Chemical Exchange Reaction Effect on Polarization Transfer Efficiency in SLIC-SABRE

Abstract

Signal Amplification By Reversible Exchange (SABRE) is a new and rapidly developing hyperpolarization technique. The recent discovery of Spin-Lock Induced Crossing SABRE (SLIC-SABRE) shows that high field hyperpolarization transfer techniques developed so far were optimized for singlet spin order that does not coincide with the experimentally produced spin state. Here, we investigate the SLIC-SABRE approach and the most advanced quantitative theoretical SABRE model. It is the goal to achieve the highest possible polarization with SLIC-SABRE at high field using the standard SABRE system, IrIMes catalyst with pyridine. We demonstrate the accuracy of SABRE model describing the effects of various physical parameters such as the amplitude and frequency of the radio-frequency field, and the effects of chemical parameters such as the exchange rate constants. The combined use of experiments and theory allows to determine the effective lifetime of SABRE-complex. Furthermore, the entropy and enthalpy of the SABRE-complex dissociation reaction based on the temperature dependence of SLIC-SABRE signal can be accessed. We show, for the first time, that this SLIC-SABRE model can be useful for the evaluation of the chemical exchange parameters that are very important for the production of highly polarized contrast agents via SABRE.

Graphical Abstract

I. Introduction

Nuclear Magnetic Resonance (NMR) is a versatile tool that is extensively applied in science and medicine. Different approaches to increase the sensitivity of the method were proposed during the last decades^1–10. One of these methods is Signal Amplification By Reversible Exchange⁴, SABRE, a ParaHydrogen Induced Polarization (PHIP) technique^11,12, that has shown quite interesting developments^13–24. SABRE hyperpolarization can be “spontaneously” generated at low (mT)^25–28, ultra-low (<μT)^21,29–32 and high (T) magnetic fields^33,34. High-field SABRE offers an advantage of producing and detecting hyperpolarization at the same location, and therefore, mitigates sample transfer requirements, and offers advantages of signal averaging³⁵ and permanent addition of pH₂³⁶. For the high-field regime, several polarization transfer sequences were developed in order to make SABRE more robust and efficient: ¹H radio-frequency pulse induced SABRE (¹H-RF-SABRE)³⁷, Low Irradiation Generation of High-Tesla SABRE (LIGHT-SABRE)³⁸, a method based on the application of adiabatic RF-pulses³⁹, SABRE-INEPT^40,41, Alternating Delays Achieve Polarization Transfer SABRE (ADAPT-SABRE)²², SABRE COSY and Sepp-HoSQC³⁵ and Spin-Lock Induced Crossing SABRE (SLIC-SABRE)^42,43. SLIC was pioneered by Rosen and co-workers⁴⁴. The sequence has been shown to be very efficient for transformation of nascent parahydrogen-derived singlet spin order into observable magnetization^38,45–48.

High-field SABRE not only provides hyperpolarized samples without a need of external polarizers, but allows as well to use all conventional NMR methods to elucidate chemical reaction parameters under fully controlled reaction conditions. For example, even before SABRE was established, modification of INEPT sequence was employed to study the reactivity of different metal-organic complexes⁴⁹.

Spin-order transfer (SOT) RF-pulse sequences are typically developed for a specific molecular system. In theory, most of these methods provide a polarization close to the absolute maximum⁵⁰. However, these theoretical values are challenging to reach experimentally. Moreover, the same high-field SOT sequences often provide a much higher polarization level for systems where pH₂ was added permanently⁵¹ as compared to systems undergoing the reversible exchange³⁹. The main reason for this is that the chemical exchange between the catalyst-bound and free states of pH₂ and substrate, S, is continuous, while the duration of a SOT sequence is finite⁴⁰. As a result, only a fraction of all complexes are subjected to the entire SOT sequence. For some pulse sequences, e.g., PH-INEPT^40,41,52, it is crucial that complex does not dissociate during the entire duration of the SOT sequence, otherwise there will be no hyperpolarization.

The substrate polarization in SABRE experiments at high and low fields strongly depends on the experimental conditions: concentration of the catalyst, substrate, pH₂ flow rate, pressure and sample temperature^{13,21,40,53–55}.

