Entanglement of Spin Transition and Elastic Interactions: Manipulating the Slow Spin Equilibrium by Guest-Mediated Fine-Tuning Elastic Frustration

doi:10.21203/rs.3.rs-4989634/v1

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Entanglement of Spin Transition and Elastic Interactions: Manipulating the Slow Spin Equilibrium by Guest-Mediated Fine-Tuning Elastic Frustration

https://doi.org/10.21203/rs.3.rs-4989634/v1

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A comprehensive analysis of the physical and chemical properties using the same family of complexes is crucial for understanding and designing structure-property relationships. However, finding the appropriate system remains challenging. Here, a series of guest-saturated states based on the 2D Hofmann-type framework [Fe^II(prentrz)₂Pd^II(CN)₄]·guest (prentrz = (1E,2E)-3-phenyl-N-(4H-1,2,4-triazol-4-yl)prop-2-en-1-imine, 1·guest) is reported, which exhibit a guest-manipulated slow dynamic effect of spin equilibrium in an incomplete two-step spin-crossover (SCO) process. Using a full-sealed method by modulating the mixing ratios and types of CH₃OH, H₂O, and D₂O, stable maintenance of guest-saturated states allows fine-tuning elastic frustration (ξ) of the framework to realize SCO behaviors in the unexplored region between one-step incomplete (HS_0.5LS_0.5↔HS) and two-step complete (LS↔HS_0.5LS_0.5↔HS) processes. A semi-sealed method enables continuous guest molecule loss until the guest-saturated state disappears, transitioning slow spin equilibrium from difficult to overcome to overcome fully. The study demonstrates that guest molecule modulation is more controllable than structural deformation effects on elastic frustration, offering a pathway to discover hidden types of SCO materials and develop new stimulus-responsive materials.

Physical sciences/Chemistry/Materials chemistry/Magnetic materials

Physical sciences/Chemistry/Materials chemistry/Metal–organic frameworks

Multistable materials that change structure and functionality in response to external stimuli have attracted increasing attention for their suitability in analyzing phase transition mechanisms and their potential applicability to molecular sensors and switches.^[1–5] Among them, Spin-crossover (SCO) materials have garnered extensive study due to their potential for multi-input multi-output characteristics. These materials respond to various stimuli such as light, heat, pressure, and guest molecules, and exhibit diverse output properties including changes in magnetism, color, dielectric constants, and mechanical properties.^[6–10] As with all multistable materials, the ultimate goal in the design of SCO materials is to achieve manipulability, entailing optimal or programmable performance during the reversible transition between the high-spin (HS) and low-spin (LS) states.^[11] The occurrence of SCO behavior requires suitable ligand field strengths, exemplified by a series of mononuclear {Fe^IIN₆} SCO compounds that have been rationally structured to enable a comprehensive analysis of hysteresis properties, with theoretical calculations confirming that the growth of the hysteresis loop is controlled by electrostatic contributions.^[12] On the other hand, the integral nature of spin-crossover (SCO) behavior is determined by the elastic cooperativity between metal centers, which is closely related to host-host and host-guest interactions.^[13–16] For example, polymorphism in SCO compounds typically exhibits different SCO properties with varying transition temperatures and number of steps.^{[17, 18]} Additionally, reversible modulation of SCO properties by different guest molecules is achieved through mechanisms such as lattice strains, hydrogen-bonding interactions, electrostatic interactions, and ligand substitution.^{[19, 20]} In addition to the study of conventional properties like multi-step and abrupt SCO with wide hysteresis, the unusual spin transitions that significantly depend on the temperature scan rate under strong cooperativity—known as the slow spin equilibrium or kinetic trapping effect—have also garnered significant attention.^[21–24] SCO complexes exhibiting slow spin equilibrium possess desirable properties, including the record-breaking highest temperature-induced excited spin-state trapping (TIESST, T_TIESST = 250 K) and long-lived light-induced excited spin-state trapping (LIESST, T_LIESST = 80 K).^[25–27] Although the slow spin equilibrium often occurs in SCO compounds with long alkyl chains, the modification with long-chain alkanes does not inevitably result in the kinetic trapping effect in SCO materials.^[28–39] Consequently, compared to the comprehensive analysis of conventional SCO behavior in a series of well-characterized compounds, the study of slow spin equilibrium presents challenges in identifying an appropriate SCO system with similar configurational and stacked structures.

