Probing Nuclear Spin Effects on Electronic Spin Coherence Via EPR Measurements of Vanadium (IV) Complexes

Supporting Information for:

Probing Nuclear Spin Effects on Electronic Spin Coherence via EPR Measurements of Vanadium (IV) Complexes

Michael J. Graham,† Matthew D. Krzyaniak,†,§ Michael R. Wasielewski,†,§ and Danna E. Freedman*,†

†Department of Chemistry and §Argonne-Northwestern Solar Energy Research Center, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208- 3113, United States

Inorg. Chem.

S1 Table of Contents Experimental details S3 Table S1  Crystallographic information for 1 S12 Table S2  Crystallographic information for 2 S13 Table S3  Crystallographic information for 3 S14 Table S4  Cw-EPR fit parameters S15 Table S5  Proton grouping scheme used to calculate dipolar coupling in 1 S16 Table S6  Proton grouping scheme used to calculate dipolar coupling in 2 S17 Table S7  Proton grouping scheme used to calculate dipolar coupling in 3 S18 Table S8  ENDOR fit parameters S19

Table S9  T1 fit parameters S20

Table S10  Fit parameters for T1 temperature dependence S21

Table S11  T2 fit parameters in DMF-d7/toluene-d8 S22

Table S12  T2 fit parameters in MeCN-d3/toluene-d8 S23 Table S13  Variable-power nutation frequencies S24 Figure S1  Cw-EPR and echo-detected EPR spectra and fits S25 Figure S2  ENDOR spectra and fits S26 Figure S3  Saturation/inversion recovery data and fits S27 Figure S4  Selected Hahn echo decay data and fits S28 Figure S5  Nutation data S29 Figure S6  Fourier transforms of nutation data S30 Figure S7  Nutation frequency vs. pulsed field strength S31 References S32

S2 Experimental Details

General Considerations. 2,6,8,10-Tetrathiobicyclo[5,3,0]dec-1(7)en-9-one (TTDEO) and the 1,2 ligands K2(C7H6S7) and K2(C9H6S8) were synthesized as previously reported. Potassium naphthalenide solution (50 mM) was synthesized by stirring 0.25 mmol naphthalene and 0.26 mmol potassium in 5.0 mL THF overnight under a nitrogen atmosphere. Vanadium tetrachloride bis(tetrahydrofuran) was synthesized as previously described.3 All other reagents and solvents were purchased from commercial vendors and dried and degassed before use. All manipulations detailed below were carried out under a nitrogen atmosphere in a Vacuum Atmospheres Nexus II glovebox equipped with a cold well.

2,4 K2(C5H6S4) was synthesized by a modified version of the previously-reported method. A solution of potassium methoxide was prepared by addition of potassium (86.8 mg, 2.22 mmol, 2.2 eq) to 0.5 mL methanol. This solution was then added to a solution of TTDEO (226.4 mg, 1.018 mmol, 1.0 eq) in 5 mL THF with stirring, resulting in immediate precipitation. The reaction was allowed to continue stirring for 6 hours to ensure complete deprotection, then filtered and rinsed with 2  2 mL THF. The off-white solid (269.8 mg, 97.2%) was collected, dried in vacuo, and used without further purification.

K2[V(C5H6S4)3]∙2C6H6 (1∙2C6H6). A suspension of VCl4(THF)2 (85.4 mg, 0.253 mmol, 1.0 eq) in 6.0 mL THF was precooled to −78 °C, then added to a suspension of K2(C5H6S4) (208.2 mg, 0.7639 mmol, 3.0 eq) in 8.0 mL THF at −78 °C dropwise while stirring. The reaction was stirred at −78 °C for 5 minutes, then allowed to slowly warm to room temperature over approximately 30 minutes, and finally stirred at room temperature overnight. The reaction mixture was then filtered and rinsed with 2  2 mL THF, yielding dark blue-green solids and a deep blue filtrate, − which contains the monooxidized species [V(C5S4H6)3] . The blue-green solids were dissolved in acetonitrile and filtered to remove a brown, insoluble solid, then the filtrate was concentrated in vacuo and layered over benzene to afford dark blue-green bladed crystals (126.1 mg, 57.4%). IR (cm–1, diamond ATR) 2895(m), 1578(w), 1474(s), 1422(w), 1408(s), 1399(m), 1273(s), 1235(s), 1172(s), 1092(w), 1032(s), 998(s), 957(s), 900(s), 866(s), 814(s), 755(w), 697(vs), 658(w),

S3 630(w), 606(w), 458(w), 434(s), 407(w). Anal. Calcd for C27H30K2S12V: C, 37.34; H, 3.48. Found: C, 36.97; H, 3.31.

K[V(C7H6S6)3]. K2(C7H6S6) (210.3 mg, ~0.583 mmol, ~3.1 eq) was suspended in 10 mL THF,

VCl4(THF)2 (64.3 mg, 0.191 mmol, 1.0 eq) was suspended in 10 mL THF, and both suspensions were cooled to −78 °C. The VCl4(THF)2 suspension was added dropwise to the K2(C7H6S6) suspension with stirring, and the reaction was allowed to stir cold for 45 minutes. The reaction was then allowed to warm slowly to room temperature and subsequently stirred at room temperature overnight. The reaction mixture was filtered and the dark green solids were rinsed with 2  1 mL THF. The solids were then dissolved in THF (solubility is ~2 mg/mL) and crystallized by diffusion of Et2O vapor into the solution. The obtained crystals were crushed and dried in vacuo to afford a dark green powder (83.7 mg, 46.7%).