Using a simplified approach to describe the polarization transfer, a “SABRE formula” was introduced⁵⁶, encompassing various chemical properties of the SABRE chemical exchange. This model attempts in a simplified manner to explain an effect of chemical exchange on the resulting SABRE polarization level.

Another, more advanced quantitative theory was introduced recently which provides the most accurate theoretical description of SABRE phenomenon to date⁵³. This method, however, is restricted to a maximum of 6–7 spins in the SABRE-complex because of computational limitations.

In this work, we investigate the properties of SLIC-SABRE experiments⁴², and demonstrate a significant improvement of hyperpolarization level. As it was shown in the original work^42,43, SLIC-SABRE is more tolerant with respect to the initial spin state of the system. At least half of the maximum polarization is retained even when fast S-T₀ mixing occurs. This is different compared to other methods, where the entire signal can be lost (e.g., LIGHT-SABRE³⁸). As a result, SLIC-SABRE is a method robustly applicable for a wide range of different metal complexes.

An additional advantage of SLIC-SABRE over other polarization pulse sequences was identified in this work: by fitting a model to experimental SLIC-SABRE data, the effective exchange rate (or mean lifetime) of the SABRE complex can be derived. Only during this time period, polarization transfer occurs before the SABRE complex dissociates⁵⁷. This parameter is critical for achieving high polarization levels. However, as one will find in the Results and discussion section, the current state of the art quantitative SABRE model⁵³ used in this work does not give a perfect explanation of the experimental results and further improvement of the theory (and experimental protocols) is necessary.

II. Materials and methods

Materials.

All experiments were carried out using a 0.1 M solution of ¹⁵N-pyridine (¹⁵N-Py) and 5 mM of IrIMes iridium N-heterocyclic carbene complex¹³ (IMes = 1,3-bis(2,4,6-trimethylphenyl)imidazole-2-ylidene) in methanol-d₄ (purchased from Carl Roth GmbH, CAS: 811-98-3). ¹⁵N-Py and IrIMes were synthesized according to earlier published procedures^13,58. The initial IrIMes complex was activated by flushing pH₂ through the mixture for 20 minutes, resulting in three molecules of substrate (Py) binding to the complex. The resulting solution consisted of SABRE-active complex [IrH₂Imes(Py)₃] and free Py, fPy, with 1 to 17 concentration ratio.

Equipment.

pH₂ was prepared using commercially available setup with a conversion temperature of 38 K that provides ≈ 90 % enrichment of the para fraction (Bruker, BPHG 90). Experiments were carried out inside a 300 MHz NMR spectrometer (Bruker AVANCE). The reaction chamber for pH₂ supply was described before³⁸. pH₂ is delivered in a standard 5 mm NMR tube (Wilmad) via a thin 1/16” capillary. pH₂ flow rate was 7 scm³/min with 1.7 bar overpressure with respect to an ambient pressure.

Pulse sequences.

We used the previously published SLIC-SABRE pulse sequence⁴² with the following modifications (Figure 1): during the acquisition, a ¹H WALTZ-16⁵⁹ block was added to decouple the pyridine protons to increase SNR and to eliminate an anti-phase spin order. As a result, net polarization of free ¹⁵N-pyridine was observed. Hereafter, ¹⁵N_bound stands for the ¹⁵N signal of bound equatorial ¹⁵N-Py, and ¹⁵N_free is for the ¹⁵N signal of free ¹⁵N-Py. During the experiment, pH₂ was constantly supplied by bubbling. No significant distortion of the ¹⁵N resonances was observed.

Figure 1.

Schematic view of the original SLIC-SABRE{¹H} (A) and modified SLIC/dc-SABRE{¹H} (B) sequences, without and with ¹H-decoupling during pH₂ bubbling, respectively. Typical parameters of the CW field were v₁ = 5 Hz, v_rf ≅ 255.5 ppm with duration t_CW = 1.17 s, the amplitude of WALTZ-16 decoupling block was 300 Hz and carrier frequency was set at 8.3 ppm, durations of 90^{o 1}H and ¹⁵N RF-pulses were 26.7 μs and 21 μs, respectively. The SLIC block in brackets was repeated n = 20 times.

