Singlet to triplet conversion in molecular hydrogen and its role in parahydrogen induced polarization

Abstract

Detailed experimental and comprehensive theoretical analysis of singlet–triplet conversion in molecular hydrogen dissolved in a solution together with organometallic complexes used in experiments with parahydrogen (the H₂ molecule in its nuclear singlet spin state) is reported. We demonstrate that this conversion, which gives rise to formation of orthohydrogen (the H₂ molecule in its nuclear triplet spin state), is a remarkably efficient process that strongly reduces the resulting NMR (nuclear magnetic resonance) signal enhancement, here of ¹⁵N nuclei polarized at high fields using suitable NMR pulse sequences. We make use of a simple improvement of traditional pulse sequences, utilizing a single pulse on the proton channel that gives rise to an additional strong increase of the signal. Furthermore, analysis of the enhancement as a function of the pulse length allows one to estimate the actual population of the spin states of H₂. We are also able to demonstrate that the spin conversion process in H₂ is strongly affected by the concentration of ¹⁵N nuclei. This observation allows us to explain the dependence of the ¹⁵N signal enhancement on the abundance of ¹⁵N isotopes.

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Introduction

Parahydrogen Induced Polarization (PHIP)^1–5 is a well-established low-cost tool to significantly enhance intrinsically weak NMR signals. PHIP makes efficient use of the spin order of parahydrogen (pH₂, the H₂ molecule in its nuclear singlet spin state) which is converted into observable NMR signals. The possibility to enrich the pH₂ component of hydrogen gas arises from the Pauli principle which dictates the total wave function of fermions to be antisymmetric under exchange. This couples the singlet (parahydrogen) and triplet (orthohydrogen) spin states of H₂ with even numbered and odd numbered rotational states respectively. As a result, cooling down hydrogen gas in the presence of a catalyst to low temperatures where only the rotational ground state is populated allows to produce hydrogen gas where all molecules are in the singlet state. Once formed and removed from the interconversion catalyst parahydrogen is relatively stable to spin-reequilibration. However, since pH₂ itself is NMR silent (as it has the zero magnetic moment) a suitable chemical processes must be harnessed to convert the spin order into an enhanced NMR signal. Such processes are given by catalytic hydrogenation reactions³ with pH₂ or by reversible interactions of pH₂ with an organometallic complex.^5,6 In the first method, hydrogenative PHIP, pH₂ is added to a substrate with an unsaturated C–C bond; when the “nascent” protons in the reaction product stemming from pH₂ are non-equivalent (chemically or magnetically), one can obtain strong NMR signal enhancements. In the second method, termed Signal Amplification By Reversible Exchange (SABRE), pH₂ and a to-be-polarized substrate bind to an Ir-based complex, where spin order transfer gives rise to polarization of the substrate. An advantage of the SABRE method is that the substrate and pH₂ only bind to the complex transiently, i.e., they are not consumed, and dissociation of substrate from the complex results in the formation of hyperpolarized free substrate molecules in solution. Hence, the substrate can be re-polarized multiple times by supplying pH₂ to the solution. The SABRE method can be used to enhance NMR signals of protons,^6,7 and “insensitive” nuclei such as ¹⁵N and ¹³C^8–15 and to polarize various molecules, notably, biomolecules,^16–18 metabolites,¹⁹ oligopeptides,²⁰ and drugs.^21–23 The possibility to continuously repeat SABRE measurements with high level of reproducibility opens great perspectives for mixture analysis²⁴ and reaction monitoring²⁵ by means of SABRE.

Both hydrogenative PHIP and SABRE have been successfully applied to hyperpolarize various compounds; however, the optimization of hyperpolarization experiments still remains challenging. Specifically, reaction conditions have to be optimized, as well as polarization transfer efficiency. In this work, we address one more issue, which turns out to be important in both PHIP and SABRE. Specifically, we address the question: “What is the spin order of H₂ in PHIP/SABRE experiments?”. At the first glance, this question seems to make no sense, as we always introduce pH₂, i.e., two protons in the nuclear singlet spin state, into the chemical reaction. However, this obvious answer holds only in the gas phase, where conversion between pH₂ and triplet H₂ (orthohydrogen, oH₂) is a very slow process. For the actual PHIP and SABRE processes the answer is not so obvious because pH₂ binds to a PHIP substrate or SABRE catalyst in such a way that the two protons occupy non-equivalent positions. In this situation, their magnetic or chemical equivalence is broken and singlet–triplet conversion in H₂ becomes operative. It is important to note that the conversion is not equivalent to a simple decay of singlet spin order via relaxation, since hyperpolarized oH₂ can be formed in a strongly non-equilibrium state, as has been confirmed by several groups.^26–28

