Manipulating and quantifying spin state in solution as a function of pressure and temperature

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Determining the spin state of a system is fundamental to understanding its magnetic properties and chemical reactivity. The study of molecular magnetic phenomena 1 relies upon the measurement of spin states under different conditions. Understanding reactivity 2 and catalytic processes 3 is greatly aided by being able to determine the spin states of various reactants, intermediates and products. Measurements of spin states in the solution phase are of particular importance, especially for the study of biologically relevant processes, including photosynthesis 4 and iron-containing enzyme activity, 5 noting that life persists at pressures in excess of 100 MPa (B1000 atmospheres). However, there is no established method of quantifying spin states in solution as a function of both pressure and temperature.
The application of hydrostatic pressure to spin-labile compounds typically favours the low spin (LS) state due to the smaller molecular volume compared to the high spin (HS) state. 6 While this has been observed in pressure-induced solution spin crossover (SCO), by the Gouy method, 7 and UV-vis 8 and 1 H NMR 9 spectroscopies, these have all been qualitative measures of spin states. Herein, we establish a method for the accurate quantitative measurement of spin states in solution at variable pressures and temperatures, by extension of the ambient pressure Evans 1 H NMR 'tube-in-tube' method 10 to enable the use of a 'single-tube' that can be pressurised to 240 MPa. In addition to quantitative spin-state information, the 1 H NMR spectra themselves can also yield useful chemical and 3D structural information about the subject complex. 11 Thus, this method adds spin-state capabilities to high-pressure NMR techniques such as those already applied to host-guest, 12 catalytic, 13 and biomacromolecular systems. 14 In order to develop this method of quantifying solution spin states under pressure, three of our recently reported solution-phase (thermally-induced) SCO-active dinuclear iron(II) complexes of 4-substituted-3,5-bis{[(2-pyridylmethyl)-sulfanyl]methyl}-4H-1,2,4triazole (PSRT) ligands, where R = Ph, Me Ph or i Bu, i.e. [Fe 2 (PSPhT) 2 ]-(BF 4 ) 4 , [Fe 2 (PS Me PhT) 2 ](BF 4 ) 4 , and [Fe 2 (PS i BuT) 2 ](BF 4 ) 4 ( Fig. 1), were investigated by high-pressure 1 H NMR spectroscopy. Spectra were recorded in CD 3 CN solution at 30 MPa intervals between 0.1 MPa (atmospheric pressure) and 240 MPa, and at 5 different temperatures in the range of 278-313 K.
In each spectrum ( Fig. 2 and Fig. S1-S3, ESI †), very broad and highly downfield shifted (up to B100 ppm) proton signals typical of a paramagnetic substance are observed, indicating population of the HS state. As pressure is increased, these downfield signals shift upfield or towards a ''normal'' position expected for a diamagnetic material, indicating that a pressureinduced SCO towards the LS state occurs. At 240 MPa, the proton signals are still relatively far downfield, indicating that a significant population of the HS state remains, consistent with the SCO being incomplete within the pressure range studied. Proton signals that were shifted upfield by the paramagnetism (to BÀ5 ppm) concomitantly move downfield towards their diamagnetic values as pressure is increased.
To quantitatively analyse the spin states at each pressure, we turned to the Evans method which under standard conditions (ambient pressure) uses a tube-in-tube experiment. The inner tube contains pure deuterated solvent and the outer tube contains the paramagnetic material in the same solvent. The frequency shift of the solvent signal, Df, in the outer tube compared to the pure solvent (to which the NMR spectrum is locked), is dependent on the magnetic susceptibility of the paramagnetic material, and hence w M T can be calculated from Df (Hz), the concentration m (g cm À3 ), and the spectrometer frequency f (Hz) using the Evans method (eqn (1)) to obtain the mass susceptibility w g (cm 3 g À1 ). 10,15 However, an inner tube is not feasible with our high-pressure cell and zirconia NMR tube, or for that matter with most high-pressure NMR setups, which typically involve specialised thick-walled glass or sapphire pressurisable tubes, or modified probes made from beryllium-copper or titanium alloys. 13b, 16 In the absence of a reference frequency for the solvent CD 2 HCN signal, our approach was to instead remove the lock on the CD 2 HCN signal such that it would shift with varying pressure.
The frequency shift at each pressure relative to atmospheric pressure is defined as DDf (Fig. 3). This quantity could then be added to the known frequency shift from that in pure CD 3 CN at atmospheric pressure, Df 0 (determined from our previous variable temperature Evans method data on these complexes), 17 to obtain Df and hence w g from eqn (1), and therefore w M T at each pressure.
For each Fe(II) solution, as the pressure increased the CD 2 HCN signal shifted upfield (Fig. 3), resulting in increasingly negative values of DDf (Fe) (Fig. 3, red), which is consistent with the SCO towards the LS state. However, with the lock signal off, the CD 2 HCN peak will gradually drift upfield with time in the absence of any pressure/temperature changes or change in magnetic susceptibility of the sample. This is due to the magnetic field strength of the NMR slowly, and reliably, decreasing with time after tuning. The magnitude of this effect is small in comparison to the signal shift upon pressure changes, but nonetheless time corrections were applied to DDf (Fe) values to minimise error (see the ESI † for details).
