with increasing temperature above 40 K, reaching a value of ∼186 MHz at 320 K; the axial ZFS tensor symmetry is conserved throughout the whole accessible temperature range. While the occurrence of a nonvanishing ZFS in such a system is necessarily caused by the distortion from hexagonal symmetry,[104] its variation with temperature is less trivial to explain; however it can be generally attributed to coupling of the paramagnetic ion to temperature-induced lattice vibrations.[105,106] A significant temperature dependence in D has been thoroughly documented with experiment and theory on systems such as MgO:Cr3+ and ruby, and has been attributed to lattice expansion and electron–phonon interactions.[107−111] However, in these cases the absolute value of D was much larger than in our system and increased only slightly in magnitude with increasing temperature (for Cr3+ in ruby, the low-temperature value is |D| ≈ 5.7 GHz, and the value increases by only ∼90 MHz over the range of 600 K).[108] Misra et al.[112] investigated the EPR properties of [Cr(H2O)6]3+ in guanidinium aluminum sulfate hexahydrate and reported values of D = −1164 and −892 MHz for the two different Cr3+ lattice sites at 1.6 K, which decreased in absolute value to D = −732 and −585 MHz, respectively, at 298 K. These values were later confirmed theoretically by Pan et al.[113] and explained in terms of a trigonal distortion of the hexagonal Cr3+ site due to a slight mismatch of the ionic radii of Al3+ (0.535 Å)[85] and Cr3+ (0.615 Å), which causes an elongated distortion around the Cr3+. In our case, the measured D values are of opposite sign but very similar in absolute value, which decreases with increasing temperature. This suggests that a comparable situation arises here. Since the difference between the ionic radii of Co3+ (0.545 Å) and Cr3+ is slightly smaller than in the case of Al3+, a smaller distortion and hence a smaller ZFS would arise. However, because of the difference in the crystal structures of the two host systems, the geometry of the distortion would be opposite (i.e., prolate vs oblate), as indicated by the opposite sign of the ZFS constant.

Figure 5

CW X-band EPR spectra of Cr(III)-doped [Co(en)3Cl3]2·NaCl·6H2O with a doping ratio of 0.1% recorded at sample temperatures between 10 and 320 K. Thin lines show 10× vertical magnifications to emphasize the weaker spectral features. The data were recorded using a microwave power of 0.02–20 μW and field modulation of 0.2 mT in amplitude and 10–100 kHz in frequency; 2048 points were recorded with a time constant of 40.96 ms and a conversion time of 81.92 ms in a single sweep.

Figure 6

Zero-field splitting constant D as a function of sample temperature. D was obtained by spectral simulation of the EPR spectra (see representative selection in Figure 5) of 0.1% Cr(III)-doped [Co(en)3Cl3]2·NaCl·6H2O using the EasySpin package.[102] Axial symmetry of the ZFS tensor was assumed for the simulations.

CW X-band EPR spectra of Cr(III)-doped [n class="Chemical">Co(en)3Cl3]2·NaCl·6H2O with a doping ratio of 0.1% recorded at sample temperatures between 10 and 320 K. Thin lines show 10× vertical magnifications to emphasize the weaker spectral features. The data were recorded using a microwave power of 0.02–20 μW and field modulation of 0.2 mT in amplitude and 10–100 kHz in frequency; 2048 points were recorded with a time constant of 40.96 ms and a conversion time of 81.92 ms in a single sweep.

Zero-field splitting constant D as a function of sample temperature. D was obtained by spectral simulation of the EPR spectra (n class="Chemical">see representative selection in Figure 5) of 0.1% Cr(III)-doped [Co(en)3Cl3]2·NaCl·6H2O using the EasySpin package.[102] Axial symmetry of the ZFS tensor was assumed for the simulations.