The aim of this work is to study in detail spin conversion of H₂ and to characterize its actual spin state. Here we perform the study for a SABRE system (using an Ir-based catalyst) and measure the SABRE-derived enhancement of ¹⁵N spins. By introducing radio-frequency pulses on the proton channel (which have no effect pH₂ since it is in a rotation-invariant singlet state, but modify the state of oH₂) we are able to probe the amount of pH₂ and to determine the state of non-thermally polarized oH₂. Furthermore, we reveal the influence of the magnetic ¹⁵N isotope on the singlet–triplet conversion in complex-bound H₂. This effect is conditioned by a weak symmetry breaking resulting in magnetic non-equivalence of the chemically equivalent pH₂-nascent protons in the SABRE complex. The study presented here is driven not only by general interest and curiosity, but has important practical consequences for optimizing PHIP and SABRE experiments and for achieving the highest possible NMR signal enhancement. There are two reasons for this. First, the lifetime of the spin order of H₂ (which is the source of NMR signal enhancement) is important to achieving maximal polarization. Second, some of the pulse sequences for transferring spin order from H₂ have been designed assuming that the initial spin order of the two protons is a pure state of singlet order: such pulse sequences might become inefficient when the spin state of H₂ is a mixture of pH₂ and oH₂. We clearly show in this work that the formation of hyperpolarized oH₂ is an important factor in PHIP and SABRE, which has a strong influence on the resulting NMR signal enhancement.

Methods

Sample preparation

All experiments presented here were done for a SABRE system using the IrCl(COD)(IMes) complex,²⁹ where IMes = 1,3-bis(2,4,6-trimethylphenyl)imidazole-2-ylidene and COD = cyclooctadiene; activation of this pre-catalyst by hydrogenation of COD and addition of pyridine forms the main dihydride Iridium complex [Ir(H)₂(IMes)(Py)₃]⁺, with Cl⁻ as a counter ion (Py = pyridine). The structure of the SABRE complex is given in Fig. 1. The SABRE process in this system is due to exchange of H₂ and Py between their free forms in solution and bound forms. It is important to note that in methanol solution there is also exchange³⁰ between the main complex and two other complexes: one with a Cl⁻ and one with an equatorial Py ligand replaced by a methanol solvent molecule. In these complexes the pH₂-nascent protons are chemically non-equivalent, which strongly affects³⁰ the spin conversion. To simplify the reacting system, we have replaced the Cl⁻ counter-ion with PF₆⁻, which does not bind to the complex. As previously described³⁰ this can be achieved by adding AgPF₆ and removing the resulting AgCl precipitate from the sample. As a SABRE substrate, we used either ¹⁵N-labelled Py-d₅ or mixtures of ¹⁵N–Py-d₅ and ¹⁴N–Py-d₅, thus varying the abundance of the spin-1/2 ¹⁵N isotopes. Using a deuterated substrate allowed to simplify the spin system and, hence, to ease the optimization and interpretation of SABRE experiments. In all experiments the sample temperature was 25 °C.

Fig. 1 Structure of the iridium SBRE complex; molecular hydrogen and the substrate (with two Py ligands in equatorial positions, and a third Py in an axial poisiton) are indicated. The spin system of the SABRE complex is also shown, here modelled as an AA′MM′ system (A-spins stand for the pH₂ protons and M-spins belong to the ¹⁵N nuclei of the two equatorial Py ligands).

The spin system of the main SABRE complex can be modelled as an AA′MM′ system, as shown in Fig. 1. Here the A-spins stand for the protons originating from pH₂, while the M-spins are the ¹⁵N nuclei of the two equatorial Py ligands.

NMR experiments

NMR experiments were mostly carried out at high magnetic fields using the protocols shown in Fig. 2. To polarize the ¹⁵N nuclei we used pulse sequences with radiofrequency (rf) pulses applied to the ¹⁵N channel. For transferring spin order from pH₂ essentially a single long ¹⁵N pulse of a low intensity is used, hereafter called pseudo continuous-wave (“pseudo cw”) pulse.

