Host Spin‐Crossover Thermodynamics Indicate Guest Fit

Abstract Spin‐crossover (SCO) metal‐organic cages capable of switching between high‐spin and low‐spin states have the potential to be used as magnetic sensors and switches. Variation of the donor strength of heterocyclic aldehyde subcomponents in imine‐based ligands can tune the ligand field for a FeII center, which results in both homoleptic and heteroleptic cages with diverse SCO behaviors. The tetrahedral SCO cage built from 1‐methyl‐1H‐imidazole‐2‐carbaldehyde is capable of encapsulating various guests, which stabilize different cage spin states depending on guest size. Conversely, the SCO tetrahedron exhibits different affinities for guests in different spin states, which is inferred to result from subtle structural differences of the cavity caused by the change in metal center spin state. Examination of SCO thermodynamics across a series of host–guest complexes enabled sensitive probing of guest fit to the host cavity, providing information complementary to binding‐constant determination.

Paramagnetic 1 H NMR experiments were performed using the zg30 program with a sweep width (sw) of 356.96 ppm and a transmitter frequency offset (o1p) of 125 ppm. Variable-temperature 1 H NMR experiments were carried out according to the following procedure: the temperature was decreased from 298 K to 243 K during which spectra were collected in 5 K or 10 K intervals. Then, the temperature was increased to 298 K to record spectra at temperatures higher than 298 K in 5 K or 10 K intervals. COSY experiments were undertaken using the cosygpppqf program and DOSY experiments were carried out using the ledbpgp2s program.
T1 measurements were conducted using the t1ir pulse program to assign the peaks in the 1 H NMR spectrum of tetrahedron 1. Experiments were undertaken within a sweep width of 10 ppm centered at the signal peak or group of signals. Data was processed with Dynamic Centre 4.6.2 and fitted with equation S1: Low-resolution electrospray ionization mass spectrometry (LR ESI-MS) was undertaken on a Micromass Quattro LC mass spectrometer (cone voltage 5-20 eV; desolvation temperature 313 K; ionization temperature 313 K) infused from a Harvard syringe pump at a rate of 10 μL•min −1 . Highresolution electrospray ionization mass spectrometry (HR ESI-MS) was undertaken on a Waters' Synapt G2-Si Quadrupole-Ion mobility-TOF hybrid instrument.
Triamine D (10.98 mg, 24.9 µmol, 4 equiv.), iron(II) triflate (8.81 mg, 24.9 µmol, 4 equiv.), and aldehyde A (8.25 mg, 74.6 µmol, 12 equiv.) were dissolved in MeCN (3 mL). The reaction mixture was degassed by three freeze-pump-thaw cycles then stirred at room temperature overnight. The product was precipitated with diethyl ether and separated by centrifugation. Then the solid was suspended in diethyl ether and washed with diethyl ether three times (3×15 mL). The resulting reddish purple amorphous solid contained unidentified impurities (6-10 ppm in the 1 H NMR spectrum, Figure S1, hypothesized to be intermediates or fragments) which were successfully removed by crystallization. For crystallization, the amorphous solid was dissolved in MeCN (3 mL), and slow vapor diffusion of diethyl ether into the solution afforded dark purple crystals of tetrahedron 1 (11.2 mg, 42%). Characterization and host-guest studies of tetrahedron 1 were carried out using crystalline samples after drying them under a stream of N2.
Figure S1 1 H NMR spectrum of the amorphous sample of tetrahedron 1 obtained by precipitation from Et2O (before crystallization, CD3CN, 400 MHz, 298 K). The above-mentioned impurities are highlighted in orange.     Solomon's equation 3 suggests that T1 is proportional to [Σ(rij) -6 ] -1 (rij stands for the distance between the paramagnetic center and the proton), which can be used to assign proton signals in paramagnetic complexes following the methods previously applied for HS Fe(II) 4 and Co(II). 5,6 The distances were obtained from the crystal structure of tetrahedron 1 (Section 3.1). The broadness of the peak at 0.98 ppm prevented the measurement of T1 due to very fast relaxation. This discrepancy could be attributed from the increased flexibility of the cage in solution and the existence of LS Fe(II) spin centers. However, the integrals in the 1 H NMR spectrum in the diamagnetic region and the cross peaks observed in the 1 H-1 H COSY spectrum of tetrahedron 1 are consistent with the assignments via T1 measurements.     Figure S13 HRMS (ESI + -QTOF, CH3CN) of tetrahedron 2.
