Isotopomeric Elucidation of the Mechanism of Temperature Sensitivity in ⁵⁹Co NMR Molecular Thermometers

Abstract

Understanding the mechanisms governing temperature-dependent magnetic resonance properties is essential for enabling thermometry via magnetic resonance imaging. Herein we harness a new molecular design strategy for thermometry—that of effective mass engineering via deuteration in the first coordination shell—to reveal the mechanistic origin of ⁵⁹Co chemical shift thermometry. Exposure of [Co(en)₃]³⁺ (1; en = ethylenediamine) and [Co(diNOsar)]³⁺ (2; diNOsar = dinitrosarcophagine) tomixtures of H₂O and D₂O produces distributions of [Co(en)₃]³⁺-d_n (n = 0–12) and [Co(diNOsar)]³⁺-d_n (n = 0–6) isotopomers allresolvable by ⁵⁹Co NMR. Variable-temperature ⁵⁹Co NMRanalyses reveal a temperature dependence of the ⁵⁹Co chemicalshift, Δδ/ΔT, on deuteration of the N-donor atoms. For 1, deuteration amplifies Δδ/ΔT by 0.07 ppm/°C. Increasing degrees of deuteration yield an opposing influence on 2, diminishing Δδ/ΔT by −0.07 ppm/°C. Solution-phase Raman spectroscopy in the low-frequency 200–600 cm⁻¹ regime reveals a red shift of Raman-active Co–N₆ vibrational modes by deuteration. Analysis of the normal vibrational modes shows that Raman modes produce the largest variation in ⁵⁹Co δ. Finally, partition function analysis of the Raman-active modes shows that increased populations of Raman modes predict greater Δδ/ΔT, representing new experimental insight into the thermometry mechanism.

Graphical Abstract

INTRODUCTION

Environmentally sensitive nuclear spins offer a route to novel magnetic resonance imaging agents or quantum-sensing molecular platforms.^1,2 One such environmental stimulus of interest is temperature because noninvasive thermometry could enable guided thermal therapies and imaging.^3–6 Cobalt-59 (⁵⁹Co) nuclear spins are highly promising for this application because of the strong temperature dependence of the ⁵⁹Co chemical shift, δ.^7–11 The current record for the sensitivity of the chemical shift to temperature (Δδ/ΔT) from a ⁵⁹Co nucleus is 3.15 ppm/°C in Co(acac)₃.¹² Higher sensitivities are ultimately necessary for utility, yet the precise molecular factors (specifically, ligand identity) that control Δδ/ΔT are unknown.

Theoretical studies decades ago^13–15 proposed strict bond-distance expansion as the mechanistic origin of Δδ/ΔT. In this picture, temperature-dependent changes in the physical structure modulate the ligand-field splitting (Δ_o) and thus determine ⁵⁹Co δ by changing the energies of the ¹A_1g and ¹T_1g states of a Co³⁺ complex, a change that affects the ⁵⁹Co paramagnetic shift as described by Ramsey’s equation.⁷ The effect is analogous to the origin of temperature-independent paramagnetism in Co³⁺ complexes.¹⁶ More “flexible” ligands could be envisioned to produce species with greater temperature-dependent inner-coordination spheres, thereby producing higher Δδ/ΔT. However, recent studies by us^17–19 and others^20,21 suggest that bond-distance expansion alone is not the dominant feature. In a prior work, we posited a model wherein structural rigidity imparted by the ligand shell engenders long-lived vibrations caused by collisions of a given ⁵⁹Co NMR thermometer with the surrounding solvent (Figure 1) and thus temperature-driven structures and Δδ/ΔT.¹⁷ If this model is correct, then we posited that changes to the donor-atom mass would affect Δδ/ΔT because changes in the mass would be expected to alter the vibrational lifetimes, amplitudes, and equilibrium Co–L distances and ultimately the electronic structure.

Figure 1.

Overview of studies of controlling ⁵⁹Co thermometric properties and donor atom deuteration. This work combines these two approaches to affect ⁵⁹Co nuclear spin (I = ⁷/₂) chemical shift thermometry in structures 1 and 2 (shown) and reveal mechanistic insight. Most H atoms and counterions are omitted for clarity.