K2[V(C7H6S6)3]∙3(MeCN) (2∙3MeCN). K[V(C7H6S6)3] (81.1 mg, 0.0865 mmol, 1.0 eq) was dissolved in 90 mL THF and cooled to −78 °C. A 50 mM THF solution of potassium naphthalenide (1.70 mL, 0.0867 mmol, 1.0 eq) was diluted to 5.0 mL by addition of THF, cooled to −78 °C, and added dropwise to the K[V(C7H6S6)3] solution over eight minutes. The reaction was stirred cold for 1.5 hours, then allowed to slowly warm to room temperature, and subsequently to stir at room temperature overnight. Solvent was removed from the resulting olive-brown reaction mixture in vacuo, and the residue was taken up in 4 mL MeCN. Olive- brown needles (51.7 mg, 54.3%) were obtained by slow diffusion of Et2O vapor into this solution. IR (cm–1, diamond ATR) 2954(w), 2903(m), 2849(m), 1619(s), 1603(m,sh), 1565(w), 1509(m,sh), 1469(w), 1458(w), 1441(m,sh), 1407(s), 1366(w), 1359(w), 1336(w), 1318(w), 1261(s), 1225(s), 1168(m), 1113(m), 1077(s), 1044(w), 1027(m), 1013(w), 1000(m), 962(w), 949(m), 901(m), 890(w), 869(s), 848(w,sh), 814(w), 786(m), 733(s), 660(w), 637(s), 612(m), 572(w), 551(w), 532(w), 515(m), 468(s), 447(w), 439(w), 427(w), 408(w). Anal. Calcd for

C27H27K2N3S18V: C, 29.48; H, 2.47; N, 3.82. Found: C, 29.53; H, 2.48; N, 3.62.

K2[V(C9H6S8)3]∙3.28MeCN (3∙3.28MeCN). Suspensions of K2(C9H6S8) (212.4 mg, 0.3908 mmol, 3.0 eq) in 8.0 mL THF and VCl4(THF)2 (44.6 mg, 0.132 mmol, 1.0 eq) in 8.0 mL THF were cooled to −78°C. (Note: An effective molecular weight of 543.56 g/mol was employed for 2 K2(C9H6S8) due to the as-synthesized salt being partially solvated. ) The VCl4(THF)2 suspension

S4 was added dropwise with stirring over 5 minutes to the suspension of the ligand salt, and stirred cold for a further 5 minutes. The reaction was then allowed to slowly warm to room temperature and stir at room temperature overnight. Solvent was removed from the reaction in vacuo and the brown residue was then washed by stirring with 10 mL dimethoxyethane for 30 minutes followed by filtration. The washed solids were then extracted into MeCN, filtered to remove insolubles, and crystallized by slow diffusion of Et2O vapor into the MeCN solution, affording dark brown needles (69.4 mg, 38.2%). Monitoring by UV-vis spectroscopy shows that the complex begins to decompose in (dry, airfree) acetonitrile solution after ~24 hours. The pure solid remains stable in the solid state at room temperature under nitrogen for at least two weeks. IR (cm–1, diamond ATR) 2998(w), 2981(m), 2963(w), 2951(w), 2905(m), 2878(w), 2868(w), 2854(w), 2286(m), 2249(w), 1543(m), 1489(m), 1448(m), 1424(w), 1407(w,sh), 1393(vs), 1361(w), 1295(w), 1269(s), 1229(m), 1186(m), 1156(w), 1121(w), 1093(m), 1085(m), 1026(m), 997(m), 979(w), 920(m), 896(w,sh), 882(vs), 862(s), 842(w,sh), 815(m), 765(vs), 719(w), 701(w), 683(w), 659(m), 641(w), 621(w), 608(w), 596(w), 538(w), 525(w), 497(s), 486(w,sh),

465(w), 443(m), 424(w), 402(w). Anal. Calcd for C33.56H27.84K2N3.28S24V: C, 29.30; H, 2.03; N, 3.34. Found: C, 29.40; H, 2.15; N, 3.22.

EPR Measurements. Solution samples for EPR measurements were prepared by dissolving 1–3 in 45 vol% MeCN-d3/toluene-d8 or 45 vol% DMF-d7/toluene-d8, loading into a 4mm OD quartz EPR tube (Wilmad 707-SQ-250M), freezing the sample in liquid nitrogen, and flame-sealing the tube under high vacuum. All measurements were taken on 0.32 mM solutions, except for the

ENDOR spectrum of 3 and the cw spectra of 3 in DMF-d7/toluene-d8 and 2 in MeCN-d3/toluene- d8, which were acquired on 1.0 mM solutions. Due to its instability in solution, samples of 3 were frozen immediately after preparation and stored in liquid nitrogen until measurement.

EPR data for 1–3 in MeCN-d3/toluene-d8, ENDOR data for 1–3 in DMF-d7/toluene-d8, and all cw data were obtained at X-band frequency (9.4–9.7 GHz) on a Bruker E680 X/W-band spectrometer equipped with a with a split ring resonator (ER4118X-MS5) and a 1 kW TWT amplifier (Applied Systems Engineering) at Northwestern University. Nutation data for 1–3 in

DMF-d7/toluene-d8 were acquired on a Bruker E580 X-band spectrometer equipped with a dielectric resonator and a 1 kW TWT amplifier (Applied Systems Engineering) at Northwestern

University. All other data (i.e. all pulsed EPR data for 1–3 in DMF-d7/toluene-d8 aside from

S5 ENDOR and nutation data) were acquired at the University of Illinois EPR Lab (Urbana, IL) on a Bruker E580 X-band spectrometer equipped with an ER 4104OR resonator and 1 kW TWT amplifier (Applied Systems Engineering). For all pulsed data, the resonator was overcoupled to minimize ringdown following application of the microwave pulses. Temperature was controlled with an Oxford Instruments CF935 helium cryostat and an Oxford Instruments ITC503 (Bruker E680 and Bruker E580 at the U. Illinois EPR Lab) or MercuryiTC (Bruker E580 at Northwestern) temperature controller.