Fig. 2 Experimental protocols used to run high-field SABRE experiments, aimed at enhancing ¹⁵N signals of free Py in solution. pH₂ is supplied to the sample using an automated bubbling device. The pseudo cw pulse on the ¹⁵N channel is applied either exactly on resonance of the complex bound Py (b and d) or slightly off-resonance (a and c); in the former case an additional 90° pulse is used to generate the longitudinal polarization. In (a and b) no pulses are applied on the proton channel, whereas in (c and d) 90° pulses on the proton channel are used. After each cycle Py-ligands bound to the Ir complex are polarized; this polarization is transferred to free Py in solution via ligand exchange. The polarization cycle is repeated n times and the ¹⁵N NMR signal is acquired after applying a 90° pulse. The delay between the cycles is equal to t_d and the duration of the ¹⁵N pseudo cw pulse is denoted as t_cw.

When the parameters of the rf field applied to the ¹⁵N channel are properly set, proton singlet spin order is transferred to ¹⁵N spins in the SABRE complex. Specifically, the effective field ω_eff (given in the frequency units) should be matched^9,31,32 to a certain combination of scalar J-couplings in the AA′MM′ system. The effective field is given by the vector sum of the transverse rf-field (in the rf-rotating frame) and the longitudinal field given by offset from resonance where ω₁ is the rf-field strength and Δ the resonance offset. A more detailed discussion of the definition of Δ for the system under study is given below. In the case of single-resonance experiments (excitation only on the ¹⁵N channel) the source of polarization is given by the population difference of the singlet and central triplet states of H₂. As we show below, this feature is critical for the performance of the pulse sequences.

The magnetization transferred to the ¹⁵N nuclei is parallel to the effective field. Hence, it is a purely transverse magnetization when Δ = 0 (on-resonance excitation); whereas for Δ ≠ 0 the magnetization has a longitudinal component. In SABRE, one seeks to generate polarization of the free substrate molecule via chemical exchange. Upon exchange, longitudinal polarization of the bound species is transferred to the free substrate pool. Thus, in the case of resonant excitation, an additional 90° pulse should be inserted to convert transverse into longitudinal polarization; when Δ ≠ 0 this may be not necessary. To maximize ¹⁵N signal enhancement, the polarization transfer cycle is repeated n times.³¹ For this reason, the additional 90° pulse should be selective, exciting only the bound substrate, but not its free form in solution. Finally, after applying a 90° pulse, the ¹⁵N Free Induction Decay (FID) signal is acquired (its Fourier transform gives the NMR spectrum). Two of the pulse sequences shown in Fig. 2 exploit resonant rf-excitation (Fig. 2b and d), whereas the other two make use of off-resonant excitation (Fig. 2a and c). The sequence in Fig. 2b is known as LIGHT-SABRE (Low-Irradiation Generation of High Tesla-SABRE).³¹

Two of the pulse sequences (Fig. 2c and d) in Fig. 2 comprise a modification which would be meaningless if we were dealing only with pure rotation-invariant singlet order: this is a 90° pulse applied to the proton channel. It turns out that this pulse strongly affects the performance of the polarization transfer experiment if some hyperpolarized oH₂ is generated. In this work, we analyse the effect of proton pulses with arbitrary nutation angles on the ¹⁵N NMR signal enhancement. The pulse sequences given in Fig. 2c and d are known⁹ as SLIC-SABRE (Spin-Locking Induced Crossing SABRE³³).

In addition to high-field NMR experiments, we also performed field-cycling NMR studies, in which polarization was allowed to build up by SABRE at an ultralow magnetic field (in the range 10 nT < B₀ < 1 μT). Subsequently the hyperpolarized sample is transferred to an 400 MHz NMR spectrometer (B₀ = 9.4 T). To run such experiments, we used a home-built device for sample shuttling with a set of coils inside the magnetic shield, as described before.^11,34

All NMR spectra were recorded using a 400 MHz Bruker NMR spectrometer. In all high-field SABRE experiments the para-component of H₂ was enriched to 85% by using a commercial Bruker parahydrogen generator. In ultralow field experiments we have used 95% enriched pH₂, obtained by cooling down H₂ in a helium cryostat CFA-200-H2CELL (CryoPribor). The pH₂ bubbling pressure was equal to 2 bar. The signal enhancement factor ε (ratio of the hyperpolarized ¹⁵N NMR signal and thermal signal both measured at 9.4 tesla) gives a measure of polarization.

Results and discussion

Theoretical analysis of singlet–triplet conversion

To analyse singlet–triplet conversion in H₂ and to optimize the pulse sequences we used spin dynamics simulations and additionally took into account exchange of H₂ or SABRE substrate.