Also, a selective ¹H WALTZ-16 decoupling block was added during the continuous wave radio frequency (CW RF) pulse (sequence SLIC/dc-SABRE) to decouple ¹⁵N from ¹H nuclei of pyridine. The signal of the two hydride protons should not be affected. The decoupling of pyridine protons and ¹⁵N significantly simplified the spin system such that the quantitative SABRE theory⁵³ was used for the simulations of the experiment.

Quantitative SABRE theory.

For a quantitative description of SABRE, the chemical reaction process has to be combined with the spin evolution. The chemical exchange reaction in SABRE can be described with the following set of equations. Association and dissociation of substrate:

$$\mathrm{I}\mathrm{r}{H}_{2}S\underset{k_a}{\stackrel{k_d}{\leftrightarrow }}\mathrm{I}\mathrm{r}{H}_2+S$$ (eq1)

Here, IrH₂S represents the Ir-complex where H₂ and substrate (S) are coordinated and mutual J-couplings exist. IrH₂ is a transient Ir-complex. k_d and k_a are dissociation and association rate constants, respectively.

Exchange of hydrogen:

$$\mathrm{I}\mathrm{r}{H}_2+H_2^{\text{'}}\stackrel{k_{ex}}{\to }\mathrm{I}\mathrm{r}{H}_2^{\text{'}}+H_2$$ (eq2)

Loss of free hydrogen to exhaust/atmosphere:

$$H_2\stackrel{W_{ex}}{\to }exhaust$$ (eq3)

Supply of fresh pH₂ ($H_2^{*}$) in solution:

$$supply\stackrel{W_{in}}{\to }{H}_2^{*}$$ (eq4)

The simulation of this set of equations is rather complicated because they are nonlinear. To address this issue, the following simplifications were proposed in the quantitative SABRE theory⁵³:

A1.

The reservoir of pH₂ in solution is large: an unlimited amount of pH₂ is always available, at a constant enrichment of 100 %.

A2.

The chemical exchange of H₂ with Ir is fast: H₂ in IrH₂ is always pure pH₂ (we will denote that complex as $\mathrm{I}\mathrm{r}{H}_2^{*}$ below).

From these simplifications, the following set of equations follows:

$$\mathrm{I}\mathrm{r}{H}_2^{*}+S\stackrel{k_a^{\text{'}}}{\to }\mathrm{I}\mathrm{r}{H}_2^{*}S$$ (eq5)

$$\mathrm{I}\mathrm{r}{H}_{2}S\stackrel{k_d^{\text{'}}}{\to }\mathrm{I}\mathrm{r}{H}_2+S$$ (eq6)

$$\mathrm{I}\mathrm{r}{H}_2\stackrel{\infty }{\to }\mathrm{I}\mathrm{r}{H}_2^{*}$$ (eq7)

where the primed association and dissociation rate constants $k_a^{\text{'}},\mathrm{ }{k}_d^{\text{'}}$ indicate that these are the constants in the simplified models. In general, they are not the same as the constants in the full model (eq 1).

When pH₂ is supplied to the system for a long period of time, a “steady-state” association rate, W_a, can be introduced:

$$W_a=\left[Ir{H}_2\right]k_a^{\text{'}}=k_d^{\text{'}}\frac{\left[Ir{H}_{2}S\right]}{\left[S\right]}$$ (eq8)

Since the ratio [IrH₂S]/[S] = complex/substrate is known from the experiment and $W_a=k_d^{\text{'}}\left[Ir{H}_{2}S\right]/\left[S\right],\mathrm{ }{k}_d^{\text{'}}$ is the only variable parameter in the model. The meaning of $k_d^{\text{'}}$ is the effective dissociation rate constant and $\tau =1/k_d^{\text{'}}$ is the mean lifetime of IrH₂S complex. In the SI we discuss how lifetime of the complex and dissociation constant rate are related as well as the effect of lifetime of the complex on polarization level.

It is expected that polarization level scales linearly with pH₂ enrichment, so that polarization level for 90% pH₂ differs from that for 100 % pH₂ by a factor of about 0.87²³. The detailed description of how to solve this set of equations was given in the original publication⁵³. Here, we used the in-house software to calculate SABRE experiments using this model, where chemical exchange, spin Hamiltonian and relaxation superoperators are implemented and only parameters like T₁-relaxation, chemical shifts, constants of J-coupling and $k_d^{\text{'}}$ and W_a need to be specified. A detailed description of the software will be published elsewhere.