A controlled test of varying the donor-atom mass on Δδ/ΔT via typical coordination chemistry strategies is, however, intrinsically challenging. For example, a simple swap of the N-donor atoms for heavier O- or P-donor atoms will simultaneously affect the ligand mass and ligand-field strength. Separately, isotopically enriched donor-atom ligands are frequently exorbitant and limited in availability. We hypothesized that a facile route to controlled variable-mass studies of the mechanistic origins of Δδ/ΔT was to use H/D exchange on protonated N-donor atoms (Scheme 1). We envisioned that the resulting N-donor atoms would retain nearly constant ligand fields while mimicking heavier-atom behavior.

Scheme 1. Depiction of the Deuteration Process for 1 and 2 to Prepare 1-d_n (n = 0–12) and 2-d_n (n = 0–6)^a.

^aEach complex has an overall 3+ charge compensated by chloride anions (omitted for clarity).

Herein, we show that H/D exchange on ligand N-donor atoms offers a new strategy to adjust Δδ/ΔT. We do so via studies of deuterated isotopomers of molecules [Co(en)₃]³⁺ (1; en = ethylenediamine) and [Co(diNOsar)]³⁺ (2; diNOsar = dinitrosarcophagine). These species contain −NH₂ (primary) and −NH− (secondary) amine donor atoms that can be deuterated when treated with D₂O.^22–24 We show that this deuteration produces a spectroscopically resolvable distribution of H/D isotopomers in solution by ⁵⁹Co NMR. Comparative analyses of the temperature dependence of the ⁵⁹Co chemical shifts of these isotopomers demonstrate that the ligand mass plays a modest role in governing temperature-dependent ⁵⁹Co NMR signals. Investigation of vibrational modes via Raman spectroscopy suggests a new model for thermometry based not on the vibration lifetime but on the number and energy of low-frequency Raman-active vibrations.

EXPERIMENTAL SECTION

General Considerations.

Compounds tris(ethylenediamine)-cobalt(III) chloride ([Co(en)₃]Cl₃, 1) and (1,8-dinitro-3,6,10,13,16,19-hexaazabicyclo[6.6.6]iscosane)cobalt(III) chloride ([Co(diNOsar)]Cl₃ 2) were synthesized according to previous literature preparations.^25,26 Properties and characterization of these complexes were as described previously by us.¹⁷ Samples that contained D₂O were allowed to complete H/D equilibration over the course of 7 days before any spectroscopic investigation. Periodic analysis of the ⁵⁹Co NMR signal during those days established when the equilibration was finalized, generally within the 7-day window. Those samples containing portions of D₂O were prepared in plastic scintillation vials after thorough drying of 1 and 2 via the high-vacuum removal of residual water.

UV–Vis Spectrophotometry.

UV–vis spectra were collected on an Agilent 8435 UV–vis spectrophotometer as 5 mM aqueous solutions at room temperature. Fully protiated and fully deuterated complexes were measured in their respective H₂O and 99.9% D₂O solutions. UV–vis spectrophotometric data were fit (Gaussian) to determine the peak values. Quantitation of the ligand fields Δ_o was permitted using a d⁶ Tanabe–Sugano diagram in correspondence to the d–d transitions of the central Co³⁺ octahedral ions in 1 and 2.

Variable-Temperature ⁵⁹Co NMR.

⁵⁹Co NMR spectra were collected on an Agilent Unity INOVA 500 MHz (¹H) spectrometer with a broadband probe using 15 mM samples in varying compositions (0%, 25%, 50%, 75%, and 99.9%) of D₂O and H₂O solution mixtures. The spectrometer magnet was locked to a sample of D₂O and tuned to the ⁵⁹ Co standard of 1 M K₃[Co(CN)₆] before collection of the highly chemical-shifted samples 1 and 2, absent of locking, shimming, and spinning. It should be noted that any error introduced to the spectra by the unlocked magnet i on the order of 0.1 Hz/h. Such deviations are negligible considering the 1–6 kHz (10–50 ppm) scale of the collected peaks. Variable-temperature measurements were made on each sample over 10–60 °C in 5 °C intervals. The temperature was controlled using a FTS Systems TC-84 Kinetics AirJet temperature controller. The probe temperature was monitored via a thermocouple output. Temperature equilibration of the sample was allowed to occur over 15 min before tuning and subsequent spectral collection. Deconvolution of all peaks in the ⁵⁹Co NMR spectra (Figure 3a,b) was achieved by fitting spectra with Lorentzian peaks. Evaluation of Δδ/ΔT for each isotopomer (Figure 4) was then based on the Lorentzian peak positions as a function of the temperature. Evaluating the complete set of isotopomers for 2 (from 2-d₀ to 2-d₆) was achievable using a single sample with 50% D₂O in H₂O. However, for 1, three separate samples in varied amounts of D₂O in H₂O had to be used (i.e., 25%, 50%, and 75% D₂O) to capture all of the isotopomers. Minute inconsistencies in the magnet (e.g., field and temperature inhomogeneities, dephasing) required alignment of the peaks between the sample spectra. Alignments to the peak positions were made with respect to the 50% D₂O in H₂O spectra. Similarly, Δδ/ΔT could be accurately compared between the three samples by simply evaluating the change in Δδ/ΔT determined at 0.006 ppm/°C (Figure S8). While the increase in Δδ/ΔT with increasing deuteration is minute between isotopomers that differ by one deuteron, the difference between fully protiated and deuterated complexes is significant relative to the error. Furthermore, the changes in Δδ/ΔT between all of the isotopomers for 1 was reproducible over three separate sample measurements.