The 1H enhancement factor ε(n class="Chemical">1H) (i.e., the ratio of the intensities of the DNP-enhanced and nonenhanced NMR spectra) shows only a minor variation as a function of the Cr3+ doping ratio. All of the 1H enhancement factors are on the order of 2–3, with a slight tendency for larger ε(1H) at the lowest chromium concentration (Figure 7). This is surprising because previous SE DNP experiments have shown a significant dependence of the enhancement factor on the concentration of the polarizing agent.[114] As a comparison, a simple calculation using the density ρ = 1.567 g cm–3 yields a Cr3+ concentration of 36.2 mM for a doping ratio of 1 mol %. On the basis of this estimate and our experience with frozen solutions of polarizing agent radicals and transition-metal complexes, we expected to observe a maximum ε(1H) at a doping ratio of ∼0.3–1 mol % (i.e., a concentration of 10.9–36.2 mM). The polarization buildup and longitudinal relaxation time constants were strongly dependent on the doping ratio, ranging from ∼0.3 s for 3 mol % up to 20 s for 0.1 mol %; in comparison, T1 for the undoped sample was measured to be as long as ∼200 s. The modest ε(1H) together with the unexpected polarizing agent concentration dependence indicates that the properties of the 1H matrix in the crystal lead to very different behavior compared with an amorphous, paramagnetically doped glass. Furthermore, the crystalline sample investigated in this study was constituted from natural-isotopic-abundance compounds, so it features a proton density of about 71 M, similar to the value of ∼100 M for 60/40 (v/v) glycerol/water. The proton concentration has already been shown to have a significant impact on DNP performance.[10,32] The effect of sample morphology on the DNP performance has also been discussed in the literature. In cases where the polarizing agent is dissolved, it has been shown that the formation of a glass upon freezing is crucial because the formation of solvent crystals would lead to phase segregation of the two immiscible solids (i.e., the solvent matrix and the polarizing agent).[24,28] In our case, however, the paramagnetic Cr(III) dopant is incorporated into the Co(III) host lattice during crystal growth, as confirmed by the EPR results (vide supra), and does not undergo phase separation with a change in temperature.

Figure 7

211 MHz/140 GHz DNP enhancements obtained for 1H (red squares), 13C (blue diamonds), and 59Co (green circles). Data were obtained as ratios of the NMR signal intensities with and without ∼5 W microwave irradiation at 80 K with MAS at 4 kHz. For the 1H enhancements, the polarization was measured indirectly (i.e., e– to 1H to 13C via CP) at a magnetic field of 5027.6 mT, while for 13C and 59Co the direct polarization (i.e., e– to 13C or 59Co) was measured during a Bloch decay (13C) and a Hahn echo (59Co) at a magnetic field of 5021.8 mT; the field values correspond to the expected SE DNP matching conditions. Polarization was read out after a buildup period of roughly 1.3TB. Error bars smaller than the data points have been omitted. The right graph shows an enlarged vertical scale.

211 MHz/140 GHz DNP enhancements obtained for n class="Chemical">1H (red squares), 13C (blue diamonds), and 59Co (green circles). Data were obtained as ratios of the NMR signal intensities with and without ∼5 W microwave irradiation at 80 K with MAS at 4 kHz. For the 1H enhancements, the polarization was measured indirectly (i.e., e– to 1H to 13C via CP) at a magnetic field of 5027.6 mT, while for 13C and 59Co the direct polarization (i.e., e– to 13C or 59Co) was measured during a Bloch decay (13C) and a Hahn echo (59Co) at a magnetic field of 5021.8 mT; the field values correspond to the expected SE DNP matching conditions. Polarization was read out after a buildup period of roughly 1.3TB. Error bars smaller than the data points have been omitted. The right graph shows an enlarged vertical scale.