In order to consider spin conversion in molecular hydrogen, we introduce a set of equations for the spin density operators, σ_f and σ_b, of free and bound H₂, respectively:

Here Ĥ_f,b stand for the Hamiltonians of the free or bound H₂ (all Hamiltonians are given in ħ units); are the corresponding relaxation superoperators; k_as is the rate of association of H₂ to form the Ir-based complex and k_dis is the dissociation rate of molecular hydrogen from the complex. Here, we choose the normalization Tr{σ_f} + Tr{σ_b} = 1. In this case, the total probability of finding H₂ either in the free form (σ_f) or in the bound form (σ_b) is equal to unity, but not their individual traces.³⁵ This model is sufficient to simulate singlet–triplet conversion, which gives rise to hyperpolarized oH₂. To carry out these simulations, we introduce Ĥ_f,b in the rotating frame (this is done to ease numerical calculations and to get rid of the large nuclear Zeeman interaction with the B₀ field, which is parallel to the z-axis). For simplicity, we take the frequency of the rotating frame equal to the NMR frequency of free H₂, so that Ĥ_f = 0 and Ĥ_b = Ω₁Î_1z + Ω₂Î_2z (here Î₁ and Î₂ are the spin operators of the two non-equivalent bound protons, Ω_1,2 are their NMR frequencies in the rotating frame). In fact, the only relevant parameter in Ĥ_b is the frequency difference δω = |Ω₁ − Ω₂|. Indeed, it is the term
which is responsible for driving the transitions between the singlet state |S〉 and central triplet state |T₀〉, as illustrated by the vector diagram³⁶ in Fig. 3. Setting δω ≠ 0 we assume that the chemical equivalence of the two protons in the complex is broken, giving rise to a non-vanishing difference in their chemical shifts. Alternatively, symmetry breaking can be due to magnetic non-equivalence, i.e., caused by a difference in J-couplings with other spin-1/2 nuclei present in the complex. In both cases we achieve δω ≠ 0. The singlet–triplet states are introduced in the usual way:
where |α〉 and |β〉 are the states of a spin-1/2 particle with z-projections equal to , respectively.

Fig. 3 Diagram explaining singlet–triplet conversion for δω ≠ 0. The arrows stand for the spin vectors of the two protons, the |S〉 state is the state with anti-parallel spins while in the |T₀〉 state the total spin is non-zero but its z-projection is zero. The spins precess about the B₀ field at different frequencies: faster precession of one of the spins (for simplicity, we assume that only I₂ precesses) gives rise to coherent S–T₀ mixing, i.e., |S〉 goes to a superposition of |S〉 and |T₀〉, then to |T₀〉, then again to a superposition and so on.

As far as relaxation effects are concerned, we merely consider the simplest case of relaxation driven by fluctuating local fields experienced by the two protons, ignoring the fluctuations of their mutual dipole–dipole coupling. We also assume that the local fields are almost completely correlated, which implies that they efficiently drive the transitions between the triplet states, but not the transitions between the singlet state and triplet states. Hence, in the absence of exchange, singlet–triplet conversion takes infinitely long (in experiments, conversion in the absence of a SABRE catalyst is indeed a very slow process). Precise details and parameters of the model are given in ESI,† as well as the method for numerical solution of the set of equations.

According to the model outlined above, singlet–triplet conversion in H₂ occurs in the following way. When H₂ binds to the complex, the chemical equivalence is lifted so that coherent transitions between the |S〉 and the central |T₀〉 states become operative. As a result, the population is distributed between these two states. This gives rise to formation of oH₂ in a non-equilibrium spin state. Subsequently, spin relaxation comes into play and tends to equalize the populations of the three triplet states; eventually, all four states acquire the same population. The rate of the first conversion step S → T₀ critically depends on δω, k_as and k_dis. Simulations assuming an initial |S〉 state of H₂ are shown in Fig. 4 for different δω values, presenting the time dependence of the populations of the |S〉, |T₀〉 and |T_±〉 states, and of the population imbalance δP = P_S − P_T0. When δω is small, the conversion process is very slow (just like the inefficient singlet–triplet relaxation in free H₂). As δω increases, the populations of the |S〉 and |T₀〉 states are redistributed in a coherent fashion via spin mixing in the complex and P_T0 ≠ 0. As the central |T₀〉 state gets populated, relaxation between the triplet states also populates the |T_±〉 states, P_T± ≠ 0. Hence, spin order conversion is a two-step process. With the parameters chosen in Fig. 3, the |S〉 and |T₀〉 state populations are rapidly equilibrated and δP → 0, whereas the |T₀〉 population remains different from that of the |T_±〉 states for longer time. Moreover, introducing the spin–spin coupling constant between two hydrid protons J_HH alters the described behavior, especially for the case of moderate δω values. This coupling induces the energy splitting between the singlet and the triplet manifolds, thus decreasing the rate of S → T₀ transitions. However, when δω exceeds J_HH, the process of δP reduction is very similar to the case of J_HH = 0.