Figure 3.

Stacked variable-temperature ⁵⁹Co NMR spectra of isotopomer ensembles of 1 (top) and 2 (bottom) from 10 to 60 °C. Measurements were made on equilibrated samples in 50% D₂O/H₂O.

Figure 4.

Peak positions of all isotopomers as a function of the temperature for 1 (circles, 10–60 °C) and 2 (diamonds, 35–60 °C). The solid lines are linear regressions for each isotopomer, and extracted values of Δδ/ΔT can be found in the main text and Tables S2 and S3.

Raman Spectroscopy.

Raman spectra of compounds 1 and 2 were collected for their fully deuterated and fully protiated forms in H₂O (deionized) and D₂O (99.9%), respectively. Preparation of the solution-phase samples included complete equilibration of the isotopomer distribution over 7 days prior to measurement. All samples were prepared in 4 mL volume vials to 30 mM concentrations and measured using a Horiba Scientific ONDAX IHR 550 spectrometer equipped with a 785 nm near-IR laser. The collected spectral range was made over 200–600 cm⁻¹ and background-subtracted from each sample’s respective H₂O or D₂O blank. Acquisitions were made for 600 s at room temperature. The collected spectra were baselined and fit to identify peak values. The peaks were modeled to pseudo-Voigt functions to yield peak maxima (frequencies, ν) and full width half-maxima (line widths, Γ). Values from the fits are tabulated in Tables S8 and S9.

Frequency and ⁵⁹Co NMR Calculations.

Frequency calculations of vibrational modes were acquired from optimized structures of complexes 1 and 2 (Tables S10 and S11). Optimization and frequency calculations were both made with the Gaussian 16 electronic software structure package²⁷ using the ωB97X-D^28,29 density functional and 6–311+g(2d,p) basis set.³⁰ Harmonic approximations via this computational method yielded Raman spectra agreeable with the experimental spectra for all computed structures (Figure 5a,b). Such an agreement allowed the assignment and depiction of experimental vibrational modes, and as a result, a scaling factor was not applied. ⁵⁹Co NMR property calculations of the vibrationally displaced structures of 1 and 2 were analyzed along the fullest extent of the distortional pathway (Q = +1 to −1) of experimentally observed vibrational modes (Table S8). These predictions were performed with the ORCA 4.11 electronic software package at the GIAO-B3LYP level³¹ with def2-TZVPP and def2/JK basis sets.³² In all predictions, the ⁵⁹Co nucleus was individually assigned a def2-QZVPP basis set.³² In both complexes 1 and 2, analysis of the isotropic shielding was used to determine the range of Δδ (⁵⁹Co) and is dominated by the paramagnetic term. Evaluation of Δδ was done only for the lowest-energy vibrational modes of the 200–600 cm⁻¹ energy regime owing to their higher predicted population of states. Thus, vibrationally driven changes to ⁵⁹Co δ are expected to be governed namely by low-energy, high-population vibrational modes of the Co–N₆ core in this low-energy regime.

Figure 5.