Both the 13C and n class="Chemical">59Co DNP enhancements increased monotonically with increasing doping ratio. At 3% Cr(III), maximum enhancement factors of 16 (Figure S2 in the Supporting Information) and ∼11, respectively, were attained at a microwave power of 5 W (Figure 7) with buildup time constants on the order of ∼48 and 7 s, respectively. The 13C DNP MAS NMR line width increased up to 15% with a Cr loading of 1% (vs 0% Cr at 83 K), which is reasonable for high-resolution work. Paramagnetic broadening became a significant issue when 3% Cr was used, whereby the line width increased by 40% (Table S3 in the Supporting Information). Therefore, further gains may be achieved at higher Cr loadings (vide supra), but care must be taken because the spectral resolution may be reduced by high paramagnetic metal cation concentration. In addition to paramagnetic relaxation, further complications may arise when large amounts of paramagnetic metals are used because hyperfine interactions (scaler and dipolar) may shift and split the resonances, as seen in other chemical systems.[56,115−121]

In principle, under the conditions faced in this study two different solid-state n class="Chemical">DNP mechanisms can be active with an inhomogeneously broadened EPR line: the solid effect (SE) and the cross effect (CE). The SE is active when the overall width of the EPR transition, constituted by the inhomogeneous breadth Δ and the homogeneous line width δ, is smaller than the nuclear Larmor frequency: Δ, δ < ω0/2π.[122−124] DNP enhancements of opposite sign are then observed at magnetic fields where the sum and the difference of the electron Larmor frequency ω0 and the nuclear Larmor frequency ω0 match the microwave frequency ωmw (i.e., DNP enhancement can be achieved when the SE matching condition ωmw = ω0 ± ω0 is satisfied). On the other hand, the CE is active when δ < ω0/2π < Δ, and cross-relaxation between two dipole–dipole-coupled electron spins can induce electron–electron–nuclear flip-flop-flips when |ω0 – ω0| = ω0.[125−129] Whereas in the case of 1H DNP it is quite clear that the SE should be the dominant DNP mechanism because ω0/2π = 214 MHz > Δ = 40 MHz and the accordingly chosen matching field, for 13C (59Co) we face the situation where ω0/2π = 53 (51) MHz ≈ Δ = 40 MHz. This does not allow us to determine straightforwardly which DNP mechanism will be active; on the contrary, SE and CE will be active at the same time with varying weights that depend on the polarizing agent concentration and microwave irradiation power. The situation of SE and CE occurring in parallel has been reported in the literature numerous times, especially for DNP of low-γ nuclei.[25,31,36,130−132] In order to assess the contributions of the SE and the CE to the DNP, we recorded the field and power dependences of the DNP enhancements for the 3% Cr(III) sample. In Figure 8 the relevant part of the 140 GHz EPR spectrum is shown, together with vertical dashed lines indicating the positions of the center of the CT (red) and the 13C (blue) and 59Co (green) double- and zero-quantum resonance fields representing the SE matching fields. The field-dependent enhancement profiles clearly show positive and negative enhancement maxima that are closer to the CT than would be expected for the SE alone. At the same time, the power dependence of the 13C and 59Co enhancements (shown in the Figure 8 inset) indicates that the slope is smaller than in the nearly linear power dependence that has been observed for the SE in previous experiments.[32,34] The effect is more pronounced in the case of 13C; however, it is still significant for 59Co as well. These observations lead us to conclude that the CE plays an important role in reaching the experimental enhancement factors for the large doping ratio of 3%, which corresponds to a polarizing agent concentration of ∼110 mM. The strong dependence of ε on the doping ratio supports this conclusion, as the CE becomes more and more efficient as the interelectronic distance is reduced and the dipole coupling between different Cr(III) centers is increased, therefore allowing more efficient electron–nuclear cross-relaxation (Table 1).

Figure 8

Normalized field-dependent DNP enhancements of 13C (blue diamonds) and 59Co (green circles) in 3% Cr(III)-doped [Co(en)3Cl3]2·NaCl·6H2O measured under 8 W of 140 GHz microwaves with 4 kHz MAS at 80 K. The data were recorded by measuring the spin polarization after constant buildup periods of 50 and 10 s using Bloch decay and Hahn echo sequences for 13C and 59Co, respectively. The 140 GHz EPR spectrum (see Figure 2 for details) is shown at the top for comparison. The abscissa is on the same scale but has been shifted because of the slightly different frequencies of the microwave sources used for EPR and DNP. Dashed lines indicate the center of the EPR resonance (red) as well as the respective matching conditions for 13C (blue) and 59Co (green). The inset shows the microwave power dependence measured at the field of maximum enhancement.