Fig. 4 Theoretical time dependence of the spin state populations of H₂ and the population difference δP = P_S − P_T0 in the presence of exchange between bound and free hydrogen. Calculation parameters: k_as = 6 s⁻¹, k_dis = 60 s⁻¹, for all subplots; the δω/2π equal to 0 Hz (subplots a and b), 2 Hz (subplots c and d), 5 Hz (subplots e and f), and to 20 Hz (subplots g and h); the spin–spin coupling constant between two hydrid protons J_HH = 0 Hz (left column), and J_HH = −7 Hz (right column). The relaxation model considers only fluctuating local fields, experienced by the two spins, which are modelled as almost completely correlated, so that singlet–triplet relaxation transitions are slow, as compared to transitions within the triplet manifold (see ESI† for a detailed explanation).

Optimization of the pulse sequence

Before comparing the performance of the pulse sequences of interest, we optimized the experimental parameters, such as the delays t_d and t_cw and the number of cycles n. The dependence of the enhancement on these parameters is presented in ESI.† In the experiments presented below we always set t_d = 500 ms, t_cw = 39 ms and n = 50, which provide substantially improved signal enhancements.

To optimize the performance of the pulse sequence, it is necessary to set the optimum resonance offset Δ for the pseudo cw pulse. As pointed out above, the optimization is different for a single pulse and for a pulse followed by an additional 90° pulse. This is indeed the case, see Fig. 5. When no extra pulses are used, the resulting longitudinal ¹⁵N polarization vanishes for Δ = 0 (the spins are polarized parallel to the effective field, and therefore do not have any longitudinal component). When an additional 90° pulse is used to convert the transverse polarization into longitudinal polarization, the resulting polarization is maximal for Δ = 0. The Δ-dependence of polarization shows positive and negative extrema, see Fig. 5a, corresponding to matching of the energy levels of the AA′MM′ spin system in the rotating frame, as explained before.⁹ To make the pulse sequences work one should also optimize the ω₁ value:⁹ when ω₁ is very small, spin mixing is inefficient, whereas if ω₁ is much larger than the relevant J-couplings, the matching conditions can no longer be fulfilled (this is the reason for using a low-intensity cw rf pulse). In the experimental ω₁ dependence of the enhancement, see Fig. 5b, the peak corresponds to the matching condition.

Fig. 5 (a) Dependence of ¹⁵N polarization in the SLIC-SABRE method on the offset Δ shown for different ω₁ values: ω₁/2π = 5 Hz (squares), ω₁/2π = 10 Hz (circles) and ω₁/2π = 15 Hz (triangles). (b) Dependence of ¹⁵N polarization on the rf nutation frequency ω₁ for SLIC-SABRE with an off-resonant pulse (for Δ = −14 Hz). The experiments were performed with substrate concentration [S] = 95 mM and catalyst concentration [C] = 7 mM; the polarization is normalized to its maximal value in both cases.

NMR signal enhancement

We have optimized the relevant experimental parameters for all four protocols shown in Fig. 2. One can see that using off-resonant excitation with a small Δ value one can achieve higher ε values, see Fig. 5. Although the theoretical treatment suggests that the efficiency of the scheme should be the same or even higher for resonant excitation (Δ = 0); this experiment is more difficult to optimize, in particular, when chemical exchange is constantly going on, as is the case in SABRE. The enhancements obtained by these two methods are moderate, ε ≈ 30 for resonant excitation and ε ≈ 150 for off-resonance excitation, for the experimental conditions used here. We attribute this to efficient S–T₀ conversion, rendering δP small. Since this population imbalance is the source of non-thermal spin order, the signal enhancement factors become low.

A simple way to re-introduce the δP population imbalance is to exploit the difference in populations between the |T₀〉 and |T_±〉 states. This can be done in different ways.⁹ Here we investigate the simple method of using a single 90° pulse on the proton channel. In this situation, the state populations change as follows (we assume that before applying the pulse P_T+ = P_T− = P_T±):

Here the populations with primes stand for the state populations after applying the pulse. Hence, the P_S population remains the same (as the singlet state is invariant to rotations), whereas the P_T0 population is altered. Hence, δP changes from the value {P_S − P_T0} to δP′ = {P_S − P_T±}. Assuming that S–T₀ conversion is considerably more efficient than S–T_± conversion, one should expect that δP should increase significantly, as should the resulting enhancement.