(a) Experimental Raman spectra of 1 (top) and 2 (bottom) between fully protiated (black) and fully deuterated (blue) isotopomers at 30 mM over 200–600 cm⁻¹. (b) Predicted Raman spectra of 1 (top) and 2 (bottom) between fully protiated (black) and fully deuterated (blue) isotopomers. (c) Depiction of the vibrational motions of the most intense Raman modes: pincer modes of ca. 260–340 cm⁻¹ (ν₁ for 1 and ν₄ for 2) and breathing modes of ca. 450–510 cm⁻¹ (ν₄ for 1 and ν₆ for 2).

RESULTS AND DISCUSSION

The initial evaluations of 1 and 2 by ⁵⁹Co NMR (11.74 T, 118 MHz) in separate solutions of H₂O and 99.9% D₂O showed the mass-dependent effect of the N–H- and N–D-donor atoms on ⁵⁹Co δ. At 10 °C, ⁵⁹Co δ of the fully protiated species 1-d₀ in H₂O is 7123 ppm, while the peak of the fully deuterated species 1-d₁₂ in D₂O is 7061 ppm (Figure S1). Similarly, the fully protiated 2-d₀ in H₂O shows a broad peak at 6857 ppm, while the fully deuterated 2-d₆ peak in D₂O is 6817 ppm (Figure S2). The mass-driven chemical shift moves ⁵⁹Co δ upfield by 62 ppm for 1 and 40 ppm for 2. The effect of deuteration on ⁵⁹Co δ is the same up to 60 °C yet produces sharper NMR signals (Figures S3 and S4).

Further ⁵⁹Co NMR analysis in 1:1 mixtures of H₂O and D₂O reveals distributions of ⁵⁹Co peaks spaced out by approximately 5.0(1) and 6.7(1) ppm in 1 (Figure 2a) and 2 (Figure 2b), respectively. We note the remarkable similarity of these spectra to the isotopic distributions sometimes observed in mass spectrometry data. Each of the different peaks in these spectra represent a unique isotopomer of 1 and 2, for which there are a total of 13 for 1-d_n (n = 0–12) and 7 for 2-d_n (n = 0–6). In this case, the number of observed peaks depends on the number of exchangeable protons to the N-donor atoms.

Figure 2.

(a) Solution-phase ⁵⁹Co NMR spectrum (500 MHz magnet) depicting an ensemble of isotopomer peaks for 1-d_n (n = 1–10) at 60 °C after equilibration in a one-to-one D₂O/H₂O mixture. (b) Isotopomer peaks for 2-d_n (n = 0–6) at 60 °C after equilibration in 50% D₂O in H₂O. (c) Solution-phase UV–vis spectra of 1 fully protiated (1-d₀ in H₂O, black) and fully deuterated (1-d₁₂ in D₂O, blue) at 5 mM. (d) UV–vis spectra of 2 fully protiated (2-d₀ in H₂O, black) and fully deuterated (2-d₆ in D₂O, blue) at 2.14 mM. Both complexes show blue-shifted transitions after complete H/D exchange.

Room-temperature UV–vis spectroscopy data demonstrate the relatively small, but measurable, ligand-field consequences of the H/D exchanges. The UV–vis spectrum of 1-d₀ in H₂O shows two peaks at 21614(9) and 29572(16) cm⁻¹. Upon dissolution and equilibration in D₂O, 1-d₁₂ shows the same two peaks but blue-shifted to 21668(8) and 29731(14) cm⁻¹ (Figure 2c). For 2-d₀, two peaks at 21008(8) and 27762(10) cm⁻¹ are observed in pure H₂O, and these also shift to higher energy, 21138(5) and 28327(8) cm⁻¹, when dissolved in D₂O (Figure 2d). For O_h Co³⁺ ions, these two peaks correspond to the ¹A_1g → ¹T_1g and ¹A_1g → ¹T_2g transitions within a low-spin d⁶ system.^7,33 Tanabe–Sugano analyses (Table S1) of the changes in the UV–vis spectra suggest a difference in Δ_ο of 77 cm⁻¹ for 1 upon deuteration, increasing from 23462 cm⁻¹ (1-d₀) to 23540 cm⁻¹ (1-d₁₂). A larger, 223 cm⁻¹ change of Δ_ο is observed for 2-d₀ (22595 cm⁻¹) versus 2-d₆ (22818 cm⁻¹).