Table 1

Electron Distributions in [Co(en)3Cl3]2·NaCl·6H2O Crystals with Increasing Paramagnetic Doping of Cr3+

crystal	Cr (mol %)	[Cr3+] (mM)	Cr3+–Cr3+ distance (nm)
[Co(en)3Cl3]2·NaCl·6H2O	0	0.0	n.a.
	0.1	3.6	7.7
	0.3	10.9	5.3
	1	36.2	3.6
	3	108.6	2.5
[Cr(en)3Cl3]2·NaCl·6H2O	100	3,650.0a	0.8a

Based on Co derivative crystalline lattice parameters.

Normalized field-dependent DNP enhancements of n class="Chemical">13C (blue diamonds) and 59Co (green circles) in 3% Cr(III)-doped [Co(en)3Cl3]2·NaCl·6H2O measured under 8 W of 140 GHz microwaves with 4 kHz MAS at 80 K. The data were recorded by measuring the spin polarization after constant buildup periods of 50 and 10 s using Bloch decay and Hahn echo sequences for 13C and 59Co, respectively. The 140 GHz EPR spectrum (see Figure 2 for details) is shown at the top for comparison. The abscissa is on the same scale but has been shifted because of the slightly different frequencies of the microwave sources used for EPR and DNP. Dashed lines indicate the center of the EPR resonance (red) as well as the respective matching conditions for 13C (blue) and 59Co (green). The inset shows the microwave power dependence measured at the field of maximum enhancement.

Even though the experimental observations clearly indicate a significant CE n class="Chemical">contribution, the exact mechanism that allows energy-conserving electron–electron–nuclear cross-relaxation is unclear. In amorphous solids, the required frequency difference between the electron spins is typically caused by a sufficiently large g anisotropy and a random orientation of the radical molecules. In the present system, the g factor is essentially isotropic, and the apparent line width of the CT should not allow for an efficient CE. Moreover, since in the crystalline system the molecular frames of all relevant interactions are identical for all centers within one crystallite,[86] orientational heterogeneity cannot lead to the necessary frequency matching, in contrast to amorphous systems. However, in a system of two S = 3/2 spins and one I = 1/2 nucleus, level degeneracies can be identified for certain orientations of the ZFS tensor that allow for energy conserving flip-flop-flips for crystallites in specific orientations with respect to the external magnetic field. This can be demonstrated by analyzing a minimal spin Hamiltonian for such a system:It should be noted that this Hamiltonian has been reduced to include only interactions leading to significant shifts in the eigenenergies of the system and does not represent all of the interactions required for the CE. Furthermore, it has been simplified with first-order perturbation theory; the introduction of higher-order terms does not lead to a qualitative change in the situation. The eigenenergies of this system can be calculated asHere it becomes obvious that two cases of degeneracies between states |m, m, m⟩ in different m subsets can be obtained: (1) for D(3 cos2 θ – 1) = ω0, the states |−3/2, +1/2, +1/2⟩ and |+1/2, −3/2, +1/2⟩ are strongly mixed with the state |−1/2, −1/2, −1/2⟩, and mixing also occurs between |+1/2, +1/2, −1/2⟩ and |+3/2, −1/2, +1/2⟩ as well as |−1/2, +3/2, +1/2⟩; (2) for 2D(3 cos2 θ – 1) = ω0, the states |±1/2, ∓1/2, −1/2⟩ are strongly mixed with |±3/2, ∓3/2, +1/2⟩. The situation is similar when a nucleus with I > 1/2 is considered, but larger shifts in nuclear Larmor frequency due to strong nuclear quadrupole interactions have to be included, while higher-order transitions with Δm > 1 may also play a role. As the ZFS is modulated by MAS, CE-enabling level crossings would occur for most crystallites during one rotor period as long as the orientation of the crystallite with respect to the spinning axis allows the matching conditions mentioned above to be achieved. Because of the smaller ω0, this applies to more initial orientations for 13C and 59Co, while for 1H only a smaller ensemble of crystallites would be able to achieve matching. The theoretical importance of MAS-induced level crossings for the CE has recently been demonstrated;[133,134] crystalline systems like the one presently studied might be suitable systems for further systematic investigation of the practical implications.