To exploit this effect, we have run two more experiments (with on- and off-resonance excitation) using an additional 90° proton pulse prior to the polarization transfer sequence. As one can see from Fig. 6, the resulting enhancement dramatically increases for both transfer schemes, here approximately by a factor of 7. This is a clear indication that fast and efficient S–T₀ conversion in H₂ is indeed taking place in the studied sample. Comparison of the pulse sequences also shows that applying a 90° proton pulse is indeed an efficient way to re-establish the desired S–T₀ population difference.

Fig. 6 Comparison of the polarization transfer schemes shown in Fig. 2. LIGHT-SABRE scheme with off-resonant CW pulse followed by a selective 90° proton pulse (a) and on-resonant CW ¹⁵N pulse (b). SLIC-SABRE scheme (with an additional hard 90° proton pulse before polarization transfer) with off-resonant CW ¹⁵N pulse followed by a selective 90° ¹⁵N pulse (c) and an on-resonant CW ¹⁵N pulse (d). Thermal signal acquired with 256 transients is presented as a reference (e). Experimental parameters: [S] = 95 mM, [C] = 7 mM, ω₁/2π = 10 Hz, n = 50, t_d = 500 ms, t_cw = 39 ms, Δ/2π = −14 Hz (for off-resonant excitation).

One should note that the resulting ¹⁵N spectra yield a broadened NMR signal with a non-Lorentzian lineshape. This is a result of exchange of deuterons in the ortho-positions of Py with dihydrogen protons, which leads to the formation of three isotopomers of free pyridine, with D–D, H–D and H–H nuclei in the ortho-positions.¹⁰ Since each isotopomer has its own spin system, the spectral pattern becomes more complex and contains several components. However, the signal of fully deuterated pyridine dominates over any other signal in the resulting ¹⁵N spectra,

The improvement of the enhancement ε by a factor of 7 allows one to calculate the populations of the spin states of H₂. Here we do so assuming that (i) ε is proportional to δP and (ii) P_T± = 0.05 (this corresponds to 85% of pH₂ enrichment). Hence, if we set P_S = x before the pulse is applied, we obtain that P_T0 = 0.9 − x. After application of the pulse we obtain and . Consequently,

Hence, we obtain about 48% of H₂ in the |S〉 state and about 42% in the |T₀〉 state and 10% in the |T_±〉 states, i.e., a relatively small population difference of about 6%. After applying the additional pulse it increases to as much as 43%.

Singlet–triplet conversion

Inspired by the strong, approximately 7-fold, improvement of ε provided by the pulse applied to protons, we decided to look more closely at the singlet–triplet conversion efficiency. To this end, we have varied the length of the proton pulse and measured ε as a function of the flip angle φ of this pulse, see Fig. 7a. The experimental data were fitted by the periodic function ε(φ) = a₁ − a₂ cos(2φ), with the maxima at φ = (1/2 + m)π and the minima at φ = mπ (m is an integer number). The maximal value is ε_max = a₁ + a₂ ∝ δP′ and the minimal value is ε_min = a₁ − a₂ ∝ δP. The ratio
thus can be used to characterize the efficiency of the S–T₀ conversion process, which is due to symmetry breaking in H₂ bound to the SABRE complex. Symmetry breaking can be due to the chemical shift difference between the two protons and/or to subtler effects of J-couplings. In the SABRE complex, the ¹H–¹⁵N J-couplings are sizeable; furthermore, there is a large difference in the couplings J_AM = J_A′M′ and J_A′M = J_AM′, so that it has been estimated that δJ = J_AM−J_A′M ≈ 20 Hz. As a consequence, the two pH₂-nascent protons become magnetically non-equivalent and the effective δω value becomes non-zero.

Fig. 7 (a) The dependence of ¹⁵N signal enhancement on the flip angle φ of the proton pulse. The experiments were performed with [S] = 95 mM and [C] = 7 mM, deuterated ¹⁵N-enriched Py was used. Experimental parameters: ω₁/2π = 10 Hz, n = 50, t_d = 500 ms, t_cw = 39 ms, offset Δ/2π = −14 Hz. (b) The dependence of ¹⁵N signal enhancement ratio on the percentage of ¹⁵N enrichment of pyridine in the solution, measured for [C] = 2 mM (squares) and 9.5 mM (circles). [S] is equal to 190 mM (total concentration of ¹⁴N–Py and ¹⁵N–Py); straight lines are drawn to guide the eye. We used solutions after ion exchange with AgPF₆.

