In seeking a molecular scaffold to support a ¹⁹F spin pair of nearly-magnetic-equivalence, we speculated, based on visual inspection, that molecule I might be a suitable candidate. Moreover, the synthetic route described by Murai et al. (2022). appeared amenable for modification such that hydrogen atoms providing deleterious singlet relaxation mechanisms may be substituted with alternative groups possessing more desirable magnetic properties for our purposes. Accordingly, we prepared molecule I, and derivative molecules II and III, bearing deuterium and methoxy- d 3 groups respectively (Scheme 1). Attempts to access molecule II by performing hydrogen/deuterium exchange on a relatively advanced precursor 4 of the synthetic route to molecule I, via electrophilic substitution under acidic conditions, was unsuccessful. However, treating commercially available acid 5 with the same conditions gave the trideuterobenzoic acid 6 as the major isotopologue, along with small amounts of the dideutero- and monodeutero-isotopologues (11 percent in each case), both as isotopomeric mixtures. Subjecting this material to the Murai synthetic route provided molecule II. Esterification of the 3,4-difluorobenzoic acid 8 with methanol- d 4 , followed by nucleophilic aromatic substitution with methanol- d 4 and DBU gave 10 as a single regioisomer in 77 percent yield over two steps. Again, following the route of Murai furnished molecule III along with a small amount of the urea 11. Vapour diffusion provided diffraction quality single crystals of both molecule III and 11, from which coordinates were collected ² . For molecule III, the major occupant of the unit cell (c. 75 percent) has an F-F distance of 2.45 Å and the dihedral angle between the carbon fluorine bonds is 46.5° (see supplementary information).

Each of the three difluoro-substituted molecules I, II and III were dissolved in DMSO- d 6 and the solution transferred into a 5 mm OD LVP J-Young valved NMR tube for the NMR experiments described below. These solutions were degassed via N 2 bubbling to remove paramagnetic O 2 traces. The naming and details of the three samples so prepared are reported in Table 1 together with their main spin system parameters as obtained from ¹⁹F and ¹⁹F-{¹H} spectra.

NMR experiments where performed using two different NMR spectrometers: a 9.4 T Bruker magnet coupled to an Avance II console and equipped with a selective fluorine probehead for observation of ¹⁹F with ¹H decoupling and z-gradients, and a 1.02 T Magritek SpinSolve 40 Carbon desktop spectrometer operating at 43.4 MHz for proton. Measurements of T 1 decay constants were performed using conventional inversion recovery methods (Hahn, 1949). For the measurement of singlet order decay constants, T S , we used the methodology based on magnetization-to-singlet pulse sequence schemes described elsewhere (Pileio, 2017) and shown in Figure 1. Note that ¹⁹F signal detection for Sample A and Sample C (see below) was done in the presence of ¹H decoupling to collapse multiplets and obtain a neater signal from which to measure the decay constant (WALTZ-90° pulse duration τ w 1 H = 65.7 μ s , corresponding to a nutation frequency of 3.8 kHz). The measurements of T S was done with and without a CW irradiation scheme (nutation frequency 2 kHz) applied on the ¹⁹F channel during the singlet storage time (t) in order to verify the presence of relaxation through scalar coupling of the second kind mechanism.

The parameters occurring in the pulse sequence in Figure 1 are reported in Table 2.

The ¹⁹F-NMR spectrum of Sample A, taken at 9.4 T and 25°C, is reported in Figure 2A and shows a complex multiplet. The spectrum is shown using a frequency scale in Hz and has been centred at 0 Hz for simplicity (the chemical shift at the centre of the multiplet is −101.7 ppm). Based on visual inspection of the linewidth, it is clear that the fluorine nuclei are strongly coupled to each other and weakly coupled to possibly all other protons of the aromatic rings. This is easily confirmed by the ¹⁹F-{ ¹ H } NMR spectrum of Sample A, taken at the same field and temperature (shown in Figure 2B), where a strong AB pattern is what remains of the ¹⁹F peaks after proton decoupling. From the frequency value of the four peaks in Figure 2B we measured a J F F = 171.4 Hz and a difference in chemical shift frequencies of the two fluorine atoms of Δ δ F F = 0.142 ppm.