Cw-EPR data were collected at 100 K for 2 in MeCN-d3/toluene-d8 and at 120 K for 1–3 in

DMF-d7/toluene-d8. Spectra were collected with a time constant of 5.12 ms, a conversion time of 10.24 ms, a modulation amplitude of 2.0 G, and a modulation frequency of 60 kHz, and 5 contained 4096 points. Spectra were fit using Easyspin using the Hamiltonian Ĥ = gμBHS – gNμNHI + IAS, where g is the electron g-tensor, μB is the Bohr magneton, H is the applied magnetic field, S is the electronic spin, gN is the nuclear g-tensor, μN is the nuclear magneton, I is the nuclear spin, and A is the vanadium hyperfine coupling tensor (see Figure S1 for data and fits, and Table S4 for fit parameters). All spectra were fit as rhombic systems, and g-strain was the only strain modeled in all cases.

ED-EPR data for 1 and 3 in MeCN-d3/toluene-d8 were collected at 30 K using a Hahn echo pulse sequence (π/2 – τ – π – τ – echo) with a 4-step phase cycle, where π/2 = 16 ns, π = 32 ns, and τ = 80–444 ns. Acquisition trigger times were set so as to capture the top half to one-third of the spin echo, and the acquired portion of the spin echo was integrated to obtain the data. The data were phased by maximization of the sum of the data points in the real component of the spectrum.

ENDOR data were acquired at 40 K in DMF-d7/toluene-d8 in stochastic mode using the

Mims ENDOR pulse sequence π/2MW – τ – π/2MW – t – πRF – t – π/2MW – τ – echo, where RF = radio frequency and MW = microwave frequency. Data were collected at a field corresponding to the highest-intensity central peak in the ED-EPR spectrum. In the experiments, π/2MW = 16 ns, t = 1000 ns, and πRF = 30000 ns. For each complex, two ENDOR spectra were acquired, one with τ = 444 ns, and one with τ = 800 ns, in order to compensate for the "Mims holes" which occur at intervals of 1/τ away from the nuclear Larmor frequency in the ENDOR spectra. The ENDOR data were fit with a model for the hyperfine interactions which included an isotropic (Fermi contact) and a dipolar component:

S6 −1 0 0 퐴tot = 퐴iso + 퐴dip [ 0 −1 0] 0 0 2 The dipolar coupling values used in the models were determined by first calculating the dipolar coupling for each proton using the equation: 𝑔 휇 𝑔 휇 퐴 = 푒 퐵 푛 푛 dip ℎ푟3 where g is the electronic g-factor (the average g-factor for the molecule was used here), B is the

Bohr magneton, gn is the proton g-factor, n is the nuclear magneton, h is the Planck constant, and r is the V–H distance (taken from the crystal structure of each complex). All values are expressed in CGS units, i.e. B and n are in erg/G, h is in erg s, and r is in cm, which yields a value for Adip in Hz. Once the dipolar couplings for each proton were calculated, the 18 protons of each molecule were divided into three groups of 6 – one group corresponding to the central protons of the propyl moiety, and the other two corresponding to the edge protons. The edge protons were separated into the two groups by ordering them by dipolar coupling strength and dividing them in half, leaving a group with weaker dipolar couplings and a group with stronger dipolar couplings. An average dipolar coupling was then calculated for each proton group. (See Tables S5–S7 for calculated dipolar couplings for each individual proton, and average couplings for each 6-proton group). The spectra were fit (using esfit function in Easyspin5) with a model incorporating three protons, each of which were assigned one of the group-average dipolar coupling constants. Thus, only the isotropic coupling and the linewidth were fit. The fits were performed simultaneously on both the τ = 444 ns and τ = 800 ns spectra to ensure accuracy of the obtained parameters. Orientation selection caused by performing the experiment on the central line in the EPR spectrum was accounted for in the fitting process; the effect of orientation selection was modeled with the saffron function of Easyspin using g and vanadium hyperfine values determined from the cw spectra, and assuming an excitation width of 62.5 MHz ((16 ns)−1). See Table S8 for fitted parameters, and Figure S2 for data and fits. Both spectra for 3 contained a broad background feature that we were unable to model; the spectra were therefore truncated for the fitting process such that only the sharp central feature was fit. Estimated errors are approximately 10% for the fitted parameters based on simulations with varying parameters.

S7 The proton grouping scheme employed in the fitting of the ENDOR data was designed to allow enough free parameters to capture the shapes of the ENDOR spectra without overparameterization. As the ligands are rigid, we expect that even in solution, the V–H distances for the ligand protons will be similar to those observed in the crystal structure, hence, why the values of the dipolar coupling for each group were fixed during the fitting process. However, the averaging of V–H distances within proton groups and the restrictions on the parameter values intrinsic to this grouping scheme almost certainly introduce inaccuracy in the model, a point which is demonstrated by the inability of the fitted spectra to capture every feature in the original data. Thus, as noted above, we estimate an error of approximately 10% for the parameters extracted from the fits.

T1 data for 1–3 in MeCN-d3/toluene-d8 were collected via a saturation recovery sequence with a 4 or 8-step phase cycle consisting of 20 24 ns pulses to saturate the transition (a picket fence sequence) followed by a delay T, then the detection sequence π/2 – τ – π – τ – echo in which π/2 = 16 ns, π = 32 ns, and τ = 380 ns. T was incremented from a starting value of 100 ns.

T1 data for 1–3 in DMF-d7/toluene-d8 were collected via an inversion recovery sequence (π – T – π/2 – τ – π – τ – echo) with an 8-step phase cycle in which π/2 = 16 ns, π = 32 ns, and T was incremented from 100 ns. The value of τ was selected to correspond to a maximum in the ESEEM (electron spin echo envelope modulation) and therefore varied from 356–420 ns depending on the experiment. In all cases, data were collected on the highest-intensity central resonance in the spectrum. Acquisition trigger times were set so as to capture the top half to one- third of the spin echo, and the acquired portion of the spin echo was integrated to obtain the data. All data were phased by maximization of the sum of squares of the data points in the real component of the spectrum and fit to the monoexponential function I(τ) = b – A exp(–τ/T1). See Table S9 for fit parameters and Figure S3 for data and fits.