A correction must also be made for the CD 2 HCN signal frequency shift with increasing pressure for a diamagnetic solution, so that the magnitude of the shift in the Fe(II) solution due to the SCO can be ascertained. For this purpose, the Zn(II) analogues of each complex, [Zn 2 (PSRT) 2 ](BF 4 ) 4 , were synthesised (see the ESI †). Typically in paramagnetic NMR studies, a free ligand is used as a diamagnetic reference; however, as this is the first high-pressure NMR magnetic susceptibility study, in order to check for any unforeseen chaotrope/kosmotrope effects with and DDf (Zn), for the Fe(II) and Zn(II) solutions respectively, are indicated, as well as their difference, DDf (SCO), which is due to a decrease in magnetic susceptibility in the Fe(II) solution. Note: to aid visualisation, both [Fe 2 (PSPhT) 2 ](BF 4 ) 4 spectra (red) and [Zn 2 (PS i BuT) 2 ](BF 4 ) 4 spectra (blue) are manually referenced such that the CD 2 HCN signal is at 1.94 ppm at 0.1 MPa, because DDf (Fe), DDf (Zn), and DDf (SCO) are defined as relative to atmospheric pressure.
varying pressure, the Zn(II) complexes, which are of the same size, shape and charge as the Fe(II) complexes and so were considered to be superior to the free ligands, were also tested. Conveniently, this test demonstrates that the free ligand is in fact a perfectly acceptable diamagnetic reference, as it responds in the same way as the Zn(II) complexes do (Fig. S4, ESI †). 1 H NMR spectra of the Zn(II) analogues, at the same concentration in CD 3 CN as the corresponding Fe(II) complexes, were recorded to determine the frequency shift of CD 2 HCN relative to atmospheric pressure for the diamagnetic Zn(II) solutions, defined as DDf (Zn) (Fig. 3, blue). This enabled point-by-point corrections, for DDf (Zn) at each pressure and temperature investigated, to be made to the Fe(II) spectra. The resulting DDf (SCO) = DDf (Fe) À DDf (Zn) values are the frequency shifts of CD 2 HCN relative to atmospheric pressure due only to a change in magnetic susceptibility of the Fe(II) solution (Fig. 3).
From the known w M T at atmospheric pressure, 17 eqn (1) can be used to calculate the Df for the particular temperature and concentration of the Fe(II) solution, which we label Df 0 , the frequency shift of CD 2 HCN at atmospheric pressure relative to that of an internal reference standard of pure CD 3 CN, if it was present in the high pressure cell. DDf (SCO) is then the change in this frequency shift, arising from the change in spin state only, as pressure is applied. Hence, the frequency shift of CD 2 HCN at each pressure relative to pure CD 3 CN at that pressure is obtained simply by Df = Df 0 + DDf (SCO). Finally, w g at each pressure can then be calculated from these Df values using eqn (1), considering the changes in the density of acetonitrile (and hence concentration of the complex), to give a quantitative description of the spin state at any pressure/temperature.
Applying this method to CD 3 CN solutions of [Fe 2 (PSRT) 2 ](BF 4 ) 4 reveals the solution SCO induced by both pressure and temperature for each of the three complexes (Fig. 4, Fig. S7-S12, and Tables S9-S11, ESI †). The SCO is gradual and incomplete within the pressure range available. The [Fe 2 (PSRT) 2 ](BF 4 ) 4 series of complexes are potential candidates for solution sensor applications, i.e. for simultaneous sensing of pressure and temperature in solution over, in particular, a wide range of pressure, based on their different magnetic susceptibility responses. 18 The proton signals observed in the 1 H NMR spectrum (Fig. 2) are the population-weighted average signals of the HS and LS states, and therefore the extent to which the signals are shifted from the fully LS spectrum reflects the magnetic susceptibility of the complex in solution. Assuming the ideal Curie behaviour, the chemical shift, d, of a proton signal has a linear relationship with w M . 11b This allows for the correlation of the processed data, w M , as calculated by our adapted Evans method, with raw d spectral data for pyridyl protons py-H4 and py-H5 ( Fig. 5 and Fig. S14-S19, ESI †). Indeed good linear relationships are observed, indicating a high level of accuracy in the adapted high pressure Evans method of calculating w M or w M T.
The most significant error here is in knowing the exact concentration of the solutions used, which is always the case for the standard Evans method and typically results in 5-10% error. 19 The error associated with the extra corrections needed (time, Zn analogues) for our adapted method is smaller (3-5%) and contains the error in accurately reading the signal position, which is also present in the standard method. Therefore, no significantly large errors are introduced through our extension   of the Evans method from a tube-in-tube method to a single tube method that can be applied to the study of pressure and temperature effects.
It is possible to calculate the fraction HS, g HS , directly from proton chemical shifts 11b,c instead of using the Evans method. However, these methods require a fully HS baseline to be reached 11b and/or a very wide (200 K) temperature range. 11c Although our method requires careful application of corrections, it produces quantitative w M T values (but not g HS ) and can operate in narrow ranges of magnetic susceptibility and temperature.
We have described a robust method for determining the spin states quantitatively in high-pressure solutions. In the test case of the [Fe 2 (PSRT) 2 ](BF 4 ) 4 complexes, an SCO was observed, and the spin state is tuned by both pressure and temperature in solution, raising the possibility of solution-based simultaneous pressure/temperature sensing. Unlike a thermally induced SCO, which is limited by the freezing/boiling points of the solvent, the pressure is limited only by instrumentation and so has the potential to allow access to a much wider range of spin states in solution. Although applied here only to simple Fe(II) SCO compounds, this robust method could be extended to study the effects of pressure on spin-labile (bio)catalysts, sensors or host-guest chemical processes.
We thank the University of Otago (for a PhD scholarship to RWH), the Marsden Fund administered by the Royal Society of New Zealand (UOO1318 to SB and 09-MAU-140 to GBJ) and the Allan Wilson Centre for Molecular Evolution and Ecology for supporting this research.

Conflicts of interest
There are no conflicts to declare.