It is therefore clear that the ¹⁹F spin pair is not isolated from the other spins in the molecule and all coupled spins should be considered in the discussion. The presence of scalar coupling to neighbouring protons may give rise to three types of problem: i) The spin Hamiltonian contains cross terms that connect the ¹⁹F singlet state to the triplet states. In fact, ¹⁹F singlet spin order may be not a good eigenoperator of the Hamiltonian superoperator; ii) The scalar couplings between ¹⁹F and ¹H nuclei can give rise to relaxation via a scalar coupling of the second kind mechanism (S2K), which will shorten the lifetime of singlet order proportionally to the magnitude of the spin couplings involved and the size of the proton T 1 decay constant (Elliott et al., 2019; Pileio and Levitt, 2007); iii) The through-space dipolar couplings to the neighbouring protons give rise to an out-of-pair dipolar coupling relaxation mechanism (oDD) that contributes, and possibly dominates, the lifetime of ¹⁹F singlet order by reducing it by an extent that is proportional to the internuclear distances between ¹⁹F and ¹H nuclei (Pileio, 2011).

Fortunately, the large value of J F F stabilises the singlet spin order between the two ¹⁹F spins and ¹⁹F singlet order is expected to remain a good eigenoperator of the spin Hamiltonian superoperator (Pileio and Levitt, 2007). The presence of a contribution to singlet relaxation due to scalar coupling of the second kind can be qualitatively probed (and, eventually, minimized) by applying a Continuous Wave (CW) irradiation on the ¹⁹F channel (or, equivalently, on the ¹H or ²H channel) as explained in Elliott et al. (2019). Unfortunately, the out-of-pair dipole-dipole ¹⁹F-¹H interactions cannot be suppressed or minimised with radio-frequency-based techniques and this is likely to be the major deleterious contribution to the size of the ¹⁹F singlet order lifetime in this sample. Clearly, such interactions can only be removed by chemical substitution - see below.

With this in mind, we measured the relaxation decay constant of ¹⁹F longitudinal spin order ( T 1 ) and that of ¹⁹F singlet spin order ( T S ) in Sample A at 9.4 T and 25 ° C (data reported in Table 3). While the presence of ¹⁹F singlet order is guaranteed by the singlet-filter in the pulse sequence (it only allows through singlet order) its decay constant is disappointingly short and comparable to T 1 . This is somewhat expected for the reasons explained above, i.e., because both scalar and dipolar couplings to the neighbouring protons generate a significant relaxation mechanism for both T S and T 1 . To probe the presence and importance of a S2K relaxation mechanism, we measured the singlet order decay constant T S using the pulse sequence in Figure 1, but where a CW irradiation scheme is applied during the singlet storage period (t) in order to decouple the protons from the fluorine atoms and therefore minimize an eventual S2K relaxation contribution (Elliott et al., 2019) (data reported in Table 3). Since the resultant value of T S was only marginally longer than that measured in the absence of proton irradiation (compare column 5 and 6 in Table 3), we conclude that a scalar coupling of the second kind relaxation mechanism is not the limiting factor for the ¹⁹F singlet order lifetime in sample A. It is therefore reasonable to think that the short relaxation decay constant observed for ¹⁹F singlet order in Sample A is due to an oDD mechanism proportional to the size of ¹⁹F-¹H dipole-dipole couplings in the molecule. Clearly, we expect to have a contribution from chemical shift anisotropy (CSA) relaxation, a known important source of relaxation in ¹⁹F-NMR spectroscopy (Gerig, 2001), but, given the small difference between the T 1 at the two magnetic fields, this may not be the dominant one in this sample. Note that the chemical shift anisotropy mechanism acts differently on T S than on T 1 (Pileio, 2017) so the conclusion above can be challenged; however, it has not been possible to measure the T S at 1.02 T for Sample A because of the large number of echoes required in the pulse sequence (due to the small chemical shift frequency difference compared to the very large scalar coupling) and the relatively short T 2 .