Calculation demands.

In this model, relaxation was included using Redfield relaxation theory⁶⁰, i.e., using relaxation superoperators that increase computational efforts. We can calculate SABRE complexes for a system with up to 6 spins-½. A single superoperator for a 6 spin-1/2 system is composed of 4⁶ × 4⁶ ≈ 16777216 ≅ 1.7 × 10⁷ numbers. Adding two more protons would increase the size of the superoperators and hence the complexity of computation by a factor of 4² × 4² = 256; in this case, the calculation of SLIC-SABRE with one set of parameters on a PC with 4.2 GHz processor would require about 180 hours. Consequently, we did not attempt to model the experimental data obtained with SLIC-SABRE (>8 coupled spins-½); instead the SLIC/dc-SABRE data is modeled with the quantitative SABRE theory (4 coupled spins-½).

III. Results and discussion

3.1. SLIC-SABRE: theoretical analysis

In order to determine the optimal conditions for SLIC-SABRE, we calculated the ¹⁵N-polarization of the free substrate (¹⁵N_free) as a function of the frequency and amplitude P(v_rf, v₁) of the CW-pulse.

The computation was performed for a 4-spin-½ SABRE complex [IrH₂S₂], where S was a single ¹⁵N nucleus (Figure 2A, simulations details are provided in the caption). P(v_rf, v₁) was found to be antisymmetric with respect to the frequency of the resonance of a bound substrate, v_rf = v(¹⁵N_bound): two polarization extrema with different signs were observed.

Figure 2.

(A) Simulated ¹⁵N_free polarization as a function of CW RF field amplitude, v₁, and frequency offset from ¹⁵N_bound resonance, v_rf − v(¹⁵N_bound) for a [IrH₂S₂] SABRE complex, where S = ¹⁵N. Note that two distinct extrema occur, symmetric with respect to the frequency of the bound substrate, v(¹⁵N_bound). The maximum polarization for ${k^{\prime }}_d=30{\text{s}}^{-1}$, $W_a=k_d^{\mathrm{\text{'}}}/17$, t_CW = 1.17 s and n = 20 occurs at v₁=5 Hz and v_rf − v(¹⁵N_bound)=17 Hz. (B) Polarization of SLIC-SABRE as a function of $k_d^{\mathrm{\text{'}}}$ for an [IrH₂S₂] complex with S=¹H (red) and S=¹⁵N¹H (blue) and the “simple analytical SABRE formula” (dashed line).

The maximum polarization ≈ 24% was found at v₁=5 Hz and v_rf − v(¹⁵N_bound)=17 Hz (for IrIMes, ¹⁵N-Py with decoupled protons in methanol, see J-coupling constants in Table S1).

Similar simulations were already performed in the original SLIC-SABRE work. However, it is important to note that P(v_rf, v₁) strongly depends on the chosen $k_d^{\text{'}}$ (see supplementary video for P(v_rf, v₁,$k_d^{\text{'}}$) and Figures S4 and S6).

Next, $\mathrm{P}\left(k_d^{\text{'}}\right)$ was simulated for fixed v₁=5 Hz and v_rf − v(¹⁵N_bound)=17 Hz for a 4-spin-½ and 6-spin-½ SABRE complex [IrH₂S₂]. Here, the substrate was assumed to be either a single ¹⁵N spin or ¹⁵N with ¹H (i.e., a substrate with one ¹⁵N nucleus and one ortho-¹H hydrogen of Py). Both systems exhibited a similar $\mathrm{P}\left(k_d^{\text{'}}\right)$ that rises quickly to one maximum and descends slowly to zero. Some of the features are reproduced by the analytical “SABRE formula” from Ref. (⁵⁶) too. The similar peak function was predicted by analytical equation for SABRE at ultra-low magnetic fields (SABRE-SHEATH)⁶¹, however it did not provide satisfactory agreement with the experiments and adaptation for high-field SLIC-SABRE experiment is necessary, therefore we will not use that method and “SABRE formula” in the work.

