Nuclear-spin-pattern control of electron-spin dynamics in a series of V(iv) complexes† †Electronic supplementary information (ESI) available: Methods, additional characterization and discussion. CCDC 1921675–1921677. For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/c9sc02899d

This report details how the design of specific nuclear-spin patterns on ligands modulates spin-relaxation times in a set of open-shell vanadium(iv) complexes.


Introduction
Magnetic molecules are next-generation components of many different technological arenas, ranging from magnetic resonance imaging (MRI) 1,2 to quantum information processing. [3][4][5][6][7][8][9][10][11] Utility in any of these applications requires long spin-lattice relaxation times (T 1 > 1 ms) and phase-memory relaxation times (T m § > 100 ms). T 1 denes the lifetime of an excited spin and is the upper limit of T m . In contrast, T m is the lifetime of the electron spin superposition, or coherence time. Designing systems where both of these parameters are long is an acute challenge because of the ubiquitous spin bath (nearby electronic spins or nuclear spins), which produces a chaotic local magnetism that shortens T 1 and T m from spin-spin interactions. [12][13][14][15] To circumvent the spin bath challenge, signicant efforts are made to engineer environments with less noise from the spin bath. This engineering is done by dilution of the paramagnetic species, using smaller-magnetic-moment isotopic substitution (e.g. 2 H, m ¼ 0.86m N for 1 H, m ¼ 2.79m N ), or complete elimination of nuclear spins. 3,[16][17][18][19][20] However, largemoment environmental spins are a critical part of utility in nearly all applications. For example, MRI applications require function in proton-rich biological environments, and information processing applications will likely feature stray magnetic elds from moving charges or other proximate magnetic materials in a device. Hence, understanding how to design complexes with long T 1 and T m in magnetic environments is a necessary advance for future technologies.
Herein, we demonstrate the rst control of T m via patterning of ligand-based nuclear spins in a metal complex (Fig. 1). In Fig. 1 Defect qubits in SiC display a long T m because only nonresonant spins can be adjacent in the structure, which disrupts nuclear spin diffusion. This manuscript tests whether such a design principle will affect T m in molecular species, specifically by probing different patterns of 1 H and 79/81 Br spins on catecholate ligands in V(IV) complexes. molecules, ligand nuclear spins are a critical component of the nuclear spin bath and control electron spin dynamics through nuclear spin diffusion. 14,15,21 In this phenomena, pairs of resonant nuclear spins (those that require identical quantities of energy to ip) engage in energy-conserving ip-op motions, wherein two oppositely oriented spins simultaneously ip, or exchange spin. 22 This process generates local magnetic noise and shortens T m for a magnetic ion. [23][24][25][26] In the absence of a nuclear spin bath, T m will approach and exceed millisecond lifetimes. [27][28][29][30] However, in spin-rich environments, lifetimes are typically less than 100 ms (ref. 31) and more frequently less than 10 ms. 19,23, A recent breakthrough in the study of paramagnetic defects in SiC might hold the key to longer relaxation times in nuclear spin-rich baths (Fig. 1). [53][54][55] The defects in SiC display longer T m values than nitrogen vacancy centers in diamond despite higher nuclear spin concentration in the former (1.1% 13 C and 4.7% 29 Si in SiC; 1.1% 13 C in diamond). 56 The relative enhancement in T m stems from a particular structural featureeach Si atom is surrounded by C and each C atom is surrounded by Si. [53][54][55]57 This interstitial patterning increases T m in two ways. First, two Si nuclear spins are never adjacent (likewise for C), and nuclear spin diffusion decreases for spins held far apart from one another. 12 Second, the difference in the nuclear g n factors for C and Si ensures that, even when adjacent, spin diffusion will not occur between the nonresonant 13 C and 29 Si nuclei. These results suggest specic positioning of nuclear spins as a potential method of T m control via synthetic chemistry.