Metal-organic frameworks (MOFs), known for their high tunability, offer a versatile platform for exploring various properties, especially those related to cooperativity.^[40–43] The intrinsic porosity of SCO-MOFs allows for the modulation of host-guest interactions through guest molecular substitutions, thereby fine-tuning the coordination environment of metal centers.^[44] In certain SCO-MOFs, the SCO behavior is highly sensitive to the guest molecule, leading to significant variations in the number of steps, hysteresis, and transition temperatures (T_1/2), without substantially altering the structure of the framework.^[45–48] Recent computational studies utilizing Monte Carlo (MC) simulations have revealed that the degree of elastic frustration (ξ) has been employed to investigate the multi-step spin transition in a rigid 2D lattice.^[49] A “frozen” anomaly (ξ = 1.045) was identified at the junction between an incomplete (HS_0.5LS_0.5↔HS) and a complete two-step (LS↔HS_0.5LS_0.5↔HS) spin transitions, hypothesized to result from kinetic effects. This "frozen" anomaly implies that the framework with the specific ξ value pospossessese potential to undergo SCO with the slow spin equilibrium. Notably, this suite of theoretical models and elastic frustration concept has been effectively applied in analyzing antiferro-elastic and ferro-elastic interactions within Hofmann-type SCO-MOFs.^[50–56] The results suggest that there exists a suitable Hofmann-type framework with a ξ value near the "frozen" anomaly, potentially imparting a slow dynamic effect on SCO behavior.

In previous studies, including our work and that of others, it has been shown that the 2D Hofmann-type MOFs [Fe^II(prentrz)₂Pd^II(CN)₄] (prentrz = (1E,2E)-3-phenyl-N-(4H-1,2,4-triazol-4-yl)prop-2-en-1-imine, 1) exhibited pore-adjustable behavior, with the ξ values of the framework fluctuating around 1 according to the SCO behavior.^{[57, 58]} Notably, CH₃OH guest molecules in as-grown crystals tend to vacate the framework when exposed to atmospheric conditions, rapidly being lost and replaced by H₂O molecules. The distinct interaction of compound 1·guest with H₂O and CH₃OH molecules has established that CH₃OH molecules within the pores increase the ξ value of the framework.^{[48, 59]} Nonetheless, the compounds 1·guest can remain stable in the dual-guest states with both CH₃OH and H₂O guest molecules when immersed in H₂O-CH₃OH mixed solvents, termed the guest-saturated state. In this work, the guest-saturated states of 1·guest are maintained through immersion in proportional solvents of CH₃OH, H₂O, and D₂O, exhibiting a guest-manipulated slow dynamic effect of spin equilibrium in an incomplete two-step spin-crossover (SCO) process. The immersion employs full-seal and semi-sealed methods. By using the full-seal method to modulate the mixing ratios and types of CH₃OH, H₂O, and D₂O, three types of mixed solvents are formed: H₂O-CH₃OH, D₂O-CH₃OH, and H₂O-D₂O. The stable maintenance of guest-saturated states allows fine-tuning elastic frustration of the framework, thereby first enabling the varying degree of slow spin equilibrium under the same temperature scan rate and framework. The semi-sealed method is employed to gradually desorb the guest-saturated state with three H₂O-CH₃OH ratios (2:8, 8:2, 10:0) through in situ heating. The continuous loss of guest molecules reveals a process in which the challenge of overcoming slow spin equilibrium transitions from difficult to easy, ultimately leading to its disappearance. Manipulating the slow spin equilibrium by two types of guest-mediated methods provides comprehensive insights into the role of guest molecules in fine-tuning elastic frustration on SCO behaviors, offering the underlying mechanisms in the unexplored region between one-step incomplete (HS_0.5LS_0.5↔HS) and two-step complete (LS↔HS_0.5LS_0.5↔HS) SCO behaviors in such Hofmann-type SCO-MOFs.