We have studied the effect of symmetry breaking through magnetic non-equivalence by varying the enrichment of ¹⁵N nuclei, i.e., by using a mixture of ¹⁴N–Py and ¹⁵N–Py (the fast relaxing quadrupolar ¹⁴N nuclei do not alter the spin dynamics of the proton system).

In Fig. 7b, the ratio is plotted as a function of the fraction of ¹⁵N nuclei (we used three values, η_15N = 10%, 30% and 100% of ¹⁵N–Py) and measured the dependence for two different concentrations [C] of the catalyst. We have set the total concentration of substrate (both ¹⁵N labelled and non-labelled) equal to 190 mM in order to achieve sufficient signal-to-noise ratio in cases where the SABRE signal was low, i.e. LIGHT-SABRE experiments with an ¹⁵N enrichment η_15NZ = 10%. One can see that the effect of ¹⁵N spins is significant, in particular, at low [C] concentration, where the violation of magnetic equivalence of the protons in bound H₂ is the dsominant mechanism. Note that increases from 1 for η_15N = 10% to approximately 5 for η_15N = 100%. For higher concentrations [C] other conversion mechanisms come into play as well, most likely coming from other complexes with molecular hydrogen. This follows from the fact that = 5 for η_15N = 10%. Nonetheless, the contribution of magnetic non-equivalence to symmetry breaking is still significant in this case, as increases by roughly a factor of 2 for η_15N = 100%. Remarkably, at high [C] and for η_15N = 100%. Hence, the contribution of symmetry breaking driven by scalar ¹H–¹⁵N couplings in the SABRE complex to overall conversion is significant. Furthermore, this contribution strongly affects the resulting enhancement.

Ultra-low field experiments

In this context, it is interesting to estimate how the resulting ¹⁵N enhancement depends on the abundance of ¹⁵N nuclei in the SABRE substrate. The experimental data shown in Fig. 7 do not give a complete and clear answer to this question: in this figure, only relative ε values are presented, but not the actual values of the enhancement. Furthermore, high-field experiments are not suitable for this purpose, because the pulse sequences have been optimized for a complex with two ¹⁵N nuclei, whereas at lower ¹⁵N abundance a fraction of the complexes have only one ¹⁵N nucleus (at low ¹⁵N abundance the fraction of the complexes with two ¹⁵N nuclei become negligible). The parameters of the complexes with one or two ¹⁵N nuclei are quite different; consequently, for such complexes optimal ε may be achieved for different ω₁ and Δ values. As a result, direct comparison of ε values measured at different ¹⁵N abundance becomes problematic.

To get around this problem, we have decided to measure ε at ultralow magnetic fields, where the ¹H and ¹⁵N nuclei become strongly coupled and “spontaneous” polarization transfer without rf-excitation between them becomes efficient. This is the essence of the SABRE-SHEATH method.^21,37,38 It is important to note that at ultralow fields the chemical shift difference of the protons bound to the SABRE complex is of no importance, so that symmetry breaking (and hence, singlet–triplet conversion) occurs solely due to magnetic non-equivalence. Furthermore, there is no need to analyse the spin dynamics in additional complexes, which strongly affect the para-to-ortho conversion at high field. Although at ultralow fields we are unable to run experiments to elucidate the relative populations of different spin states since we cannot apply any pulses to the protons, we can measure ε over a wide range of fields.

Comparison of the SABRE field dependences measured as a function of the ¹⁵N enrichment (at the same total concentration of ¹⁵N–Py and ¹⁴N–Py) is shown in Fig. 8. The measured signal enhancement indicates that the SABRE polarization efficiency at ultra-low field increases when the abundance of ¹⁵N nuclei is lowered. It is noteworthy that the position of the maximum of the field dependence also depends on the concentration of labelled substrate, which is due to the difference in the parameters of the spin system of the SABRE complex for each specific solution.

Fig. 8 Magnetic field dependence of the ¹⁵N signal enhancement under ZULF conditions (5 nT < B₀ < 100 μT), obtained for the percentage of ¹⁵N pyridine in the solution, measured for [C] = 2 mM, while [S] = 40 mM (= total concentration of ¹⁴N–Py and ¹⁵N–Py) was kept constant. We used solutions without removing Cl⁻.