In the synthesis of tetrahedra 1 and 2, Fe(OTf)2 was used instead of Fe(NTf2)2 because encapsulation of NTf2 − was observed in an analogous LS cage. 8 However, tetrahedron 3 could not form in the presence of Fe(OTf)2, possibly due to the lack of a template; thus, Fe(NTf2)2 was used in the self-assembly of tetrahedron 3. Encapsulated NTf2 − in tetrahedron 3 can be observed in the 19 F NMR spectrum ( Figure  S14).
An analogous synthetic procedure as for tetrahedron 1 and 2 was applied for tetrahedron 3. Triamine D (6.00 mg, 13.6 µmol, 4 equiv.), iron(II) triflimide (4.81 mg, 13.6 µmol, 4 equiv.), and aldehyde C (4.61 mg, 3.6 μL, 40.8 µmol, 12 equiv.) were dissolved in MeCN (1.5 mL), the solution degassed and stirred at room temperature overnight. A dark purple solid precipitated after the addition of diethyl ether to the assembly solution and was washed three times with diethyl ether prior to further characterization (yield: 11.2 mg, 76%). Dark purple single crystals were obtained for X-ray crystallography via slow vapor diffusion of diethyl ether into the solution.
However, signals for the cage were not detected by low-resolution ESI-MS. Only singly-charged species corresponding to cage fragments were observed, which might be attributed to the instability of the cage when diluted to very low concentration for mass spectrometry (less than 0.1 mg/mL). A similar situation was encountered in the HR-MS, where fragments comprised the majority of the signals. Cage signals can be observed only with very low intensity, however, one well-resolved isotope pattern was observed ( Figure S17). Nevertheless, the DOSY spectrum reveals a similar diffusion coefficient (tetrahedron 3: 6.72×10 -10 m 2 /s) as for the other two cages (tetrahedron 1: 4.22×10 -10 m 2 /s, tetrahedron 2: 3.51×10 -10 m 2 /s) and single crystals suitable for X-ray crystallography have been obtained to confirm its tetrahedral structure.
Triamine D (1.31 mg, 3.0 µmol, 2 equiv.), tetraamine E (5,10,15,20-Tetrakis(4-aminophenyl)porphyrin (3.00 mg, 4.0 µmol, 3 equiv.), iron(II) triflimide (5.48 mg, 9.0 µmol, 6 equiv.), and aldehyde A (2.94 mg, 27.0 µmol, 18 equiv.) were dissolved in MeCN (1 mL). The reaction mixture was degassed by three freeze-pump-thaw cycles then stirred overnight at room temperature. The product was precipitated with diethyl ether and washed with diethyl ether three times (The ratio of cube to trigonal prism is around 4 : 5 = 1.1 : 1 according to 1 H NMR integrations). Crystals of 4 and 5 were grown by diffusion of diethyl ether into an acetonitrile solution of the product mixture. However, the crystals of cube 4 only diffracted to low resolution and no reasonable solution was obtained. Crystals of trigonal prism 5 diffracted well and the structure was fully refined. In theory the formation of tetrahedron 1 should also be observed, but tetrahedron 1 seems to be less stable than the other structures involved in this equilibrium. A putative dynamic library containing the subcomponents of 1 was observed in the 1 H NMR spectrum from 6-10 ppm.
Cube 4 can also be obtained as the sole product via the self-assembly of tetraamine E (1 mg, 1.5 µmol, 6 equiv.), iron(II) triflimide (1.22 mg, 2.0 µmol, 8 equiv.), and aldehyde A (0.065 mg, 6.0 µmol, 24 equiv.) in MeCN. The yield was quite low which might be due to undefined fragments/intermediates like they were also observed in the self-assembly of tetrahedron 1. These undefined intermediates/fragments also resulted in to quite low quality of spectra for cube 4. Since cube 4 shows similar properties to another porphyrin-based SCO cage 7 , it is not the focus of this work.
For trigonal prism 5, which stays at the HS state, relaxation in NMR is quick and gives rise to very broad signals at room temperature. The 1 H NMR spectrum of trigonal prism 5 at 338 K displays sharper signals.
Peaks are assigned largely based on VT NMR (section 5.12), as signals of SCO cube 4 and HS trigonal prism 5 move towards opposite directions. 2D NMR characterizations are not as useful as for diamagnetic complexes for assignments here due to the wide distribution of peaks on the spectrum and fast relaxations of the HS state. 1