Crystal structures of 1·3H ₂ O·3/2CH ₃ OH and deduced sequence of guest distribution Modulation. Due to the tendency to crystal fragmentation during spin transitions, a relatively small crystal of the guest-saturated state 1·3H₂O·3/2CH₃OH was selected from the samples immersed in a solution with 5:5 H₂O-CH₃OH ratio. This selected single crystal was further sealed in a quartz tube with the same mixed solution for Single-crystal X-ray diffraction (SC-XRD) measurement. The compound 1·3H₂O·3/2CH₃OH crystallizes in the triclinic space group P\(\:\stackrel{-}{1}\) at temperatures of 293, 190, 150, 130, 120 and 85 K, respectively (Table S1). The asymmetric unit of 1·3H₂O·3/2CH₃OH remains consistent across all temperatures, containing two crystallographically independent Fe ions (Fe1 and Fe2) situated at inversion centers, two prentrz ligands with distinct conformations (conformer 1 for Fe1 and conformer 2 for Fe2), three H₂O and two-thirds CH₃OH guest molecules, and one[Pd(CN)₄]²⁻ bridging ligand (Figures S1 and S2, see supporting information for details). The guest-saturated state 1·3H₂O·3/2CH₃OH corresponds to the large channel-type pore (lcp) phase described in previous work, exhibiting the same 2D layer, supramolecular structure, and channel pores extending along the crystallographic a-axis direction (Figs. 1a, S3 and S4).^[57]

Based on the distribution of CH₃OH and H₂O molecules in the pore of compound 1·3H₂O·3/2CH₃OH, it can be inferred that CH₃OH molecules preferentially replace the H₂O molecules and occupy the center of the channel-type pore (Figs. 1b and S5). When immersed in pure CH₃OH solution for a week, the samples turned off-white and lost crystallinity. This supports the hypothesis that the weak O − H···N hydrogen bond between the prentrz ligand (N3) and H₂O (O5) molecule plays a crucial role in stabilizing the framework structure (Figure S6). PXRD analyses were performed to examine the expansion/contraction of the framework at different guest-saturated states (Figs. 1c and S7). H₂O and D₂O, with precisely the same kinetic diameters (2.64 Å), as well as CH₃OH, were used to substitute gradually the original guest molecules in the pore cavity to achieve a gradient effect. The principal diffraction peak in the low-angle region of the guest-saturated samples, identified as (001), suggests a peak position shift attributed to the displacement of guest molecules. This indicates that the 2D network in [110]-direction undergoes a certain degree of expansion/contraction. Starting with the guest-saturated sample with 10:0 H₂O-CH₃OH ratios (pure H₂O), an increase in the proportion of CH₃OH causes the characteristic peak to shift to a lower angle, indicating framework expansion. This indirectly suggests the disruption of the hydrogen bonding network among H₂O molecules. Replacing H₂O with D₂O results in the characteristic peak, as well as all major peaks, shifting to lower angles, indicating expansion of the framework in all dimensions. This finding contrasts with the common understanding that deuterium substitution typically leads to stronger hydrogen bonds and a more contracted structure. Such structural expansion may arise from the rearrangement of donor-acceptor distances in the O − H···N (H₂O and host structure) and O − H···O (H₂O and H₂O) hydrogen bonds within the pore cavity, i.e., isotopic polymorphism and the geometric H/D isotope effect (GIE).^{[60, 61]} Further replacing D₂O with CH₃OH continues to shift the characteristic peak to lower angles, suggesting the effect on increasing the ξ value of the framework follows the order: CH₃OH > D₂O > H₂O.

Variable-temperature magnetic susceptibilities of the guest-saturated samples with 2:8, 5:5, 8:2, and 10:0 H₂O-CH₃OH ratios were first measured using the full-sealed method, directly probing the guest-exchange influence on the slow spin equilibrium of Fe2 (Figs. 2a and S8-S11). Each sample shows χ_MT values of 3.48 − 3.63 cm³ K mol^− 1 above 210 K, consistent with a complete HS phase (γ_HS = 1). Upon cooling at 1 K min^− 1, the γ_HS values drop rapidly to around 0.5 at 190 K, and then remain tiny decrease until 113 K. Further cooling reveals a guest-manipulated slow spin equilibrium for Fe2—with γ_HS values decreasing from 0.44 (2:8), 0.41 (5:5), 0.32 (8:2), to 0.28 (10:0) at 50 K, indicating that reducing methanol content enhances the effectiveness in overcoming the slow spin equilibrium of Fe2, as alcohols generally impede the flexibility (↑ξ).^[59] The γ_HS values of 0.25 (8:2) and 0.22 (10:0) at 50 K under a scan rate of 0.5 K min^− 1 exhibit higher SCO completeness compared to those at 1 K min^− 1, indicating that the scan rate-manipulated slow spin equilibrium persists in the guest-saturated samples with a dominant water proportion. During warming, γ_HS values for 1 K min^− 1 unexpectedly drop at specific temperatures (65 K for 5:5, 60 K for 8:2, and 61 K for 10:0), reaching minimum values of 0.36 (5:5) at 88 K, 0.28 (8:2) at 84 K, and 0.26 (10:0) at 84 K, with further heating recovering the γ_HS values (Figure S11). The SCO of Fe1 in the guest-saturated state 1·3H₂O·3/2CH₃OH (5:5 H₂O-CH₃OH ratios) occurs at the first-step spin transition, accompanied by a change in average Fe1 − N bond length from 2.156(5) Å at 293 K to 1.959(5) Å at 190 K (Δd_Fe−N = 0.197 Å)^[62] and a contraction of unit-cell volume by 4.4% (Figure S12, Tables S2 and S3). The average Fe2 − N average bond length remains essentially constant over the temperature interval of 70 K: 2.162(5) at 190 K, 2.161(5) at 150 K, 2.162(5) at 130 K, and 2.166(6) at 120 K. Temperature reduction to 85 K witnesses a slight decrease in the average Fe2 − N bond length to 2.138(13) Å, representing the occurrence of a possible SCO of Fe2 (Δγ_HS = 12.2%), while a further completeness is limited by the temperature control system.