Drawing inspiration from SiC, we address the questions: can patterning of nuclear spins on ligand shells inuence the electronic T m of a ligated metal? Freedman and co-workers showed that separation between an open-shell ion and nuclear spins is important, 58 and there is signicant literature demonstrating the impacts on replacement of 1 H (m ¼ 2.79m N ) with low-moment magnetic nuclei e.g. 2 H (m ¼ 0.86m N ). 19,42,46 In this paper we probe a different question: can the impacts of high-magnetic-moment nuclei on T m be mitigated instead by controlling nuclear spin to nuclear spin interactions in a molecule? To address these questions, we prepared and investigated, via pulsed EPR spectroscopy, a series of Bu 3 NH + salts of the canonical tris(catecholato)vanadate(IV) complex [V(C 6 H 4 O 2 ) 3 ] 2À : (n-Bu 3 NH) 2 (3), (n-Bu 3 NH) 2 [V(4,5-Br 2 -C 6 H 2 O 2 ) 3 ] (4), and (n-Bu 3 NH) 2 [V(C 6 Br 4 O 2 ) 3 ] (5). In this series, the specic pattern of 1 H and 79/81 Br is varied on each ligand ( Fig. 2 and 3). These nuclear spins have signicantly different resonance frequencies, 56 and, on this basis, we hypothesized that ligand-based nuclear-spin diffusion would be modulated in 1-5. Furthermore, we predicted that such change would lead to a variation in V(IV) T m dependent on the exact substitutional pattern of H and Br on the ligand. In this report, we show for the rst time that this patterning design strategy is an effective means of inuencing T m . Importantly, these studies also include the rst investigation of the pulsed EPR spectroscopic properties of the V(IV) ion at very high eld and frequency (>4.0 T, 120 GHz).

Results and discussion
Preparation of the targeted complexes proceeded via a simple ligand metathesis scheme using VO(acac) 2 , tri-n-butylamine, and the ligands shown in Fig. 2 (see also ESI, Fig. S1-S4 †). The general scheme for these syntheses follows previous reports of  Counter ions are omitted for clarity. Green, maroon, red, gray, and white spheres represent vanadium, bromine, oxygen, carbon, and hydrogen atoms, respectively. the triscatecholato complex of V(IV). 18,41,[59][60][61][62] Recrystallization afforded crystals suitable for single crystal X-ray diffraction of 2, 4, and 5 (but not 3, see Fig. 3, Tables S1-S3, and ESI †). Single crystal X-ray diffraction experiments on crystals of 1, 40 2, 4, and 5 ( Fig. 3) reveal similar molecular structures of the VO 6 core. In these structures, all vanadium(IV) ions are in a six-coordinate environment, with average V-O bond lengths varying over a tight range across the series, from 1.938(4)Å for 1 to 1.943(9)Å for 5. The continuous-shape-measurement (CSM) analyses using SHAPE 2.0 soware 63,64 of 1-5 provide symmetry measures for an octahedron of 1.67, 2.39, 3.97, and 1.41 for 1, 2, 4, and 5, respectively (here, a value of 0 corresponds to a perfect octahedron). The symmetry measures for a trigonal prismatic geometry are much higher (>5), indicating that 1, 2, 4, and 5 are better described as slightly distorted octahedra (Table S4 † . 40 One critical aspect of the tested design principle relies on a difference between the spin-ip energies of the 1 H and 79/81 Br nuclear spins. On this merit, high-eld and high-frequency EPR (120 GHz) was selected for studying 1-5. With this technique, the differences in Larmor frequencies between 1 H (ca. 187 MHz) and 79 65 Importantly, such conditions will decouple not only the 1 H and 79/81 Br nuclear spins, but potentially 79 Br from 81 Br due to the bigger difference in Larmor frequencies (ca. 4 MHz)rendering the Br atoms inert spin blocks to disrupt 1 H nuclear-spin diffusion. High-eld, high-frequency investigations of the relaxation times of V(IV) are, to the best of our knowledge, unprecedented.