X-ray crystallography and volume calculations
Data for tetrahedron 1 was collected using a Bruker D8 VENTURE diffractometer equipped with highbrilliance IμS Cu-Kα radiation (1.54178 Å), with ω and ψ scans at 180(2) K, and the rest were collected at Beamline I19 of Diamond Light Source employing silicon double crystal monochromated synchrotron radiation (0.6889 Å) with ω scans at 100(2) K. 8 Data integration and reduction were undertaken with SAINT 9,10 and XPREP7 or Xia2. [11][12][13] Subsequent computations were carried out using the WinGX-32 graphical user interface 14 and Olex-2. 15 Multi-scan empirical absorption corrections were applied to the data using SADABS 16 or the AIMLESS 17 tool in the CCP4 suite. 18 Structures were solved by intrinsic phasing using SHELXT-2013 19 then refined and extended with SHELXL-2014. 20 In general, nonhydrogen atoms with occupancies greater than 0.5 were refined anisotropically. Carbon-bound hydrogen atoms were included in idealized positions and refined using a riding model. Disorder was modelled using standard crystallographic methods including constraints, restraints and rigid bodies where necessary (SIMU, ISOR, DFIX, etc). Crystallographic data along with specific details pertaining to the refinement follow. Crystallographic data have been deposited with the CCDC (2176135-2176139). * R1 = ||Fo|-|Fc||/|Fo| for Fo>2(Fo); wR2 = (w(Fo 2 -Fc 2 ) 2 /(wFc 2 ) 2 ) 1/2 all reflections Specific refinement details: The asymmetric unit of tetrahedron 1 was found to contain one twelfth of a Fe4L4 assembly. The anions and solvent molecules within the structure are highly disordered and solvent loss contributes to a significant amount of void volume in the lattice, which results in some smeared electron density. Consequently, the SQUEEZE 21 function of PLATON 22 was employed to remove the contribution of the electron density associated with anions and highly disordered solvent, which gave a potential solvent accessible void of 5117 Å 3 per unit cell (a total of approximately 1849 electrons). Thus, the molecular weight and density given above are underestimated.

Adamantane⊂1
A B Figure  The asymmetric unit of adamantane⊂1 was found to contain one twelfth of a Fe4L4 assembly and the adamantane. The anions and solvent molecules within the structure are highly disordered and solvent loss contributes to a significant amount of void volume in the lattice, which results in some smeared electron density. Consequently, the SQUEEZE function of PLATON was employed to remove the contribution of the electron density associated with anions and highly disordered solvent, which gave a potential solvent accessible void of 4561 Å 3 per unit cell (a total of approximately 1483 electrons). Thus, the molecular weight and density given above are underestimated.