Another matching condition can be desn class="Chemical">cribed when one of the two electron spins is situated at a 53Cr nucleus. This situation is represented by the following spin Hamiltonian:In eq 4, the additional terms with the index (53Cr) are not to be confused with the nuclear spin parameters without the index: the latter represent the nucleus to be polarized, while the nuclear spin of 53Cr leads only to shifts in the eigenenergies of the first electron spin. The eigenenergies in this case are given byThis is analogous to the situation described above but allows for additional matching as a function of the 53Cr spin state. An interesting situation arises, however, when only the m = {−1/2, +1/2} subspace is considered. In this subspace the ZFS can be neglected, since all of the levels experience the same ZFS shift. This leaves us with a reduced set of levels:Here we can identify degeneracies under the condition n|a(53Cr)| = |ω0| with n = 1, 2, 3 in the case of I(53Cr) = 3/2. This is an interesting situation since it is not orientationally dependent and hence would always be active during MAS or nonspinning experiments. Also, since ω0(13C) ≈ ω0(59Co) ≈ a(53Cr) and 3a(53Cr) < ω0(1H), this effect could be active only for 13C and 59Co but not for 1H, which we observed. However, the limitations that both electrons have to be in the m = {−1/2, +1/2} subspace and at least one electron must be situated at a 53Cr site leads to a reduced probability of finding matching pairs. Unfortunately, with the present data on hand, an unambiguous attribution of the dominant matching mechanism has not been successful.

Figure 9 shows a representative n class="Chemical">DNP-enhanced 59Co NMR signal for the compound containing 3% Cr(III) in comparison with a non-DNP-enhanced signal recorded under otherwise identical conditions. The enhancement factor in this case was ∼11, which allowed us to acquire the above spectrum in 0.7 h (TB = 7.1 s, 256 scans, 45 μL sample volume). Longer DNP experiments (∼4 h) revealed the separation of the 59Co satellite (±3/2 ↔ ±1/2) peaks to be 4000–5000 ppm. In the non-DNP-enhanced spectra at 85 K these satellite transitions are difficult to observe, limiting the experimentalist’s ability to determine the quadrupole coupling constant because of the noise even though the experiment was averaged for >14 h (T1 = 10 s, 4096 scans, 45 μL sample volume). By measurement of the separation between the satellites in the DNP-enhanced 59Co MAS NMR spectra (0.1 to 3% Cr), the quadrupole coupling constant and asymmetry parameter were determined to be CQ = 3.2 ± 0.3 MHz and η < 0.1, respectively. At 85 K the molecular complex has an isotropic chemical shift (δiso) of 7020 ppm, as determined by simulation of a series of nonspinning and MAS experiments (Figure S3 in the Supporting Information), a span (Ω) of 525 ± 40 ppm, and a skew (κ) of >0.9. The change in temperature from 85 to 290 K has an effect on the 59Co chemical shielding parameters: in particular, δiso is shifted to a higher frequency of 7160 ppm (Figure 10) and Ω is reduced to 380 ± 25 ppm (Figure S3), as seen in similar Co(en3)Cl3 complexes (Table S4 in the Supporting Information) maintaining axial symmetry as required by crystal symmetry (vide supra).[65,88] The 140 ppm change in δiso and the increase in shielding span (at 85 K) are thought to be caused by changes within the lattice and the Co bonding character as one cools the DNP target; similar to the EPR effects described above. It should be noted that spectral changes have been reported previously when studying other challenging NMR nuclei using DNP, wherein both temperature and the solvent have affected the NMR parameters in nuclei that have considerable quadrupolar or chemical shielding interactions.[132,135]

Figure 9

(a) DNP-enhanced and (b) non-DNP-enhanced 59Co NMR spectra of 3% Cr(III)-doped [Co(en)3Cl3]2·NaCl·6H2O at 85 K recorded at 5021.8 mT (50.444 MHz) under 4 kHz MAS.