There are two types of mixed solvents with D₂O used to manipulate the SCO of guest-saturated samples: H₂O-D₂O ratios (10:0, 5:5, and 0:10) and D₂O-CH₃OH ratios (10:0 and 8:2) (Figs. 2b, 2c and S13-S16). The γ_HS values of the guest-saturated samples with different H₂O-D₂O ratios reached 0.28 (10:0), 0.33 (5:5), and 0.470 (0:10) at 50 K, respectively, during the cooling process at 1 K min^− 1 (Figures S13 and S14). In the warming process, the γ_HS values of the three ratio samples started to decrease anomalously at 61 K, reaching 0.26 (10:0) at 84 K, 0.29 (5:5) at 81 K, and 0.467 (0:10) at 81 K, respectively. The slow spin equilibrium of Fe2 in structures of pure D₂O is more difficult to thermally overcome than that of pure H₂O, with scan rates of either 1 or 0.5 K min^− 1 (Figure S15a). For guest-saturated samples with varying D₂O-CH₃OH ratios, replacing 20% of the pure D₂O solution with CH₃OH resulted in the spin transition of Fe2 being unaffected by changes in scan rates (Figure S15b). The SCO behavior of the sample with an 8:2 D₂O-CH₃OH ratio is similar to that observed in the 2:8 H₂O-CH₃OH sample, which contains a higher proportion of CH₃OH and contrasts with the behavior seen in the 8:2 H₂O-CH₃OH sample (Figs. 2d, 2e and S17). The more difficult it is to thermally overcome the slow spin equilibrium, the less it is affected by changes in scan rates, and the greater the ξ value corresponding to the framework, consistent with the abnormal expansion of the framework with D₂O observed via PXRD (Fig. 2f). The O − H···N hydrogen bond distance in 1·3H₂O·3/2CH₃OH is 2.904(4) Å at 293 K, indicating that the samples with the guest-saturated states are weak H-bonded compounds (D: proton donor, A: proton acceptor, d_D···A > 2.90 Å). However, minute shifts in H-bonded distance can be propagated cooperatively through the crystal lattice, with deuteration effects influencing the physical and chemical properties of the materials (Table S3).^[63] The thermal hysteresis loops of Fe1 fluctuate with changes in the immersed solvent system, directly indicating the involvement of guest molecules in the strong cooperative interactions among the metal centers.^{[56, 59]} The SCO behavior of the framework, particularly the slow spin equilibrium of Fe2, exhibits high sensitivity and can be manipulated by the guest molecules, including both CH₃OH, H₂O, and D₂O. Additionally, hydrogen-bonding distances decrease upon cooling (Table S3), suggesting ferro-elastic interactions between the host and guest.^[45]