Adamantane⊂2
A B Figure  The asymmetric unit of adamantane⊂2 was found to contain a complete Fe4L4 assembly and an adamantane with associated counterions. One of the triflate anions and two benzimidazole rings were modelled as disordered over two locations.
The anions and solvent molecules within the structure are highly disordered and solvent loss contributes to a significant amount of void volume in the lattice, which results in some smeared electron density. Consequently, the SQUEEZE function of PLATON was employed to remove the contribution of the electron density associated with anions and highly disordered solvent, which gave a potential solvent accessible void of 16161 Å 3 per unit cell (a total of approximately 5586 electrons). Thus, the molecular weight and density given above are underestimated. Despite the use of synchrotron radiation few reflections at greater than 1.0 Å resolution were observed and the data were trimmed accordingly.

Tetrahedron
The asymmetric unit of 3 was found to contain one twelfth of a Fe4L4 assembly and the adamantane. Thermal parameter restraints (SIMU, RIGU) were applied to all atoms except for iron. The anions and solvents within the structure are highly disordered and solvent loss contributes to a significant amount of void volume in the lattice, which results in some smeared electron density. Consequently, the SQUEEZE function of PLATON was employed to remove the contribution of the electron density associated with the remaining anions and highly disordered solvent, which gave a potential solvent accessible void of 56259 Å 3 per unit cell (a total of approximately 25018 electrons). Thus, the molecular weight and density given above are underestimated. The asymmetric unit was found to contain half of a Fe6 Fe6(C39H39N15)2(C64H50N16)3 assembly and associated counter ions. Two phenyl rings on the triazine ligand were modelled as disordered over two locations with bond length and thermal parameter restraints applied to facilitate a reasonable refinement.
The anions and solvent molecules within the structure are highly disordered and the solvent loss contribute to a significant amount of void volume in the lattice, which results in some smeared electron density. Consequently, the SQUEEZE function of PLATON was employed to remove the contribution of the electron density associated with anions and highly disordered solvent, which gave a potential solvent accessible void of 35043 Å 3 per unit cell (a total of approximately 13583 electrons). Thus, the molecular weight and density given above are underestimated.
Guest volumes were calculated with MoloVol 1.0.0 23 (Table S3) based on molecular force field simulations (MM2 force field) obtained with Scrigress 3.4.5 (Fujitsu Limited, Figure S36). The following parameters were used in the volume calculations:
Van der Waals volumes VvdW and molecular volumes Vmol (including cavities) were calculated (Table  S3). Considering the molecular volume Vmol when comparing sizes of mono-, bi-, and tetracyclic hydrocarbons is crucial, because their cavities will not appear in the in their van der Waals volumes but have a considerable contribution to their sizes. The molecular volumes of the investigated guests increase in the order cyclohexane < adamantane < cis-decalin < 1-adamantanol.
However, due to its open, convex structure, cis-decalin has larger dimensions than 1-adamantanol albeit having a smaller volume. The empty space within the convex side of cis-decalin's structure does not contribute to its volume, but that "void" is not accessible to the cage cavity either, rendering cisdecalin larger than 1-adamantanol. To correct for that discrepancy between volume and size, we introduce the sphericity Ψ 24 (Equation S2): with Vmol being the molecular volume of the guest, and Sexcl the probe excluded molecular surface (Table  S3). 23 The higher the sphericity of a non-tetrahedral guest at a given volume, the better the match to a tetrahedral or nearly spherical cavity.

Zn(II) analogue of tetrahedron 1 and its host-guest compounds
The synthetic procedure for a Zn(II) analogue of tetrahedron 1 (Zn1) is similar to that of tetrahedron 1.

Guest binding affinity depending on the spin states of tetrahedron 1
As cage 1 is a SCO system and exists in mixed spin states at room temperature, determining the association constants of different guests to tetrahedron 1 is not straightforward. The following sections demonstrate, how we developed a simple approximation to derive the association constants for the two extremes of the SCO process, i.e. all high-spin or all low-spin metal centers, from a simple 1:1 isotherm. Association constants were determined by NMR titrations as detailed below (Section 4.9.2).