The difference in Δ_ο observed between protiated and deuterated species permits the evaluation of ligand-field strength changes per deuteration step. For 1, the total 77 cm⁻¹ increase in Δ_ο corresponds to a ca. 6.7 cm⁻¹ increase per deuteron. For 2, a greater sensitivity in Δ_o of ca. 37.2 cm⁻¹ per deuteron is observed. Extensive prior analysis of multiple families of O_h N-donor Co³⁺ complexes revealed a nearly linear relationship between the ⁵⁹Co δ and Δ_o (6.5 ppm/cm⁻¹).^8,10 The stepwise 5.0 ppm shift in the ⁵⁹Co δ peak location and 6.7 cm⁻¹ shift in Δ_o per deuteron for 1 are thus consistent with those prior studies. Complex 2, in contrast, exhibits a much larger effect with half as many deuterons.

The observed change in the chemical shift is due to the extraordinary sensitivity of the ⁵⁹Co nuclear spin to the electronic structure of the Co³⁺ ion. The deuterated ligands are slightly heavier (by ~13% mass for N–D₂ vs N–H₂ and ~7% for N–D vs N–H) and, because of that heavier mass, are likely to remain at slightly different equilibrium distances from the Co³⁺ ion in solution. This changing distance, which is likely too small to measure by normal structural methods, enables a change to the Co–N orbital overlap and, thus, Δ_o. In principle, the more closely bound N atom will cause the antibonding e_g* orbitals to raise in energy, increasing Δ_o. The increase in Δ_o then weakens the ⁵⁹Co paramagnetic shift and causes ⁵⁹Co δ to move upfield, which is observed for both complexes. In a way, the effect demonstrates that the ⁵⁹Co nucleus serves as an extraordinarily sensitive detector of minute structural differences. Finally, we note that the spectroscopic resolution of the different isotopomers in the ⁵⁹Co NMR spectra crucially permits their individual interrogation to test how deuteration affects Δδ/ΔT.

The mass effect of the H/D exchange on Δδ/ΔT was tested by investigating the variable-temperature ⁵⁹Co NMR spectra of 1 and 2 from 10 to 60 °C. These studies were performed in multiple different mixtures of D₂O and H₂O to ensure that the behaviors of all isotopomers were captured (Figures S5 and S6). With increasing temperature from 10 °C, all ⁵⁹Co NMR peaks shift downfield for 1 and 2 (Figure 3). For 1, all peaks remain resolvable over the temperature range and shift over an approximate 70 ppm window. For 2, however, the peaks appear to broaden and coalesce with decreasing temperature (relative to the 60 °C spectrum), and the peak itself moves by approximately 100 ppm over the studied temperature range. All peaks were identified from deconvolution of the spectra where possible (10–60 °C for 1 and 35–60 °C for 2). The relative magnitudes of the temperature-driven chemical shifts are consistent with prior analyses of the fully protiated versions of 1 and 2.¹⁷ The relative intensities appear to be consistent as a function of the temperature, indicating negligible redistribution of the isotopomer populations during the measurements.

Analysis of the ⁵⁹Co δ (ppm) peak positions as a function of the temperature T (°C) for individual isotopomers provides the key test of the role of deuteration on Δδ/ΔT (Figure 4). For 1, the well-resolved peaks enable the isolation of Δδ/ΔT values for all possible H/D isotopomers. In the case of 2, the discernability of each isotopomer signal is obscured below 35 °C, and analyses were applied only above this temperature (Figure S7). In both complexes (and across all samples), a comparison of the Δδ/ΔT values for the different isotopomers shows a mild but consistent change in the temperature sensitivity with increasing deuteration (Tables S2 and S3). For 1, the trend across all isotopomers shows a steady increase in Δδ/ΔT (Figure S8) with deuteration, from 1.35(1) to 1.42(1) ppm/°C from 1-d₀ to 1-d₁₂, respectively. Over the 35–60 °C temperature range, 2, in contrast, shows a decrease in Δδ/ΔT with increasing deuteration, from 2.03(3) to 1.96(2) ppm/°C from 2-d₀ to 2-d₆, respectively.