The temperature dependence of T1 was fit using the curve fitting toolbox of MATLAB R2016a with the following function:

9 1 푇 휃퐷 log ( ) = log (퐴dir푇 + 퐴Ram ( ) 퐽8 ( )) 푇1 휃퐷 푇 in which T is temperature, Adir is the direct process coefficient, ARam is the Raman process 6 coefficient, and θD is the Debye temperature. J8 is the transport integral:

S8 휃퐷 ⁄푇 휃 푒푥 퐽 ( 퐷) = ∫ 푥8 푑푥 8 푇 (푒푥 − 1)2 0 which can be analytically expressed (in the form of MATLAB code) as

J8(x) = real(-(x.^8./(-1+exp(x)))+8.*(-(x.^8./8)+x.^7.*log(1-exp(x))+7.*x.^6.* polylog(2,exp(x))-42.*x.^5.*polylog(3,exp(x))+210.*x.^4.*polylog(4,exp(x))-840.* x.^3.*polylog(5,exp(x))+2520.*x.^2.*polylog(6,exp(x))-5040.*x.*polylog(7,exp(x))+ 5040.*polylog(8,exp(x)))-8.*(5040.*polylog(8,1))) 1 Fitting was performed with the above equation instead of the equation = 퐴dir푇 + 푇1 9 푇 휃퐷 퐴Ram ( ) 퐽8 ( ) since fitting with the latter results in the fit being overweighted towards the 휃퐷 푇 high-temperature data. Fits of the temperature dependence of T1 for data acquired in DMF- d7/toluene-d8 were performed using only data in the 10–120 K regime since the higher temperature data are influenced by additional relaxation processes, as has been previously observed for vanadyl species.7 Attempting to account for those processes in the fits results in overparameterization. The T1 data for samples in MeCN-d3/toluene-d8 were fit using data from all temperatures collected. See Table S10 for fit parameters.

T2 data in both solvent systems were collected on the highest-intensity central resonance in the spectrum via a Hahn echo sequence (π/2 – τ – π – τ – echo) with a 4-step phase cycle, in which π/2 = 16 ns, π = 32 ns, and τ was incremented from an initial value of 80 ns in MeCN- d3/toluene-d8 and 276 ns in DMF-d7/toluene-d8. Acquisition trigger times were set so as to capture the top half to one-third of the spin echo, and the acquired portion of the spin echo was integrated to obtain the data. The data were phased by maximization of the sum of the data points in the real component of the spectrum and fit to a function which modeled the decay as the product of a damped modulation and an exponential decay:8 휏 2휏 푞 퐼(휏) = 퐴 (1 − 퐵 cos(휔휏 + 푑) exp (− )) exp (− ( ) ) 푇osc 푇2 where A is the overall amplitude, B is the modulation amplitude, ω is the ESEEM (electron spin echo envelope modulation) frequency, Tosc is the ESEEM decay time, and q is the stretch factor.

See Tables S11 and S12 for fit parameters for DMF-d7/toluene-d8 and MeCN-d3/toluene-d8, respectively, and Figure S4 for data and fits.

S9 In addition to the ED-EPR, ENDOR, and relaxation data, we assessed the viability of our complexes as qubits via the acquisition of nutation data.9–11 In this experiment, a tipping pulse is employed to place the spins into a superposition of states, followed by a Hahn echo detection sequence which reads out the state of the spin qubit. Over the course of the experiment, the length of the tipping pulse is incremented, causing a qubit to cycle through all possible superposition states. The result, for a viable qubit, is a decaying oscillation in echo intensity when plotted versus the length of the tipping pulse, known as a Rabi oscillation. Other phenomena, including coupling to nuclear spins and cavity effects, can also result in oscillations in a nutation experiment.12 However, only true nutations exhibit a linear dependence of oscillation frequency on pulsed microwave field (which is related to microwave power). Nutation data were therefore collected at three different microwave powers for each complex on the highest-intensity central resonance in the spectrum via the application of a standard nutation sequence (tp – T – π/2 – τ – π – τ – echo). During the data collection we employed an 8- step phase cycle, in which T = 600 ns and tp is augmented in 4 ns increments from an initial value of 4 ns. For solutions in MeCN-d3/toluene-d8, π/2 = 16 ns, π = 32 ns, τ = 384 ns, and the data were acquired out to out to tp = 1024 ns. For solutions in DMF-d7/toluene-d8, π/2 = 16–28 ns (depending on pulse power), π = 32–56 ns (depending on pulse power), τ = 400 or 412 ns, and the data were acquired out to out to tp = 2048 ns. Acquisition trigger times were set so as to capture the top half to one-third of the spin echo, and the acquired portion of the spin echo was integrated to obtain the data. The data (see Figure S5) were phased by maximization of the amplitude of the real component of the spectrum. All data were then baseline corrected by subtracting the mean of the data and zero-filled out to 16 times the original length of the data before performing a Fourier transform. The experiments resulted in oscillations (Figure S5) which displayed a linear dependence on pulsed microwave field (Table S13 and Figures S6 and S7), confirming them as true nutations.

X-ray Structure Determination. All diffraction data were acquired in the X-ray Crystallography lab of the Integrated Molecular Structure Education and Research Center (IMSERC) at Northwestern University. Single crystals suitable for X-ray analysis were coated with Paratone N oil and mounted on a MiTeGen MicroLoop™. Data were acquired on a Bruker KAPPA diffractometer equipped with a MoKα IμS microfocus X-ray source with Quazar Optics

S10 and a Bruker APEX II detector. All datasets were collected at 100 K and temperature was controlled via an Oxford Cryosystems Cryostream. Raw data were integrated and corrected for Lorentz and polarization effects with SAINT v8.27B.13 Absorption corrections were applied using SADABS.14 Space group assignments were determined by examination of systematic absences, E-statistics, and successive refinement of the structures. Structures were solved using direct methods in SHELXT and further refined with SHELXL-201315 operated with the OLEX2 interface.16 Hydrogen atoms were placed in ideal positions and refined using a riding model for all structures. Compound 1 crystallized as a racemic twin. The structure of 2∙3MeCN contained one MeCN for which the CN group was disordered over two sites. As such, hydrogen atoms were not assigned on the methyl group of that molecule. Full crystallographic information for 1– 3 is listed in Tables S1–S3, respectively.