Although, addition of ¹H to the substrate does not change the shape of $\mathrm{P}\left(k_d^{\text{'}}\right)$, the absolute polarization is reduced by a factor of 2.5. Thus, a reduced spin system appears to be quite beneficial for an increased hyperpolarization yield. Experimentally, we realized that by applying frequency selective ¹H WALTZ-16 decoupling on the Py-protons (see Figure 1, 3, 4 and discussion below). Before, attempts were made to simplify the SABRE system using e.g., substitution of ¹H by ²H^33,39, however, deuterons also have J-couplings with ¹⁵N and often ²H exchanges with ¹H₂ in the solution as a result of pH₂ bubbling in the presence of an Ir-complex. Unfortunately, we were not able to simulate the system where S = (¹⁵N¹H¹H), i.e., with both ortho-protons of pyridine taken into account, because of our current computational power limitations.

Figure 3.

(Top) High-resolution ¹⁵N NMR spectra of free (¹⁵N_free) and bound (¹⁵N_bound) ¹⁵N-Py signals after application of SLIC/dc-SABRE{¹H} with v₁ = 5 Hz, n=20 and v_rf − v(¹⁵N_bound)=−17 Hz (red) or −7 (black) at T = 15 ^oC,. (Bottom) Normalized polarization level of SLIC/dc-SABRE{¹H} (green circles) and SLIC-SABRE{¹H} (blue squares) as a function of v_rf − v(¹⁵N_bound). Green lines are the result of quantitative SABRE model for [IrH₂S₂] complex with S = ¹⁵N and ${k^{\prime }}_d=14{\text{s}}^{-1}$ (solid line) or 60 s⁻¹ (dashed line). Arrows indicate the offsets corresponding to the spectra demonstrated above.

Figure 4.

Experimentally measured SLIC-SABRE{¹H} (blue squares) and SLIC/dc-SABRE{¹H} (green circles) signal amplitudes as a function of temperature and effective dissociation constant rate, $k_d^{\mathrm{\text{'}}}$. Corresponding quantitative SABRE theory simulations (solid lines) for a [IrH₂S₂] complex with S=¹⁵N. To interrelate temperature and dissociation rate, Eyring equation with entropy ΔS^‡ = 52.9 J/mol·K and enthalpy ΔH^‡ = 79.4 kJ/mol of activation was used.

To summarize, for an optimization of polarization yield, it is required to find the appropriate values of v₁, v_rf and t_CW. Furthermore, the polarization is strongly dependent on $k_d^{\text{'}}$ (see supplementary video or Figure 6S), which, in turn, depends on the temperature, the choice of substrate, solvent and catalyst.

3.2. SLIC-SABRE RF-field matching

Using the optimal parameters deduced from simulation, v₁ = 5 Hz and v_rf − v(¹⁵N_bound)=17 Hz, the maximal signal was experimentally observed for a CW duration t_CW = 1.17 s. After n=20 repetitions of SLIC, a constant polarization level was achieved. Holding v₁ = 5 Hz and t_CW constant, we varied the frequency offset of the CW RF-pulse, v_rf − v(¹⁵N_bound), at T = 15 °C for both variants of the sequence (Figure 3).

For SLIC/dc-SABRE, the two main extrema at frequencies ±17 Hz and two minor extrema at ±8 Hz were observed. These were well reproduced by the simulations with ${k^{\prime }}_d=14{\text{s}}^{-1}$. For SLIC-SABRE, the main extrema were shifted to ±20 Hz and no other extrema were observed.

This experimental data proves that the matching conditions for SLIC-SABRE and SLIC/dc-SABRE are different (because the effective spin systems are different). Note that both ortho-protons effectively contribute and enlarge the spin system in SLIC-SABRE. The polarization is 2.6 times larger in the effectively smaller spin system.

To demonstrate the effect of $k_d^{\text{'}}$, the simulations were repeated with ${k^{\prime }}_d=60{\text{s}}^{-1}$ (Figure 3). This calculation fails to reproduce experimentally observed SLIC/dc-SABRE data. For more examples of simulated frequency/amplitude/$k_d^{\text{'}}$ dependences we refer the reader to Figure S6 (SI) or supplementary video.