Given that the non-bonding nature of the ¹⁹F-¹⁹F scalar coupling relies on partial orbital overlap, we decided to explore whether the magnitude of the J F F coupling depends upon temperature. To do so, we monitored the value of the ¹⁹F-¹⁹F scalar coupling and the difference in chemical shift between the two fluorine nuclei over a small temperature range (see Figure 3A). We observe a small linear decrease (slope = −0.586 ppb/°C) in the chemical shift difference as the temperature is increased. Similarly, the value of J F F increases linearly, but slowly, with temperature (slope = 0.05 Hz/°C). Additionally, we measured T 1 and T S decay constants at some selected temperature values between 20°C and 50°C, finding that both these constants increase almost linearly with temperature, although not by much (see Figure 3B). Such a trend correlates well with the reduction in viscosity of the solvent (literature data on (CH₃)₂SO show a reduction from 2.24 cP to 1.286 cP as the temperature is increased from 20 to 50 ° C).

In order to remove dipolar interactions with the neighbouring proton, we synthesised molecule II (prepared as Sample B, see Materials and Methods), which is an analogue of molecule I with the aromatic ring hydrogens substituted with deuteriums so to scale down the size of the ¹⁹F dipolar couplings by a factor of about six (the ratio between hydrogen and deuterium gyromagnetic ratios). The ¹⁹F-NMR spectrum of Sample B, taken at 9.4 T and 25°C, is reported in Figure 4, where a set of asterisks mark the four peaks of the expected AB pattern for the two fluorine peaks in the sample (couplings to neighbouring deuterium nuclei fall within the linewidth). Other than these four marked peaks, the spectrum shows a series of other minor peaks that are due to the trace isotopologues containing mixtures of hydrogen and deuterium atoms (see Section 2.1 and supplementary information).

A measurement of the longitudinal order decay constant at 9.4 T and 25°C on this sample resulted in a rather short value of T 1 = 1.31 ± 0.02 , which is only marginally longer than the one found for Sample A (see Table 3). This is not surprising since the value of T 1 for these two samples are expected to be dominated by the ¹⁹F-¹⁹F dipolar interaction relaxation mechanism. Unfortunately, the measurement of the singlet order decay constant in this sample, done in the same conditions and using the pulse sequence in Figure 1 and the parameters in Table 2, still resulted in a rather short value of T S that is only marginally longer than T 1 by a factor of 1.7 (see Table 3). These results led us to hypothesise that either the CSA relaxation mechanism dominates, or in substituting hydrogens with deuteriums we may have gained by minimising dipolar coupling interactions to hydrogens but reintroduced a more serious S2K mechanism. Unfortunately, it has not been possible to measure the T S of Sample B at 1.02 T, for the same reasons occurring in Sample A, nor the CSA contribution can be easily calculated in absence of the full chemical shift tensors of the two fluorine nuclei. Similarly, the S2K contribution depends on both the size of the scalar coupling between the fluorines and the deuterons and the relaxation time of these latter nuclei (for deuterium this is dominated by its quadrupolar coupling interaction) and therefore it is not easy to predict whether a deuterium is actually worse than a hydrogen in the vicinity of the fluorine, as it could be the case here. Fortunately, one can experimentally probe the presence of the S2K mechanism by measuring the T S decay constant with the pulse sequence in Figure 1 and in the presence of a CW irradiation applied during the time interval t. The results, obtained with a CW nutation frequency of 2 kHz applied on the ¹⁹F channel and reported in Table 3, did not show an extension in T S and therefore led us to conclude that S2K is not a limiting relaxation mechanism for Sample B.