We attribute these results to conversion between different forms of H₂, driven by the interaction with ¹⁵N spins. Such interactions not only give rise to spin order transfer to the nitrogen spins, but also to singlet-to-triplet conversion in bound H₂, by perturbing the spin state of H₂. As a consequence, at high concentration of ¹⁵N isotopes, pH₂ is converted to thermally polarized H₂, which can no longer provides any NMR enhancements. When the abundance of ¹⁵N nuclei is low, the source spin order survives for a longer period of time, giving rise to a stronger ¹⁵N signal enhancement. Our observations also explain why ¹⁵N-NMR enhancement factors are so high, of the order of 30 000 for natural isotopic abundance (which is only 0.365%).²² The absolute signal intensity, which is given by the product of the concentration (proportional to η_N, the fraction of ¹⁵N containing molecules) and the maximal enhancement ε_opt, is the highest for large η_15N. The reason is that at low η_15N¹⁵N containing molecules very seldom bind to the SABRE complex, resulting in slow polarization build-us and lower signal intensity.

Another effect, which supports our conclusions, is the striking dependence of SABRE enhancement levels on the pH₂ bubbling pressure. The results of SABRE experiments performed at bubbling pressures in a range from 5 to 25 bars are presented in ESI† (Fig. S3). The linear growth of SABRE enhancement with increasing bubbling pressure (which leads to an increasing pH₂ concentration in the sample) demonstrates that the excess of fresh pH₂ in the solution attenuates the negative effect of singlet–triplet conversion. However, it is noteworthy, that even at 25 bar with reasonable gas flow rates, the enhancement level does not reach saturation, which possibly indicates the substantial effect of singlet–triplet conversion even at ultra-low field conditions.

Conclusions

Our work gives a clear evidence that singlet–triplet conversion in bound H₂ plays an important role in SABRE experiments. Due to the spin dynamics, this conversion becomes fast in the Iridium complex. An important feature of this conversion is that it favours one of the three triplet states, here to the central triplet state, producing polarized oH₂ that does not obey a Boltzmann distribution. This can be unequivocally proven by running polarization transfer experiments with an additional pulse applied to the proton channel. Such experiments allow one to estimate the populations of the three spin states of oH₂ experimentally. In the present case, the additional proton pulse giving rise to a strong additional gain in ¹⁵N signal, which is more than 10-fold in some cases. Hence, studying the conversion process is not a matter of pure curiosity, but it is of great practical importance for the performance of the SABRE method. In addition, we demonstrated that the conversion process is strongly affected by the presence of ¹⁵N nuclei, which make the pH₂-nascent protons in the complex magnetically inequivalent. This effect is of great importance for polarization transfer experiments at ultralow fields, where the signal enhancement decreases when the isotopic abundance of ¹⁵N nuclei is increased. The reason is that the limited source of pH₂-derived polarization is exhausted upon polarization transfer to ¹⁵N nuclei.

Thus, we can conclude that spin order conversion processes from pH₂ to oH₂, and within the triplet manifold of oH₂ are an important for the success of PHIP and SABRE experiments. We believe that consideration of these processes and corresponding optimization of experimental parameters (concentrations, extent of isotopic labelling, pH₂ pressure, parameters of NMR pulse sequences) can significantly improve the signal enhancements that can be achieved by PHIP and SABRE.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Financial support for the theoretical part by the Russian Science Foundation (grant No. 20-62-47038) is gratefully acknowledged. We acknowledge the Ministry of Science and Education of RF (contract No. 075-15-2021-580) for providing financial support for the experimental work at ITC. Prof. Geoffrey Bodenhausen (ENS, Paris) suggested several editorial changes. Prof. Konstantin L. Ivanov passed away on the 5th of March, 2021 at the age 44. In his early career, he made major contributions to the theory of chemical reaction kinetics in liquid phase. Later, he significantly contributed to unraveling the mechanisms of light-induced nuclear hyperpolarization in liquids and solid state using the concept of level anti-crossing (LAC). In recent years, his main research efforts, both theoretical and experimental, were concentrated on spin and chemical dynamics in PHIP and SABRE methods using LAC; for this, he was awarded the Günther Laukien Prize in 2020. He also was the scientific PhD adviser of two authors (DAM and VPK). Theoretical explanation of singlet to triplet conversion of nuclear spins molecular hydrogen and its experimental verification was his last project. He worked on this manuscript shortly before being deadly infected.

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Footnotes

† Electronic supplementary information (ESI) available: Model of S–T conversion and optimization of experimental parameters. See DOI: 10.1039/d1cp03164c

‡ These authors have contributed equally.

§ Konstantin Ivanov deceased on March 5th 2021.

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