Other Physical Measurements. Elemental analyses for all complexes were performed by Midwest Microlabs LLC (Indianapolis, IN). Infrared spectra were recorded under inert atmosphere on a Bruker Alpha FTIR spectrometer equipped with an attenuated total reflectance accessory.

S11 Table S1  Crystallographic information for the structural refinement of K2[V(C5H6S4)3]∙2C6H6 (1∙2C6H6)

Empirical Formula C27H30K2S12V Formula weight 868.67 g mol–1 Temperature 100 K Wavelength 0.71073 Å Crystal System Orthorhombic Space Group Pca21 Unit Cell Dimensions a = 20.1186(7) Å b = 10.7301(4) Å c = 16.3342(6) Å Volume 3526.1(2) Å3 Z 4 Density (calculated) 1.636 g cm–3 Absorption coefficient 1.249 mm–1 F000 1780.0 Crystal color Dark blue Crystal size 0.536  0.133  0.06 mm3 θ range 2.025 to 36.396˚ Index ranges –26 ≤ h ≤ 33 –17 ≤ k ≤ 17 –27 ≤ l ≤ 27 Reflections collected 104489 Independent reflections 17058 [Rint = 0.0521] Completeness to θ = 36.396˚ 99.26% Absorption correction Multi-scan Maximum and minimum transmission 0.7471 and 0.6526 Refinement method Full-matrix least-squares on F2 Data / restraints / parameters 17058 / 1 / 380 Goodness-of-fit on F2a 1.020 b Final R indices [I > 2σ (I)] R1 = 2.78%, wR2 = 5.52% R indices [all data] R1 = 3.49%, wR2 = 5.79% Largest diff. peak and hole 0.62 and –0.67 e Å–3 Flack parameter 0.475(17)

a 2 2 2 1/2 GooF = [[w(Fo –Fc ) ] / (n–p)] where n is the number of reflections and p is the total b 2 2 2 2 2 1/2 number of parameters refined. R1 = ||Fo|–|Fc|| / |Fo|; wR2 = [[w(Fo –Fc ) ] / [w(Fo ) ] ]

S12 Table S2  Crystallographic information for the structural refinement of K2[V(C7H6S6)3]∙3CH3CN (2∙3CH3CN).

Empirical Formula C27H27K2N3S18V Formula weight 1099.85 g mol–1 Temperature 100 K Wavelength 1.54178 Å Crystal System Monoclinic Space Group C2/c Unit Cell Dimensions a = 46.5937(16) Å b = 6.9639(2) Å, β = 125.054(2)° c = 33.3368(11) Å Volume 8854.8(5) Å3 Z 8 Density (calculated) 1.650 g cm–3 Absorption coefficient 11.72 mm–1 F000 4472.0 Crystal color Olive Crystal size 0.267  0.082  0.055 mm3 θ range 2.690 to 58.971˚ Index ranges –51 ≤ h ≤ 51 –7 ≤ k ≤ 5 –36 ≤ l ≤ 37 Reflections collected 23042 Independent reflections 6310 [Rint = 0.0456] Completeness to θ = 58.971˚ 99.03% Absorption correction Multi-scan Maximum and minimum transmission 0.7516 and 0.4988 Refinement method Full-matrix least-squares on F2 Data / restraints / parameters 6310 / 0 / 481 Goodness-of-fit on F2a 1.027 b Final R indices [I > 2σ (I)] R1 = 3.66%, wR2 = 9.25% R indices [all data] R1 = 4.92%, wR2 = 10.03% Largest diff. peak and hole 0.69 and –0.34 e Å–3

S13 Table S3  Crystallographic information for the structural refinement of K2[V(C9H6S8)3]∙4CH3CN (3∙4CH3CN).

Empirical Formula C27H27K2N3S18V Formula weight 1405.36 g mol–1 Temperature 100 K Wavelength 0.71073 Å Crystal System Monoclinic Space Group P21/c Unit Cell Dimensions a = 17.6480(5) Å b = 26.1218(7) Å, β = 108.8860(10)° c = 12.5794(3) Å Volume 5486.9(3) Å3 Z 4 Density (calculated) 1.701 g cm–3 Absorption coefficient 1.281 mm–1 F000 2852.0 Crystal color Brown Crystal size 0.321  0.135  0.034 mm3 θ range 1.447 to 29.627˚ Index ranges –24 ≤ h ≤ 24 –36 ≤ k ≤ 36 –17 ≤ l ≤ 17 Reflections collected 113124 Independent reflections 15438 [Rint = 0.0379] Completeness to θ = 29.627˚ 99.77% Absorption correction Multi-scan Maximum and minimum transmission 0.8559 and 0.7686 Refinement method Full-matrix least-squares on F2 Data / restraints / parameters 15438 / 0 / 599 Goodness-of-fit on F2a 1.085 b Final R indices [I > 2σ (I)] R1 = 4.07%, wR2 = 10.03% R indices [all data] R1 = 5.23%, wR2 = 10.67% Largest diff. peak and hole 1.80 and –0.70 e Å–3

S14 Table S4 | Cw-EPR parameters for 1–3. Data in MeCN-d3/toluene-d8 were collected at 100 K; data in DMF-d7/toluene-d8 were collected at 120 K. No assignment of the sign of A was attempted. Cw-EPR data could not be acquired for 1 and 3 in MeCN-d3/toluene-d8 due to the relatively high background signal from the resonator and low signal-to-noise of the complexes. Echo-detected spectra were acquired for these two complexes, and plots of those spectra with simulations based on the parameters obtained from the DMF-d7/toluene-d8 data are depicted in Figure S1, alongside all cw spectra and simulations.