3.3. SLIC-SABRE temperature dependence

To investigate the effect of $k_d^{\text{'}}$, we performed experiments at different temperatures with fixed CW RF-field amplitude v₁ = 5 Hz and frequency offset, v_rf − v(¹⁵N_bound)=17 Hz (SLIC/dc-SABRE) and 20 Hz (SLIC-SABRE) (see Figure 4 and Figure S4 in the SI), t_CW = 1.17 s and n = 20. The experimental SLIC/dc-SABRE results were simulated using quantitative SABRE theory for a [IrH₂S₂] complex with S = ¹⁵N. We also think that it is interesting to mention that temperature variation was used before for optimization of low field ¹H-SABRE⁵⁴.

To correlate simulated $\mathrm{P}\left(k_d^{\text{'}}\right)$ with experimental P(T), we used conventional Eyring equation in the form $k_d^{\text{'}}=\frac{k_{B}T}{h}\text{exp}\left(\frac{\mathrm{\Delta }{S}^{‡}}{R}-\frac{\mathrm{\Delta }{H}^{‡}}{RT}\right)$ that couples rate constant, $k_d^{\text{'}}$, and temperature, T. A step-by-step procedure of fitting experimental data is given in SI (Figure S7).

The same system has been investigated before and data sets for k_d (T) are available, measured with EXSY¹³ and SABRE-INEPT⁴⁰. The corresponding entropy, ΔS^‡, and enthalpy, ΔH^‡, of activation are given in Table 1. Beside EXSY and SABRE-INEPT methods one can use e.g., variation of line-width with temperature to determine the average lifetime of the SABRE complex⁶¹, however, this data for IrIMes with Py are not available and is very hard to obtain, because field homogeneity is disturbed by the bubbling system and a simulation of spectrum of SABRE complex is necessary⁶¹.

Table 1.

Entropy, ΔS^‡, and enthalpy, ΔH^‡, of activation for dissociation of pyridine from SABRE complex obtained by fitting EXSY¹³, SABRE-INEPT⁴⁰ and SLIC/dc-SABRE (this work) temperature dependences of the dissociation rate constant.

	ΔS‡, J/mol·K	ΔH‡, kJ/mol
Ref. 13	97±9	93±3
Ref. 40	33.3±4	76.2±3
this work	52.9±14	79.4±4

Within the error margin the enthalpy, ΔH^‡, obtained with SLIC-SABRE method coincides with the results reported in Ref. 40 (SABRE-INEPT). Both SABRE-INEPT and SLIC-SABRE data deviate from the data obtained with EXSY.

Matching the dissociation rate parameters with the previously reported data support the validity of quantitative SABRE theory for describing not only various SABRE polarization transfer methods but also chemical exchange processes responsible for the production of hyperpolarization.

3.4. SLIC-SABRE polarization level

We simulated SLIC/dc-SABRE experiment for various experimental parameters: v₁, v_rf, t_CW and for different values of $k_d^{\text{'}}$ (see Figure 2, S6 and supplementary video). The high level of ¹⁵N-polarization, ~25 %, was found for the following model parameters: t_CW = 1.17 s, n = 20, v₁=5 Hz,|v_rf −v(¹⁵N_bound)| in the range from 10 Hz to 20 Hz, ${k^{\prime }}_d\cong 10-30{\text{s}}^{-1}$, T₁ relaxation times of IrH₂, ¹⁵N in the complex and in the bulk equal to 1 s, 6 s and 60 s respectfully and J-coupling constants given in Table 1S. However, the maximum level of polarization experimentally achieved here with SLIC/dc-SABRE is about 0.45 %, which is far from the theoretical maximum.

We have compared the performance of SLIC-SABRE and LIGHT-SABRE reported in Refs. (38,42,43) with our results (see Table 2S in SI). In all cases, the levels of ¹⁵N polarization are moderate and fall in the range from 0.0067% to 0.545%. However, for application not only the level of polarization but the total intensity of the polarized signal is very important. To characterize total intensity, we introduce the quantity S which is a product of polarization level (in %) and the concentration of free substrate (in mM). This parameter characterizes the available NMR signal, therefore its value is a measure of efficiency of hyperpolarized agents production.