Echo-detected EPR spectra of 1-5 were collected to test for variation in the spin-Hamiltonian parameters as a function of ligand. To do so, 1-5 were dissolved in d 14 -o-terphenyl (d 14 -OTP) at a 1 mM concentration, leveraging the solubility in nonpolar media afforded by the tri-n-butylammonium cations. 40 The echo-detected, eld-swept (EDFS) spectra of 1-5 were then collected at 5 K and 120 GHz (Fig. 4, S6 and Table S5 †). The recorded spectra starkly differ in appearance from the 100 mTwide, eight-line patterns observed at X-band frequency (Fig. 4). Instead, each 120 GHz spectrum reveals a single broad transition, spanning from 4.3-4.5 T. Such spectral width is attributed to enhanced broadening of the electronic g-factor ("g-strain") at high magnetic elds. 15 Simulations of the spectra were performed using Easyspin 66 and the following spin Hamiltonian: Here, g e and A correspond to rhombic electronic g factors and 51 V hyperne coupling constants, respectively. Q is the nuclear quadrupolar constant for 51 V,Ŝ andÎ are electronic and nuclear spin operators, respectively, m B and m N are the Bohr and nuclear magnetons, respectively, g n the nuclear g factor for 51 V and B the magnetic eld. More simulation details and the exact spin Hamiltonian values extracted can be found in the ESI and Table  S4. † We note that the best simulations of the g-factors at 120 are only slightly different from those obtained at X-band. 40, 41 We place higher condence on the g-factors determined here, since greater accuracy on this parameter is a hallmark of high frequency EPR. 15,[67][68][69] Most importantly, we note that the obtained parameters are similar in magnitude and anisotropy, demonstrating a relatively consistent electronic structure for the V(IV) ion in 1-5. As the g and A values for V(IV) ions are also extremely sensitive to the symmetry of the ligand eld, 70 the similarity of these parameters highlights a relatively consistent local coordination geometry for 1-5 when frozen in d 14 -OTP.
Spin-lattice relaxation rates (1/T 1 ) were obtained as the rst step toward understanding the impact of ligand nuclear-spin patterning on the V(IV) spin dynamics. To determine these rates for 1-5, variable-temperature inversion recovery experiments were performed at the highest-intensity peaks in the 120 GHz EDFS spectra at 5 K, which is B 0 ¼ 4.4 T for all ve complexes (Fig. 5, S7-S11 and Table S6 †). For 1-5, 1/T 1 is slowest at low temperature, with an average 1/T 1 of 0.88(6) ms À1 at 5 K. With increasing temperature, T 1 rapidly decreases for 1-5, in concert with a rapidly hastening relaxation rate, 1/T 1 . Owing to instrumental limitations related to the deadtime, performance of these experiments was precluded above 40 K. An immediate observation from these data is the near-two-ordersof-magnitude enhancement of 1/T 1 (average 1/T 1 ¼ 0.88 (6) ms À1 ) at 120 GHz versus the 5 K, 9.4 GHz 1/T 1 of 1: 0.0141(4) ms À1 . 40,41,43 Comparison of 1/T 1 across the series of complexes, in contrast, reveals remarkable similarity between the temperature-dependent curves at this eld/frequency.
The enhancement of spin-lattice relaxation rates (1/T 1 ) at high eld/frequency gives valuable information about the dominant high-eld relaxation process for V(IV). Indeed, there are a collection of different mechanisms potentially responsible for spin-lattice relaxation: direct, Raman, local-mode, tunneling, and thermally activated processes. 