Parameters for 1–3 in DMF-d7/toluene-d8

Compound g1 g2 g3 g1 g2 g3 A1 A2 A3 strain strain strain (MHz) (MHz) (MHz) 1 1.972 1.988 1.995 0.0051 0.0048 0.0014 321 43 5 2 1.962 1.983 1.992 0.0037 0.0054 0.0025 337 73 6 3 1.960 1.986 1.993 0.0041 0.0047 0.0022 343 57 7

Parameters for 2 in MeCN-d3/toluene-d8

Compound g1 g2 g3 g1 g2 g3 A1 A2 A3 strain strain strain (MHz) (MHz) (MHz) 2 1.960 1.984 1.993 0.011 0.0080 0.0046 341 57 0.08

S15 Table S5  Table showing the grouping scheme employed to calculate the dipolar couplings used in ENDOR data fitting for complex 1. Distances are taken from the crystal structure of the compound, and values for Adip are calculated as described on pages S7–S8. A figure depicting the location of the protons in each group is shown below the table, with the protons of the center, edge 1, and edge 2 groups colored orange, lavender, and blue, respectively.

Proton index V–H distance Adip (MHz) Group Group average number from CIF ( ) Adip (MHz) H00D 7.536 0.1826 H00H 7.517 0.1840 H01F 7.493 0.1858 center (orange) 0.2035 H01E 7.080 0.2202 H00G 7.048 0.2232 H00C 7.024 0.2255 H00A 6.921 0.2357 H00F 6.864 0.2416 H01D 6.864 0.2416 edge 1 (lavender) 0.2413 H01A 6.858 0.2423 H00I 6.856 0.2425 H00L 6.842 0.2440 H00B 5.853 0.3897 H00E 5.782 0.4043 H00K 5.747 0.4117 edge 2 (blue) 0.4097 H00J 5.744 0.4123 H01C 5.711 0.4195 H01B 5.706 0.4206

S16 Table S6  Table showing the grouping scheme employed to calculate the dipolar couplings used in ENDOR data fitting for complex 2. Distances are taken from the crystal structure of the compound, and values for Adip are calculated as described on pages S7–S8. A figure depicting the location of the protons in each group is shown below the table, with the protons of the center, edge 1, and edge 2 groups colored orange, lavender, and blue, respectively.

Proton index V–H distance Adip (MHz) Group Group average number from CIF ( ) Adip (MHz) H01D 10.896 0.06016 H00D 10.889 0.06028 H01J 10.625 0.06489 center (orange) 0.06559 H01I 10.428 0.06863 H00C 10.386 0.06947 H01C 10.355 0.07009 H01H 10.140 0.07465 H00A 10.086 0.07585 H01B 10.080 0.07599 edge 1 (lavender) 0.07684 H01K 10.040 0.07690 H01M 10.006 0.07769 H01F 9.911 0.07994 H01G 9.163 0.1012 H01L 9.099 0.1033 H00B 9.085 0.1038 edge 2 (blue) 0.1070 H01A 9.064 0.1045 H01N 8.827 0.1132 H01E 8.747 0.1163

S17 Table S7  Table showing the grouping scheme employed to calculate the dipolar couplings used in ENDOR data fitting for complex 3. Distances are taken from the crystal structure of the compound, and values for Adip are calculated as described on pages S7–S8. A figure depicting the location of the protons in each group is shown below the table, with the protons of the center, edge 1, and edge 2 groups colored orange, lavender, and blue, respectively.

Proton index V–H distance Adip (MHz) Group Group average number from ( ) Adip (MHz) CIF H00D 13.814 0.02954 H01K 13.661 0.03054 H01C 13.643 0.03066 center (orange) 0.03227 H01L 13.192 0.03392 H00C 13.123 0.03446 H01D 13.120 0.03448 H00B 13.084 0.03476 H01A 12.959 0.03578 H01N 12.946 0.03589 edge 1 (lavender) 0.03603 H01E 12.920 0.03611 H01I 12.838 0.03680 H01H 12.832 0.03685 H00A 12.041 0.04460 H01B 11.939 0.04576 H01F 11.817 0.04719 edge 2 (blue) 0.04709 H01G 11.754 0.04795 H01M 11.746 0.04805 H01J 11.667 0.04903

S18 Table S8  Best-fit simulation parameters from ENDOR spectra in DMF-d7/toluene-d8. "Iso" indicates the isotropic (Fermi contact) coupling, "dip" indicates the dipolar coupling, and center/edge indicate the position of the protons within the propyl group. The dipolar couplings were fixed at the values shown below during fitting and are reproduced from Tables S5–S7 for clarity. All A values and the linewidth are expressed in MHz. Note that the absolute signs of the isotropic and dipolar couplings cannot be obtained by fitting Mims ENDOR data – only their relative sign. Thus in the simulations, all dipolar couplings were defined to be positive. Errors in the fitted parameters are estimated at 10% based on simulations with varying parameters.

Parameter 1 2 3 center 퐴iso 0.40 −0.15 −0.070 edge1 퐴iso 0.43 0.16 0.071 edge2 퐴iso −0.16 −0.030 −0.025 center 퐴dip (fixed) 0.2035 0.06559 0.03227 edge1 퐴dip (fixed) 0.2413 0.07684 0.03603 edge2 퐴dip (fixed) 0.4097 0.1070 0.04710 Linewidth 0.077 0.025 0.013 (FWHM) Root-mean- square 7.1% 4.0% 4.6% deviation

S19 Table S9  Fitted T1 values for 1–3 in milliseconds. The standard error for each fit is reported in parentheses.