We also tested the temperature dependence of the dynamic magnetic properties, specifically spin–lattice, T₁, and spin–spin dephasing, T₂*, relaxation of the ⁵⁹Co nuclei for the different isotopomers (Figures S9–S17 and Tables S4–S7) but did not see any appreciable difference between the isotopomers. We note the expectation of a trend to be perhaps overambitious because there may be many different H/D substitutions for the same d_n isotopomer. Each of these isomers could have differing symmetries (e.g., 1-d₂ possessing two deuterons could be distributed on the same N-donor atom across different ligands), and thus different T₁ and T₂* values, because ⁵⁹Co T₁ is typically governed by quadrupolar relaxation. This relaxation mechanism is intimately tied to the ligand structure, and the longer relaxation times in 1 likely stem from a closer-to-O_h symmetry structure compared to 2.^19,34

The foregoing data demonstrate that deuteration produced opposing effects on the change in ⁵⁹Co Δδ/ΔT. Previous studies of ours suggested a correlation between longer lifetimes for low-energy vibrations (hypothesized to be predominantly Co–N in character)^35,36 and higher Δδ/ΔT.¹⁷ Here, we collected solution-phase Raman spectroscopy on 1, 1-d₁₂, 2, and 2-d₆ from 200 to 600 cm⁻¹ to test that hypothesis. Experimental data for 1 revealed four significant active modes at 279(1), 376(1), 445(1), and 529(1) cm⁻¹. Upon deuteration, all four peaks showed a modest red shift to 273(1), 353(1), 419(1), and 497(1) cm⁻¹, respectively (Figure 5a). The red-shifted frequencies of the Raman peaks are attributed to the higher mass of the N–D₂. For 2-d₀, eight significant modes were present, ranging from 219(1) to 546(1) cm⁻¹ (Table S8). Upon deuteration, 2-d₆ showed a similar red shift in the vibrational modes but smaller in magnitude relative to 1. The largest change, in both intensity and energy, was observed for the vibrations at ca. 500 cm⁻¹ in both complexes. Lifetimes, defined as τ = 1/fwhm (fwhm = full width at half-maximum), were averaged over all observed Raman peaks (Table S9). As protiated species, τ_avg was 0.61(3) ps for 1 and 0.7(1) ps for 2. Upon deuteration, both spectra sharpened, and τ_avg increased to 0.70(2) and 0.8(1) ps for 1 and 2, respectively. In both complexes, deuteration yielded longer τ, but Δδ/ΔT does not increase for both. We therefore interpret these results as disproof of our prior hypothesis that longer vibration lifetimes alone enhance Δδ/ΔT.¹⁷

Despite this disproof, the very clear spectral differences between 1, 1-d₁₂, 2, and 2-d₆ provide an exciting opportunity to test for the possible consequences of deuteration on vibrations and therefore ⁵⁹Co δ. We consider a new hypothesis for the governing phenomena of Δδ/ΔT. We propose that the population of the molecular vibrational states (Raman- and IR-active modes) within the inner coordination shell guides the structural distortions that dictate Δδ/ΔT. If true, then changes in the populations, energies, and types of specific vibrations, not lifetimes, should correlate to Δδ/ΔT and provide the true design strategies for controlled ⁵⁹Co temperature sensitivities.

We sought to test this picture against our experimental observations with two separate analyses that estimated the relative populations of the different vibrational states and the individual impacts on ⁵⁹Co δ. We considered 1, 1-d₁₂, 2, and 2-d₆ and the record-holding Co(acac)₃, which displayed a Δδ/ΔT of 3.15 ppm/°C in CDCl₃.¹² Frequency calculations were first performed to obtain a complete picture of the vibrational activity. Computed Raman spectra nicely agree with the experimental spectra and reproduced the experimentally red-shifted Raman-mode peaks upon deuteration (Figure 5b).

The performed frequency calculations enabled a qualitative assignment of the observed vibrations. Within the low-energy regime below 600 cm⁻¹, many of the vibrations were complex, incorporating bond stretches, scissoring, and bending motions of the Co–N₆ coordination sphere (Tables S10 and S11). The most intense modes (experimentally and computationally) were found to possess strong symmetric Co–N stretching character. These were at 261 and 512 cm⁻¹ for 1 and 338 and 487 cm⁻¹ for 2 (Figure 5b). These predicted frequencies agree with the experimentally collected solution-phase Raman spectra and are supported by literature values.^37,38 Of these two stretching modes, the lower-energy vibrations (261 cm⁻¹ for 1 and 338 cm⁻¹ for 2) are described by a N–Co–N pincer-like mode of the ethylenediamine ligands in 1 and the ethylenediamine-like side arms in 2 (Figure 5c). The higher-energy mode (512 cm⁻¹ for 1 and 487 cm⁻¹ for 2) arises because of symmetric stretching of the six N-donor atoms along their bonds to the metal center. This higher-energy vibration, which showed the greatest red shift after deuteration in both structures, is best-described as the A_1g breathing mode of the octahedral Co–N₆ core.