Figure 10

Comparison of 59Co MAS NMR spectra obtained at (a) 85 K (256 scans, DNP) and (b) 290 K (8192 scans, non-DNP) under MAS with a rotation frequency of 5.3 kHz. Spectra were acquired using an echo sequence at a field of 5.0218 T (50.44 MHz 59Co frequency) and are referenced to aqueous K3Co(CN)6.[88] The double dagger (⧧) represents the 59Co isotropic chemical shift (δiso).

(a) DNP-enhanced and (b) non-n class="Chemical">DNP-enhanced 59Co NMR spectra of 3% Cr(III)-doped [Co(en)3Cl3]2·NaCl·6H2O at 85 K recorded at 5021.8 mT (50.444 MHz) under 4 kHz MAS.

Comparison of n class="Chemical">59Co MAS NMR spectra obtained at (a) 85 K (256 scans, DNP) and (b) 290 K (8192 scans, non-DNP) under MAS with a rotation frequency of 5.3 kHz. Spectra were acquired using an echo sequence at a field of 5.0218 T (50.44 MHz 59Co frequency) and are referenced to aqueous K3Co(CN)6.[88] The double dagger (⧧) represents the 59Co isotropic chemical shift (δiso).

Conclusion

We have shown that significant DNP enhancements of n class="Chemical">13C and 59Co can be achieved using Cr(III) as a paramagnetic dopant within a diamagnetic host lattice at a rather large molar doping ratio of 3%. Both the microwave power and field dependences suggest that the CE is at least partially involved as a DNP mechanism at this large paramagnet concentration. In contrast, polarization of 1H, where the SE is supposedly the active DNP mechanism, is limited to ε ≤ 3. However, we emphasize that the experiments were performed on samples with natural-abundance isotopes, leaving a large potential for optimization of the proton concentration and Cr(III)/Co(III) doping ratio.

The 59Co NMR isotropic line width with n class="Chemical">DNP at cryogenic temperatures is not compromised compared with the NMR line width at room temperature using an undoped sample [i.e., 100% Co(en3)3+ complex] at 5 T. The maximum 59Co DNP enhancement factor (ε) of 19 at a microwave power of 9 W together with a ∼3.5-fold increase in Boltzmann polarization compared with room temperature leads to an overall signal enhancement of ε† = 66. Doping of the crystalline lattice enables faster accumulation of transients as a result of shortening of TB and T1, which would otherwise be increased because of the use of cryogenic temperatures. High-field DNP NMR spectroscopy offers an ability to expand the area of challenging NMR nuclei that suffer from both quadrupolar and chemical shielding interactions, such as 59Co. The span of the 59Co CSA was increased by nearly 40% and shifted to lower frequency by 140 ppm relative to room temperature while maintaining axial symmetry, illustrating the sensitivity of 59Co to its local chemical environment.

The highly symmetrical system studied here clearly can be considered an idealized can class="Chemical">se to some degree. However, simple considerations show that the symmetry of the Cr(III) site can be significantly reduced without compromising the EPR line width and therefore the DNP efficiency. In our case, the symmetric environment imposes a ZFS constant of D = 740 MHz under DNP conditions (T = 80 K). At 140 GHz, this leads to an effective broadening of the CT by only about 10 MHz; the observed EPR line broadening of 40 MHz is likely dominated by unresolved hyperfine coupling to 1H. Therefore, we estimate that significant line broadening by second-order ZFS is of no practical concern unless D reaches values on the order of 2 GHz (e.g., the maximum breadth of the second-order broadening effect on the CT for D = 2.0 GHz and S = 3/2 is ∼40 MHz at the commonly used DNP field of B0 = 9.4 T). In a more general description, any paramagnetic metal with an effectively narrow EPR line may be used as a dopant in a similar manner as described in this study. Nevertheless, the applicability of dopants with larger line widths (exceeding the nuclear Larmor frequency) should not be ruled out per se, as the underlying effects are not yet fully understood and have to be individually investigated by experiment, especially for higher doping ratios, where the CE might become efficient.