Values for 1–3 in DMF-d7/toluene-d8: Temperature 1 2 3 10 8.0(6) 5.9(4) 5.3(3) 20 1.32(5) 0.76(2) 0.97(4) 30 0.288(5) 0.210(4) 0.213(4) 40 0.1080(12) 0.0766(10) 0.0856(9) 50 0.0590(6) 0.0425(5) 0.0444(5) 60 0.0365(3) 0.0270(3) 0.0249(2) 70 0.0239(2) 0.0165(2) 0.01498(14) 80 0.0134(2) 0.01061(12) 0.00757(8) 90 0.00981(9) 0.00709(9) 0.00529(5) 100 0.00747(5) 0.00488(6) 0.00402(5) 110 0.00578(4) 0.00349(5) 0.00307(5) 120 0.00436(3) 0.00253(4) 0.00232(3) 130 0.00331(4) 0.00194(3) 0.00177(2) 140 0.00260(2) 0.00156(2) 0.00143(2)

Values for 1–3 in MeCN-d3/toluene-d8: Temperature 1 2 3 10 6.8(6) 2.8(2) 2.5(2) 20 0.54(2) 0.42(2) 0.37(2) 30 0.33(2) 0.128(5) 0.116(3) 40 0.138(8) 0.0499(14) 0.0466(15) 50 0.044(2) 0.0245(6) 0.0254(5) 60 0.026(1) 0.0151(4) 0.0153(3) 70 0.018(1) 0.0083(2) 0.0098(3) 80 0.011(1) 0.00649(15) 0.0065(2) 90 – 0.00513(11) – 100 – 0.00347(6) – 110 – 0.00287(5) –

S20 Table S10  Fit parameters for fits of the T1 temperature dependence of 1–3. The standard error for each fit is reported in parentheses.

DMF-d7/toluene-d8 (fit through 120 K)

−1 −1 Compound Adir (K s ) ARam (MHz) θD (K) 1 13(3) 2.3(5) 153(12) 2 19(6) 3.2(11) 150(18) 3 23(6) 6.4(22) 186(20)

MeCN-d3/toluene-d8 (fit through maximum measured temperature)

−1 −1 Compound Adir (K s ) ARam (MHz) θD (K) 1 14(9) 1.0(9) 110(36) 2 36(7) 3.6(8) 136(11) 3 40(7) 2.2(6) 116(12)

S21 Table S11  Fitted parameters for T2 measurements of 1–3 dissolved in DMF-d7/toluene-d8. The standard error for each fit is reported in parentheses. Values of the ESEEM oscillation frequency ω are consistent with the deuterium angular Larmor frequency (ω = 2π*(2.21 MHz) = 13.9 17 12 MHz). The fits of Tosc converged to unrealistically large values (~10 μs) above 100 K, however this did not affect fitting of the other parameters. 1 2 3 Temperature T2 (μs) q T2 (μs) q T2 (μs) q 10 7.21(5) 0.909(5) 7.48(3) 1.082(5) 6.89(6) 0.854(6) 20 7.46(3) 1.023(5) 7.17(3) 1.144(5) 7.00(4) 0.944(5) 30 7.21(2) 1.261(4) 6.62(2) 1.251(5) 6.61(2) 1.151(5) 40 7.31(2) 1.385(5) 6.768(15) 1.356(5) 6.81(2) 1.291(5) 50 6.46(2) 1.347(5) 5.927(15) 1.297(5) 6.17(2) 1.252(5) 60 5.419(14) 1.330(5) 4.973(14) 1.262(5) 5.024(15) 1.230(5) 70 4.259(12) 1.333(6) 3.738(12) 1.261(5) 3.866(12) 1.239(5) 80 2.707(10) 1.345(7) 2.809(10) 1.269(6) 2.409(10) 1.235(6) 90 2.32(10) 1.313(7) 2.159(10) 1.236(6) 1.964(10) 1.199(7) 100 1.963(10) 1.276(8) 1.720(10) 1.168(7) 1.626(10) 1.148(7) 110 1.693(11) 1.217(8) 1.346(12) 1.088(8) 1.344(11) 1.102(8) 120 1.404(12) 1.148(9) 1.027(14) 1.034(10) 1.051(13) 1.044(9) 130 1.131(14) 1.105(11) 0.78(2) 1.005(14) 0.799(15) 0.991(11) 140 0.93(2) 1.069(14) 0.63(2) 1.00(2) 0.65(2) 0.99(2)

1 2 3 Temperature Tosc (μs) ω (MHz) Tosc (μs) ω (MHz) Tosc (μs) ω (MHz) 10 3.31(8) 14.070(7) 3.15(7) 14.124(6) 3.20(9) 14.113(8) 20 3.13(6) 14.076(6) 3.10(6) 14.119(6) 3.20(8) 14.108(7) 30 3.08(4) 14.062(4) 3.17(5) 14.111(5) 3.25(6) 14.092(5) 40 3.10(5) 14.055(5) 3.22(5) 14.102(4) 3.27(5) 14.081(5) 50 3.32(6) 14.051(5) 3.47(6) 14.102(5) 3.50(6) 14.079(5) 60 3.65(7) 14.053(5) 3.89(8) 14.104(5) 3.95(9) 14.078(5) 70 4.25(12) 14.054(6) 4.8(2) 14.104(6) 4.8(2) 14.076(6) 80 6.7(4) 14.050(8) 6.8(4) 14.102(8) 8.9(8) 14.084(9) 90 8.9(9) 14.060(10) 11.0(13) 14.099(10) 14(2) 14.086(11) 100 14(2) 14.050(12) 21(5) 14.106(11) 32(13) 14.084(12) 110 — 14.048(13) — 14.11(2) — 14.07(2) 120 — 14.04(2) — 14.08(2) — 14.07(2) 130 — 14.03(2) — 14.02(3) — 14.06(3) 140 — 14.01(3) — 13.94(6) — 13.92(5)