Analysis of the populations of vibrational states revealed what we believe is the mechanism governing Δδ/ΔT. We compare Δδ/ΔT to the total vibrational partition functions, q_Total, of 1, 1-d₁₂, 2, and 2-d₆ using the computed vibrations from the frequency calculations including Raman- and IR-active modes (Figure S18). We also computed q_Total of additional Co³⁺ complexes with reported Δδ/ΔT in the literature including Co(acac)₃, [Co(NO₂)₆]³⁻, [Co(CN)₆]³⁻, [Co(NH₃)₆]³⁺, [Co(tn)₃]³⁺, and [Co(tame)₂]³⁺.^12,15,17 Harmonic frequency calculations were first made to predict the normal modes (3N–6) of each structure. Total vibrational partition functions, q_Total, are calculated from the product of each normal mode by q = 1/(1 − e^−E/kBT), where E is the normal-mode energy (cm⁻¹), k_B is Boltzmann’s constant, and T is the temperature (K). These partition functions depend on the number of vibrational normal modes, their respective frequencies, and the temperature. At 25 °C, the value of q_Total for 1 (5.4 × 10³) is surpassed by 2 (2.0 × 10⁷) by 4 orders of magnitude, and the value of Co(acac)₃ (2.2 × 10¹¹) is even larger. Higher values of q_Total reflect a higher population of vibrational states for a given molecule, enabled by greater numbers of low-energy vibrations. Out of all of the computed normal vibrational modes of 1, 23% are below 600 cm⁻¹. Similarly, 25% of the modes in 2 and 32% of the modes in Co(acac)₃ are below 600 cm⁻¹. The number of low-energy modes in each complex roughly reflects the 25 °C value of q_Total.

Owing to this result, we posit that higher values of Δδ/ΔT are attributed to generally higher populations of low-energy modes at a given temperature. This insight is unique from all prior proposed models of the origin of the temperature dependence of ⁵⁹Co δ.^14,15,17,39 The result also establishes a key design principle for Δδ/ΔT, wherein synthetic strategies to change q_Total may guide the enhancement of Δδ/ΔT. However, analysis of q_Total alone did not account for the differing effects of deuteration on Δδ/ΔT between 1 and 2. Above, we proposed that the individual vibrations and their respective impacts on ⁵⁹Co δ must be active, and subsequent calculations were performed to test the relevance of this concept to ⁵⁹Co Δδ/ΔT.

In principle, one might expect all 3N–6 vibrations for a complex to be important for ⁵⁹Co δ because all modes may contribute to a varying structure. However, different vibrations will affect the ¹A_1g and ¹T_1g energies to different extents depending on how they affect the e_g* orbital energies. We hypothesized that only Raman-active vibrations, such as the Co–N₆ breathing mode, would be the most influential on ⁵⁹Co δ because symmetric distortions should produce large-amplitude changes in the metal–ligand overlap (and thus e_g* and Δ_o). To test this idea, we computed ⁵⁹Co δ as a function of the atomic displacement along the coordinate pathway Q (Figure 6) for vibrations between 200 and 600 cm⁻¹. The vibrational coordinate Q describes the displacement away from the optimized structure (Q = 0) following the progression of a given vibration. Δδ/ΔQ curves were then constructed from computed ⁵⁹Co chemical-shift calculations at individual points along Q.

Figure 6.

(a) ⁵⁹Co δ as a function of the vibrational coordinate Q, for experimentally determined Raman modes in 1 between 200 and 600 cm⁻¹. (b) ⁵⁹Co δ as a function of Q for Raman modes in 2 between 200 and 600 cm⁻¹. The Co–N₆ symmetric A_1g breathing mode is indicated by filled circles with solid traces.