15,71 Yet, only direct, tunneling, and thermally activated processes are elddependent. Of these, tunneling is typically suppressed under an applied eld and thermally activated processes are likely precluded for V(IV) owing to the absence of low-lying excited states for this S ¼ 1/2 ion. Hence, we hypothesized that a dominant direct process is responsible for the stark shortening of T 1 . To test this hypothesis, we modelled the temperature-dependence of the spin-lattice relaxation rate (1/ T 1 ) at 120 GHz. We found that the data for all complexes were readily modeled using the sum of a direct and Raman process in the following equation (see Fig. 5 and S12 †): 15 Here, T is temperature, A dir is the direct process coefficient, B is the magnetic eld, A Ram is the Raman process coefficient, q D is the Debye temperature, J 8 (q D /T) is the transport integral (see ESI † for full expression and resulting t parameters). Qualitatively, because the Raman process is eld-independent, the twoorder-of-magnitude shortening of T 1 at 120 GHz compared to 9.4 GHz is strongly suggestive of the direct process importance. Indeed, the two-order of magnitude difference in T 1 between these two data sets would be expected from the B 2 dependence of this process. 12 Furthermore, we can successfully simulate the T 1 data using the Raman process from X-band analyses and modulating only A dir , (see ESI †). Finally, we note that the shortening of T 1 at the high elds of these analyses agrees with reported ac magnetic susceptibility studies. 41,43 The most important observation, however, is that the relaxation mechanisms for 1-5 appear invariant with ligand identity. Nuclear spin diffusion is expected to exert the greatest impact on T m , not T 1 . 3,12,21,23 Hence, T m was measured for 1-5 to test for a pattern-dependent effect. Variable-temperature, twopulse Hahn echo experiments were performed on 1-5 in d 14 -OTP at 1 mM concentration to evaluate the echo decay as a function of ligand ( Fig. 6 and S13-S17 †). Stretched exponential functions were t to these decays to extract T m and the stretch parameter, b, (see ESI, Table S6 †) which can give mechanistic insight into the decay of the superposition. All complexes display the longest T m s at the lowest temperatures. At 5 K, the T m values of 1, 2, 3, and 5 range from 4.36(8) to 5.36 (9) ms. For 4, T m is about 2 ms shorter, 2.75(3) ms. With increasing temperatures, T m drops sharply for 1-5. By 20 K, the T m of 4 is 0.7(1) ms, which precluded pulsed measurements at any higher temperatures owing to low signal to noise. In contrast, T m remains appreciable for 1-3 and 5 up to at least 30 K. Interestingly, above 20 K, T m for 3 is slightly higher than the other complexes. The stretch parameters increase with increasing temperatures for 1-5. For 1-3 and 5, b ranges over 0.6 to 0.8 at the lowest temperatures, and venture closer to 1 at the highest temperatures. For 4, however, b is close to 1 at the The difference in T m for 4 relative to 3, and 3, 4 relative to 1, 2, and 5, represent two signicant ndings. First, these data, particularly for 3 (T m ¼ 4.36(8) ms) and 4 (T m ¼ 2.75(3) ms), reveal for the rst time that two substitutional isomers of the same magnetic metal complex can have signicantly different T m values. Second, the data for 3 versus the rest of the series highlight the possibility of enhancing T m via patterns that avoid two adjacent protons (though that impact is modest in the present system). However, in that context, it is particularly puzzling that 4 demonstrates a signicantly shorter T m than 1 and 5, which possess the highest number of adjacent 1 H and 79/ 81 Br spins, respectively. It is further puzzling that 4 displays a shorter T m than 3, when the protons in 4 are clearly further separated than those of 3. Changes in geometry of the coordination site and electronic structure are powerful mechanisms for adjusting T m . 12 However, the similarity of the spin-Hamiltonian parameters, crystallographic data, and T 1 values for 1-5 suggests that the different substitutional patterns of the ligands do not affect these aspects of the V(IV) ion. These results thus suggest that the impact of the pattern on T m is truly magnetic in nature, stemming from the 1 H and 79/81 Br ligand nuclear spins (vide infra).