As done for Sample A, we report the results of a series of experiments to study the temperature dependence of the spin system parameters (Figure 5A) and the relaxation decay constants T 1 and T S (see Figure 5B) for Sample B. Similarly to what seen in the previous section, even for Sample B we found a slow decrease (slope = −0.454 ppb/ ° C) of the difference in chemical shift between the two fluorine nuclei and a slow increase in the value of the ¹⁹F-¹⁹F scalar coupling (slope = 0.048 Hz/°C) as temperature is increased. Moreover, both T 1 and T S increase slightly with temperature but this seems again consistent with the decrease in solvent viscosity over that temperature range.

With the aim of removing any immediate nuclear spin coupled to the fluorine atoms, we synthesised a third molecule (molecule III in Scheme 1, prepared as Sample C as described in Materials and Methods) where we aimed to replace the closest spin to the two fluorine nuclei with - OCD 3 groups. The ¹⁹F-NMR spectrum of Sample C, taken at 9.4 T and 25°C, is reported in Figure 6A. It consists of an AB pattern where each transition is further split into two. This is compatible with a strongly-coupled ¹⁹F spin pair which is further coupled to one proton on the aromatic ring (and possibly to the other, although with a scalar coupling that falls within the linewidth). The pattern is compatible with these spin system parameters: J F F = 175.7 Hz, Δ δ F F = 1.028 ppm and J F H = 7.5 Hz. The proton-decoupled fluorine spectrum of the same sample is reported in Figure 6B and shows the simple AB pattern expected for the proton-decoupled ¹⁹F spin pair. The relatively large chemical shift difference between the two fluorine atoms corresponds to a chemical shift frequency difference of 387.2 Hz at 9.4 T. At such magnetic field, the condition J F F < Δ ω F F is not met and therefore singlet order is not a good eigenoperator of the spin Hamiltonian anymore and an RF irradiation (Pileio and Levitt, 2009) is required in order to lock such form of order. Moreover, the pulse sequences in Figure 1, designed for strongly-coupled/nearly-equivalent spin pairs, performs badly at producing singlet order in this regime. For this reason the pulse sequence reported by Sarkar et al. (2007) was used to measure the T S of Sample C at 9.4 T. The resulting T S values, reported in Table 3 with and without CW irradiation on the ¹⁹F channel, still show a relatively short singlet lifetime which is longer than T 1 by only a factor of around three. Note the importance of the CW decoupling which is in this case required because of the presence of a large chemical shift difference between the two fluorine spins (Pileio and Levitt, 2009).

At this point, we found it very interesting to prepare ¹⁹F singlet spin order in the low magnetic field of a desktop spectrometer operating at 1.02 T, where the chemical shift frequency difference is only 42.1 Hz and the two fluorine nuclei would remain strongly-coupled. For this, we coded the pulse sequence in Figure 1 into a Spinsolve and measured both T 1 and T S values of Sample C at 1.02 T, data reported in Table 3. The value of T 1 is essentially the same as in the other two samples, again this may simply reinforce the idea that T 1 in these molecules is dominated by the dipolar interaction between the two fluorine nuclei, with a small contribution from CSA (Ahuja et al., 2007; Pileio et al., 2012; Stevanato et al., 2015) (compare the values of T 1 at the two magnetic fields for all three molecules reported in columns 2 and 3 of Table 3). T S at 1.02 T, however, is appreciably longer than T 1 of the same sample at the same field, and also longer than the values of T S measured for the other two samples in this paper. While there is a clear contribution from CSA in determining such a long lifetime, this alone cannot justify the measured value (CSA scales with the square of the magnetic field). Hence, the mechanism(s) that set the limit to the observed value of T S are not fully clear from this set of experiments and further work needs to be done in terms of experimental measurements and numerical simulations. Preliminary relaxation data taken on ¹H and ¹³C nuclei in these molecules may suggest the presence of dimerization (or some other form of molecular aggregation) that, if present, would reduce the molecular tumbling correlation time and therefore scale down the absolute value of both T 1 and T S achievable in these molecules. Given the nature of the scalar coupling in these systems, arising from orbital overlap under steric constraints, it is also possible that scalar coupling of the first kind (S1K) plays a role in determining the size of singlet relaxation decay constants.