We found that in all cases the ⁵⁹Co δ values vary over thousands of parts per million and often nonlinearly between the extremes of Q (−1 and +1). For a given vibration, we can describe the change in ⁵⁹Co δ relative to Q via Δδ/ΔQ at Q = 0, which represents a coupling strength between the vibration and ⁵⁹Co δ. The symmetric Co–N₆ breathing modes yielded the largest values of Δδ/ΔQ: 7922 ppm/Q for 1, 6436 ppm/Q for 2, and 6113 ppm/Q for Co(acac)₃ (Figure S19). The pincer modes showed the second highest Δδ/ΔQ values, of 2338 ppm/Q and 1445 ppm/Q, for 1 and 2, respectively. In contrast, Δδ/ΔQ for IR-active modes were all substantially smaller (3–17 ppm/Q), reflected by the parabolic functions centered at Q = 0 (Figure S20). These results collectively suggest that Raman-active modes (not IR) are key vibrational influences of ⁵⁹Co δ, with the breathing mode exhibiting the highest effect. It is likely that these modes are most impactful because they shift the e_g* orbitals by the highest amount. This change then induces the largest difference in the paramagnetic shift via changes to the low-lying excited-state energies.

The revealed importance of the Raman modes inspired us to evaluate their role in Δδ/ΔT with regard to the partition function of just these modes, q_Raman. A comparison of Δδ/ΔT to q_Raman (Figure 7) improves upon the original trend with q_Total, further suggesting that Raman-active modes are the fundamental vibrational components driving Δδ/ΔT. The key finding of this analysis also follows the opposing trends in Δδ/ΔT between 1 and 2: q_Raman increases from 10.4 to 16.6 at 25 °C for 1 to 1-d₁₂ and decreases from 559.4 to 463.3 at 25 °C for 2 to 2-d₆. The values of q_Raman follow the changes in Δδ/ΔT upon deuteration. For both IR- and Raman-active modes, deuteration was expected to lower vibrational energies, yet, on the basis of the Δδ/ΔQ values, we propose that changes in the energies of the Raman-active vibrations, thus changing to the populations of these states, will significantly contribute to Δδ/ΔT. For 1, deuteration lowered the energies of the Raman vibrations to foster higher Δδ/ΔT via higher q_Raman. For 2, deuteration also lowered the Raman vibration frequencies, but q_Raman decreased. In 2, the IR vibrations also dropped in energy such that they consequently leach population from Raman to IR vibrational states, thus the reason for producing a lower Δδ/ΔT upon deuteration.

Figure 7.

Relationship between the ⁵⁹Co Δδ/ΔT temperature sensitivity and total vibrational partition function of Raman modes, q_Raman (logarithmic) for 1, 1-d₁₂, 2, 2-d₆, and other Co³⁺ complexes with known Δδ/ΔT sensitivities.^12,15,17 The linear correlation by R² is 0.82. The error bars for the Δδ/ΔT values are within 0.03 ppm/°C and the edges of the symbols. The shaded areas highlight the trends in protiated (black) and deuterated (blue) pairs of 1 and 2.

The foregoing data inform potential synthetic design strategies aimed at complexes with higher ⁵⁹Co thermometric sensitivities. (1) The higher numbers of vibrations at low energy are advantageous, meaning that potentially higher-coordination numbers, or more complex coordination geometries than the O_h, six-coordinate molecules here may produce higher Δδ/ΔT. (2) The larger mass for donor atoms can be used for potentially enhancing Δδ/ΔT, although this effect appears to be ligand-specific. (3) Raman vibrations appear to be the most important for Δδ/ΔT, and thus low-symmetry coordination shells are desirable because these should feature more Raman-active vibrations. Tests of these ideas will be reported in due course.

CONCLUSION

The foregoing data establish a rationale for how ligand identity enhances ⁵⁹Co Δδ/ΔT, namely, by increasing the number and populations of Raman-active vibrations that include the first coordination shell of the Co³⁺ ion because these modes produce the largest-amplitude changes in ⁵⁹Co δ. As a result of this discovery, we generate a new figure of merit to target in the molecular design of high Δδ/ΔT: q_Raman. This parameter describes not only existing trends in Δδ/ΔT identified in a family of Co(III) complexes but also the observed opposing impacts of deuteration, where Δδ/ΔT increases with deuteration for 1 but decreases for 2. We note q_Raman can be computed independently of molecular isolation. Thus, the pursuit of highly temperature-sensitive ⁵⁹Co-based spin probes is no longer limited to strict synthetic exploration but can potentially proceed in silico. More broadly, the approach here may be useful in estimating or predicting the temperature response of other metal-complex physical properties that involve vibrations, such as reactivity⁴⁰ or magnetic relaxation.^41,42