For ligand-based nuclear spin diffusion to operate efficiently, the nuclear spins should have the same resonant NMR frequency (chemical shi). To probe the environment of nuclear spins for the molecules in this paper, we collected the 1 H NMR spectra of the ligands. 3,15 The 400 MHz (¼ 9.4 T eld) 1 H NMR spectra of the ligands of 1, 2, and 3 demonstrate peaks of varying multiplicity over a range of chemical shis (in frequency, 68, 93, and 61 Hz, respectively) (Fig. 7). The observed range of 1 H chemical shis in the ligands of 1-3 is a consequence of two factors. First, the presence of different quantities and arrangements of bromine on the ligands adjust the 1 H chemical shis. Second, J-coupling between the aromatic 1 H protons split the individual 1 H peaks into multiplets. In contrast, the aromatic protons of 4,5-dibromocatechol (the ligand of 4) yield a single peak with a full-width half-maximum of 2 Hz. The protons in this ligand are constrained to this tight chemical-shi window by the two-fold rotational symmetry and weak J-coupling (0-1 Hz) for aromatic 3,6 protons. 72,73 On the basis of the NMR data, we rationalize the observed T m data in terms of synthetic control via ligand-shell nuclear spin diffusion. First, the high symmetry of the 4,5-dibromocatechol and weak J-coupling ensure nearly identical chemical shis for the aromatic 1 H nuclei. In the other ligands, in contrast, asymmetry and stronger 1 H-1 H J-coupling spread the 1 H chemical shis out over >60 Hz. Owing to the relatively tight range (2 Hz) of the 1 H frequencies in the ligand of 4 relative to 1-3, we posit that a given ligand proton in 4 is signicantly more likely to have a proximate nucleus (across the aromatic ring) with the same chemical shi. Hence, the ligand-based protons in 4 are more likely to engage in nuclear spin diffusion and impact T m . In the other complexes, J-coupling and differing chemical shis spread the spin-ip frequencies of the 1 H protons over a wider range, ensuring a lower probability that a given 1 H will have a neighbor with precisely the same chemical shi. Hence, 1-3, with non-resonant 1 H spins, would be expected to display less-efficient spin diffusion and show a longer T m . This effect may also be operative for the ligand bromines, due to the different isotopes of bromine ( 79 Br and 81 Br). Hence, this argument may explain why 5 has a T m in the same range of 1-3. We note that the stretch parameters b are slightly higher for 4 relative to 1-3 and 5, suggesting that nuclear spin-diffusion may be more operative for 4 (and consistent with our rationale). 21 However, the typical values of b for dominant nuclear-spin diffusion are closer to 2-2.5, 12 and this discrepancy may be related to the limitation of T m by the short T 1 in 1-5. Given the fast spin-lattice relaxation at high eld, lower-eld measurements may engender stronger nuclearspin-diffusion control by pushing ligand-based nuclear spin resonant frequencies closer together. 69,74-77 Such measurements are exciting next studies.

Conclusions and outlook
The foregoing results demonstrate, for the rst time, that control of phase memory relaxation times is possible via nuclear-spin patterning within a molecule. Importantly, we interpret our data to suggest that tuning relative chemical shis, which are dictated by the symmetry and chemical makeup of the molecule, are a key future design strategy for manipulating T m in magnetic complexes. However, multiple new avenues of work are necessary to fully test the presented design strategy. In particular, learning how to harness said strategy to improve T m is a pressing concern. Indeed, we note that the "optimally patterned" species 3 only exhibits a slight enhancement of T m over a fully-protonated complex and the most dramatic impact is a shortening, not lengthening of T m . Toward the understanding to use this mechanism to lengthen T m , our future work spans studying the nuclear spin dynamics (in particular, the time constants for spin diffusion and spinspin relaxation) of the ligands and metal complexes. In this context, an important absence in the above analyses is a direct picture of the spin dynamics of the 79/81 Br nuclear spins, which is extremely challenging to obtain with solution-phase NMR. A system patterned with 19 F nuclei is in contrast particularly advantageous since 19 F NMR is readily performed. [78][79][80] It is in these directions that we are now working.

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

Acknowledgements
This research was performed with the support of Colorado State University (CSU) and the National Science Foundation (CHE-1836537). Standard molecular characterization experiments were performed at the CSU Central Instrument Facility, which is supported by an NIH-SIG award (1S10OD021814-01) and the CSU-CORES Program. C. E. J. and J. M. Z. thank Mr J. Joyce and Prof. Sandra Eaton for helpful insight. A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by the National Science Foundation Cooperative Agreement No. DMR-1644779 and the State of Florida.
Notes and references § In this paper, we use T m to describe the time constant associated with the decay of the echo intensity in a Hahn-echo experiment. This parameter is frequently also labelled T 2 , the spin-spin relaxation. However, the T 2 designation is typically ascribed to relaxation in the xy-plane primarily from electronic spin ip-op motions. In contrast, T m is a broader, all-encompassing term for all relaxation processes that affect relaxation in the xy-plane. The T m designation is particularly appropriate in this manuscript because there may be other factors controlling T m (e.g. a short T 1 ) under the experimental conditions. Further reading on this distinction can be found in ref. 12.