Deriving individual association constants for both spin states of tetrahedron 1
A simple host-guest equilibrium between a guest G and a host H can be described by Scheme S5.
The association constant Kobs is defined as If the metal centers of the cage, which acts as the host here, can reside in different spin states at a given temperature, the simple equilibrium of Scheme S5 leads to the thermodynamic cycle depicted in Scheme S6 (also Figure 4a in the main text) under the simplifying assumption, that all spin centers are either high-spin (HS) or low-spin (LS) and no mixtures of spin states exist within one structure. and, hence,

Scheme S5
which shows that the ratio of association constants between the high-spin and low-spin states of the host, HS and LS, respectively, are directly related to the spin-crossover behavior of host H and hostguest complex HG. The ratio of the association constants of the different host spin states to the guest can therefore be written as The thermodynamic parameters were determined by VT NMR (Section S5) and are summarized in Table S4. The resulting ratios of KG⊂HS and KG⊂LS are summarized in the same table. If Eq. S8 and Scheme S6 hold true, the ratio KG⊂HS and KG⊂LS of can be directly derived from the spinstate populations γ (determined in Section S5) of the host (HS, LS) or host-guest complexes (G⊂HS, G⊂LS) a given temperature.
We define the overall host concentration as (S19.) Given the concentrations of the four host and host-guest species derived from the spin-state populations (Eqs S15, S16, S18, S19), the ratio of the host-guest association constants of the different spin states KG⊂HS and KG⊂LS (Eqs S6&S7) can be derived: which is equivalent to Equation S11. Inserting Eqs S15,S16,S18,S19 into S20 results in As expected, S21 results in similar values as S12 (compare Tables S4 and S5). and Hence KG⊂HS and KG⊂LS can be calculated directly from Kobs and the spin state populations γLS and γG⊂LS :

NMR titrations
NMR titration data of the different guests binding to tetrahedron 1 can be fitted to a simple 1:1 isotherm to determine Kobs (see section 4.9.1). With Eqs S26 and S27, the association constants of the guests to the two spin states (all high-spin HS or all low-spin LS) KG⊂HS and KG⊂LS can be calculated.
Solutions of the different guests (between 4.12 and 18.5 mM, CD3CN) containing two internal standards, 1,3,5-trimethoxybenzene and 1,4-dimethoxybenzene at 1.683 mM and 1.954 mM, respectively, were titrated into solutions of tetrahedron 1 (0.32 mM, 0.4 mL, CD3CN) containing internal standard at 1,3,5trimethoxybenzene at 1.683 mM. After each addition, the system was left to equilibrate for four minutes at room temperature before the 1 H NMR spectrum (Figures S63−S66) was taken (equilibrating for longer times leads to the formation of the host-guest complex from NMR silent fragments/intermediates in the mixture via templation by the guest). Additionally, a spectrum of each guest stock solution was recorded. Since host and guest solutions both contained the same internal standard (1,3,5trimethoxybenzene) at the same concentration, the concentration of the standard 1,3,5trimethoxybenzene remained constant throughout the titration. Concentrations of tetrahedron 1 and its host-guest complexes G⊂1 were determined via integration with reference to internal standard 1,3,5trimethoxybenzene. The second internal standard, 1,4-dimethoxybenzene, was only present in the guest solutions and, hence, it's concentration in the samples rose together with the guest concentration. Therefore, precise guest concentrations were determined with reference to both internal standards and not directly from integration of guest signals, because these often overlapped with other signals. Integrals were determined by calculated Lorentzian peaks.
As guest binding is slow on the NMR time scale, the data were analyzed by plotting the ratio of occupied cage G⊂1 to total concentration of tetrahedron Note that the maximum value of this isotherm is 1, because there cannot be more than 100% of the cages occupied. Hence, the isotherm does not need as many points above [G]/[1]=1 as a system, which is on fast exchange on the NMR timescale and the maximum value of the isotherm δmax is unknown and needs to be determined by fitting.
To reduce errors, two signals were followed for each titration and the collated data fitted using Origin's Global Fit function (Figures S67−S68, Table S6).
In this equation, is the chemical shift of the selected peak; is the chemical shift of the peak when the compound is at the LS state; C is a constant; T corresponds to the temperature; ΔH and ΔS correspond to the enthalpy and entropy change of the SCO process and R is the gas constant. In most cases where the spin crossover process is almost complete but the absolute LS state cannot be reached, the value of was fixed to the value of their diamagnetic Zn analogue (see Section S4.8) in the fitting. This method has the key advantage that the selected chemical shifts of the 1 H NMR resonances of the SCO complex directly reflect its magnetic state and will not interfere with other compounds in the mixture, which is a drawback of bulk methods such as the Evans method.
Spin state populations were calculated with the thermodynamic parameters obtained from the fitting. 30