S22 Table S12  Fitted parameters for T2 measurements of 1–3 dissolved in MeCN-d3/toluene-d8. The standard error for each fit is reported in parentheses. Values of the ESEEM oscillation frequency ω are consistent with the deuterium angular Larmor frequency (ω = 2π*(2.21 MHz) = 13.9 MHz).17 1 2 3 Temperature T2 (μs) q T2 (μs) q T2 (μs) q 10 3.19(5) 0.841(11) 1.56(6) 0.634(11) 1.42(5) 0.607(10) 20 4.20(7) 1.03(2) 1.75(6) 0.631(10) 1.48(4) 0.602(8) 30 3.44(4) 0.939(12) 1.90(5) 0.667(10) 1.65(4) 0.639(8) 40 4.08(6) 0.982(14) 2.15(8) 0.654(12) 1.74(6) 0.633(10) 50 4.00(7) 0.95(2) 1.83(8) 0.612(12) 1.39(5) 0.595(10) 60 3.76(10) 0.83(2) 1.11(6) 0.527(11) 0.84(4) 0.512(9) 70 3.52(15) 0.67(2) 0.69(3) 0.505(8) 0.50(3) 0.447(9) 80 2.8(2) 0.55(2) 0.57(3) 0.493(8) 0.26(2) 0.404(9) 90 — — 0.39(2) 0.482(7) — — 100 — — 0.284(13) 0.475(6) — — 110 — — 0.229(12) 0.482(7) — —

1 2 3 Temperature Tosc (μs) ω (MHz) Tosc (μs) ω (MHz) Tosc (μs) ω (MHz) 10 4.2(5) 13.93(3) 3.9(6) 14.05(4) 3.7(4) 14.05(3) 20 8(3) 13.76(4) 4.5(7) 14.02(3) 3.4(3) 14.04(3) 30 4.5(5) 13.88(2) 4.6(7) 14.01(3) 3.7(4) 14.03(3) 40 6.1(10) 13.91(3) 5.7(11) 14.02(3) 4.3(6) 14.07(3) 50 6.0(13) 13.94(3) 6.3(14) 14.00(3) 5.0(8) 14.04(3) 60 8(3) 13.97(4) 6.4(14) 13.98(3) 4.7(7) 14.04(3) 70 7(2) 13.88(3) 6.5(13) 13.95(3) 5.3(9) 13.98(3) 80 7.3(14) 13.85(3) 6.2(13) 13.97(3) 7(2) 13.94(4) 90 — — 6.5(14) 13.95(4) — — 100 — — 5.3(10) 13.93(4) — — 110 — — 7(2) 13.86(4) — —

S23 Table S13  Variable-power nutation frequencies of 1–3. Frequencies tabulated below are those with the maximum magnitude in the Fourier transform of the raw nutation data (see Figure S6). Here, the pulsed magnetic field B1 is expressed relative to its value at the lowest pulsed −0.1퐴 √10 microwave power attenuation used for a given complex (relative 퐵1 = ⁄10−0.1푍 where A is the microwave power attenuation and Z is the lowest power attenuation value of the set of three for a given complex).

Data acquired in DMF-d7/toluene-d8 Nutation Frequencies by Complex as a Function of Power (MHz) Relative B1: 2.00 1.41 1.00 Power Power Power Frequency attenuation Frequency attenuation Frequency attenuation (MHz) (dB) (MHz) (dB) (MHz) (dB) 1 15.1 7.0 10.7 10.0 8.3 13.0 2 12.7 6.7 10.7 9.7 8.3 12.7 3 12.2 7.7 9.8 10.7 7.3 13.7

Data acquired in MeCN-d3/toluene-d8 Nutation Frequencies by Complex as a Function of Power (MHz) Relative B1: 2.00 1.41 1.00 Power Power Power Frequency attenuation Frequency attenuation Frequency attenuation (MHz) (dB) (MHz) (dB) (MHz) (dB) 1 14.2 12.0 15.1 15.0 15.6 18.0 2 10.3 12.0 10.7 15.0 10.7 18.0 3 7.3 12.0 7.8 15.0 7.3 18.0

S24

Figure S1  Cw-EPR spectra for 1–3 in DMF-d7/toluene-d8 (left) and for 2 in MeCN-d3/toluene- d8 (center right). Echo-detected EPR spectra for 1 and 3 in MeCN-d3/toluene-d8 (top and bottom right). Fits to the cw spectra and simulations of the echo-detected spectra based on cw parameters from the DMF-d7/toluene-d8 samples (for 1 and 3) are shown in black and offset from the data, shown in color. Fit parameters are listed in Table S4.

S25

Figure S2  Mims ENDOR spectra of 1–3 in DMF-d7/toluene-d8. Fits are shown as black lines and the data are shown in color. Fit parameters are listed in Table S8. Left: data acquired with τ = 444 ns. Right: data acquired with τ = 800 ns.

S26

Figure S3  Inversion recovery curves for 1–3 in DMF-d7/toluene-d8 (left) and saturation recovery curves for 1–3 in MeCN-d3/toluene-d8 (right). Fits to the spectra are shown as black lines. Fit parameters are listed in Table S9.

S27

Figure S4  Selected Hahn echo decay curves for 1–3 in DMF-d7/toluene-d8 (left) and in MeCN- d3/toluene-d8 (right). Fits to the spectra are shown as black lines. Fit parameters are listed in Tables S11 and S12.

S28

Figure S5  Nutation data for 1–3 in DMF-d7/toluene-d8 (left) and in MeCN-d3/toluene-d8 (right). Fourier transforms of these data are depicted in Figure S6.

S29

Figure S6  Fourier transforms of raw nutation data for 1–3 in DMF-d7/toluene-d8 (left) and in MeCN-d3/toluene-d8 (right). The frequencies of maximum magnitude (excluding those that correspond to a nuclear Larmor frequency) are listed in Table S13. The additional frequency components in the nutation data are likely the result of the Hartmann-Hahn effect.18

S30

Figure S7  Nutation frequencies of 1–3 in DMF-d7/toluene-d8 (left) and in MeCN-d3/toluene-d8 (right) as a function of pulsed field strength (B1). See Table S13 for discussion of relative B1.

S31 References

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