The achieved values of parameter S are in the range from 0.134 to 45. It is noteworthy that the optimized SLIC-SABRE⁴³ and the original LIGHT-SABRE³⁸ experiments give almost the same values (10.9 and 9.7, respectively), while with our optimization and experimental settings the value of 45 was achieved.

The data collected in Table 2S demonstrate clearly that not only the experimental settings used in various studies are different (e.g., duration of some RF pulses) but also the concentration of substrates, catalyst, pH₂ pressure and pH₂ flow differ as well. SABRE experimental setups are not unified and therefore it is hard to compare the results obtained in different laboratories. However, we are certain that decoupling of substrate protons will always be beneficial for direct and efficient polarization transfer to ¹⁵N nuclei in high field SABRE experiments.

At the same time, we note that here the theory is employed for a qualitative estimation of the real system, because several simplifications were used. The main simplification is neglecting the chemical exchange with H₂. Theoretically, one can say that an unlimited supply of pH₂ in the bulk is available, however, by SABRE-SHEATH experiment it was perfectly demonstrated that it is not the case: ¹⁵N polarization in SABRE-SHEATH experiment increases together with increase of pH₂ pressure and a flow rate²¹. Our current theoretical approach is more descriptive of the experimental condition of significantly higher pH₂ concentration and gas pressure and therefore, future modifications of the theory are necessary and will be attempted. We believe that including pH₂ exchange will be the next step in understanding moderate performance of high field SABRE.

Moreover, the vast majority of modern high-field high-resolution NMR spectrometers have significant experimental and fundamental shortcomings in the context of maximizing the efficiency of SLIC-SABRE. First, and foremost, only a small fraction of the sample is encompassed by the RF coil – as a result, RF pulses often cover only a fraction of the sample. Moreover, the irradiated sample fraction is constantly changing due to continuous pH₂ bubbling. Second, significant RF field gradients exist at the ends of the RF coil resulting in sub-optimal sample irradiation. Third, parahydrogen bubbling creates some susceptibility gradients, which may additionally contribute to lower than expected SLIC pulse efficiency. Last but not least, ¹⁵N chemical shift anisotropy decreases the ¹⁵N T₁ at high magnetic fields⁶², thereby potentially limiting the maximum attainable ¹⁵N polarization due to disproportionately greater T₁-associated losses compared to those at lower magnetic fields. Most of these experimental and fundamental limitations can be overcome through the use of lower field magnets (e.g. 1.5 T or lower MRI scanners), which in principle can be equipped with RF coils encompassing the entire SABRE sample with better RF homogeneity and reduced susceptibility induced gradients. Moreover, ¹⁵N T₁ times are longer at lower magnetic fields than at higher magnetic fields in the context of SABRE⁶². We also point out that these hardware advances have already been enjoyed by conventional hydrogenative PHIP technique enabling higher polarization values^36,63.

Conclusion

We have analyzed and optimized SLIC-SABRE polarization transfer technique for IrIMes SABRE catalyst with pyridine in methanol. Under optimal conditions we obtained the polarization level of 0.45% for 100 mM Py which corresponds to about 1900-fold enhancement at 7 T. When parameter S which is equal to the product of polarization and concentration is compared, the signal intensity achieved in this work is higher than in the original SLIC-SABRE and LIGHT-SABRE experiments. We have shown that quantitative SABRE model is valid for the description of SABRE experiments at high fields even though for calculations performed on a personal computer the SABRE complex can comprise only up to 6 spins ½, whereas for bigger spin systems more powerful computational facilities are required. Alternatively, one can use a ¹H decoupling strategy proposed in this work. Moreover, proton decoupling during the pulse sequence not only simplifies the computation procedure but also increases the level of achievable polarization. Using quantitative SABRE model approach, we have shown that SLIC-SABRE method allows one to determine the effective lifetime of the complexes that varies from 8 ms to 476 ms with temperature variation from 35 °C down to 0 °C, and that is similar to the previously published INEPT-based analysis⁴⁰. When one determines an effective lifetime of the complex, the quantitative model can be used to predict the most appropriate low or high field conditions for any SABRE polarization transfer procedure. However, for evaluation of kinetic parameters the use of conventional EXSY experiments may still be more reliable. We believe that this work is important in the context that current elaborate SABRE theory give a hint but does not quantitatively reproduce experimental results, and further improvement of the theory is necessary.