Figure S85
Chemical shifts of encapsulated 1-adamantanol (Hx, black squares) and spin state population of 1-adamantanol⊂1 (blue and red curves) in the investigated temperature range. The SCO T1/2 is given as a vertical line.

Figure S86
VT 1 H NMR spectra of cyclohexane⊂1 (CD3CN, 500 MHz, from 298 K to 243 K).         (Figures S85, S86). The imine signals become too broad to be observed at low temperature and fitting with the available data points at higher temperatures did not provide a good and reasonable fit.

Figure S97
Spin state population of cis-decalin⊂1 in CD3CN calculated according to Equations S30 and S31.

Tetrahedron 2
The behavior of tetrahedron 2 was completely different from that of tetrahedron 1. At above 273 K, signals corresponding to tetrahedron 2 moved upfield upon heating, displaying HS paramagnetic nature following Curie's law. However, cooling from 273 K also resulted in an upfield shift of the signals, which indicated the loss of paramagnetism. This might be attributed to the SCO process. However, even at the lowest temperature (243 K) in the experiment, the value of the imine proton resonance (Ha) was above 100 ppm, implying that only a small proportion of HS Fe(II) starts to transit into LS. Due to the line broadness at low temperature, only experiments within a small range of temperatures provided usable values of chemical shifts for the model, which was far from enough for a rationalized calculation. Thus, thermodynamic parameters could not be determined. Nonetheless, it can be concluded that tetrahedron 2 preferred the HS state at all investigated temperatures in solution. This is consistent with aldehyde B used for assembling tetrahedron 2 offering a weaker ligand field compared to aldehyde A used in tetrahedron 1.

Adamantane⊂2
The encapsulation of adamantane in tetrahedron 2 still gave rise to a HS complex, behaving very similar to 2. Upfield shift also only started when temperature decreased below 273 K.

Tetrahedron 3
SCO of tetrahedron 3 was initially studied in CD3CN as well. However, due to the limit of the boiling point of acetonitrile, data points at higher temperature where more HS population would be reached could not be obtained. Fitting with the same equation (Equation 29) used for tetrahedron 1 didn't converge in the case of tetrahedron 3. Thus, CD3CN was replaced by CD3NO2 which has similar polarity as CD3CN but a higher boiling point which allows investigation at higher temperatures than CD3CN. Similar SCO behaviors were observed in both solvents and the study in CD3NO2 led to converged fitting results.

Adamantane⊂3
The encapsulation of adamantane did not have much influence on tetrahedron 3's SCO behavior. Since tetrahedron 3 was already a mostly LS cage within the investigated temperature range, the cavity volume change was not significant with varying temperature. Furthermore, adamantane preferred the small cavity that LS tetrahedron 3 offers, so the influence of the guest on tetrahedron 3's SCO was little.