To further elucidate the high sensitivity of slow spin equilibrium to guest molecules, a comprehensive analysis was performed on varying scan rates (10, 5, 2, 1, 0.5, 0.25, and 0.1 K min^− 1) and in-situ varying guest-saturated states (intact and partially guest-depleted state in 8:2 and 10:0 H₂O-CH₃OH ratios) using the semi-sealed method (Figs. 3 and Fig. S18-25). The guest-saturated samples with 8:2 and 10:0 H₂O-CH₃OH ratios were loaded at 250 K to maintain the intact states, and the corresponding partially guest-depleted states were achieved by heating in situ to 300 K and holding for 10 min. The four types of guest-saturated samples exhibit two-step incomplete SCO properties at all scan rates, while the completeness of the 2nd-step spin transition is significantly affected by varying scan rates. For the guest-saturated with an initial 10:0 H₂O-CH₃OH ratio, the minimum γ_HS values of the intact state are from 0.412 at 10 K min^− 1 (max. scan rate) to 0.159 at 0.1 K min^− 1 (min. scan rate), and from 0.224 at 10 K min^− 1 to 0.104 at 0.1 K min^− 1 for partially guest-depleted state (Figs. 3a and 3b). In comparison, the min. γ_HS values of the intact and partially guest-depleted states of the guest-saturated samples with 8:2 H₂O-CH₃OH ratio are higher than those of the two states of the sample with 10:0 H₂O-CH₃OH ratio at each scan rate (Figs. 3c and 3d). Specifically, the min. γ_HS values range from 0.469 at 10 K min^− 1 to 0.194 at 0.1 K min^− 1 for the intact state and from 0.329 at 10 K min^− 1 to 0.157 at 0.1 K min^− 1 for the partially guest-depleted state. The partially guest-depleted state has a higher completeness of SCO at high scan rates compared to the intact state with the same initial H₂O-CH₃OH ratio, showing an increase of 18.8% at 10 K min^− 1 for 10:0 H₂O-CH₃OH ratio and 14% at 10 K min^− 1 for 8:2 H₂O-CH₃OH ratio (Fig. 3e). As the scan rate decreases, the gap between the two states diminishes, resulting in an increase in SCO completeness at 0.1 K min^− 1 by 5.5% for the 10:0 H₂O-CH₃OH ratio and 3.7% for the 8:2 H₂O-CH₃OH ratio.

The thermal hysteresis loops of Fe1 (1st-step SCO) become slightly narrower after the partial loss of the guest molecules, with the hysteresis width remaining largely unaffected by changes in the scan rate. The slow spin equilibrium of Fe2 (2nd-step SCO) is shown to be influenced by the manipulation of guest molecules, exhibiting regular behavior under the influence of guest load: In the partially guest-depleted state, the slow spin equilibrium of Fe2 is more easily overcome by scan rates than in the corresponding intact state, showing a larger difference at higher scan rates and a smaller difference at lower scan rates between the two states; For each guest-saturated sample, high scan rates (10 and 5 K min^− 1) have a minimal effect on the completeness of the 2nd-step spin transition. In contrast, medium scan rates (2, 1, and 0.5 K min^− 1) amplify the effect, low scan rates (0.25 K min^− 1) have a minor effect, and ultra-low scan rates (0.1 K min^− 1) exhibit an enlarged effect (Figs. 3f and 3g).

To thoroughly investigate the number of guest molecules influences SCO properties, magnetic susceptibilities of the guest-saturated sample with a 2:8 H₂O-CH₃OH ratio were measured across various temperature cycles during in-situ gradual desolvation (Figs. 4 and S26 –S29). When loaded at 250 K to maintain the intact state, the slow spin equilibrium of Fe2 was noted to be difficult to thermally overcome at 1 K min^− 1 (Fig. 4a). Upon in-situ warming to 300 K (holding for 10 min), the spin transition completeness of Fe2 in the partially guest-depleted state significantly improved, dropping unexpectedly from 62 K and reaching a min. γ_HS value of 0.20 at 85 K during the warming process (Figs. 4b and S26). The dynamic phenomenon is attributed to a temperature-induced excited spin-state trapping (TIESST) effect or slow spin equilibrium. Further in-situ heating to 310 K (holding for 10 minutes) caused additional loss of guest molecules, allowing the spin equilibrium of Fe2 to be rapidly achieved, with a min. γ_HS value ultimately reaches 0.03 in this cooling-warming cycle (Fig. 4c). This indicates a two-step complete SCO behavior, suggesting that the slow spin equilibrium of SCO has entirely disappeared. Subsequently, the sample was heated to 395 K to ensure most guest molecules were lost, leading to a two-step SCO without a plateau, corresponding to a single-crystal-to-single-crystal transformation as described in previous studies (Figure S27).^[57] Those high-temperature-treated samples were immersed in water, and the magnetic susceptibilities of the reabsorbed guest-saturated samples were collected, retaining the slow spin equilibrium of SCO (Figures S28 and S29). Hence, the slow spin equilibrium of the guest-saturated samples shifts with the loss of guest molecules—from being difficult to thermally overcome, to easily thermally overcome, to a full spin transition indicative of fast spin equilibrium. The regulation of SCO with slow spin equilibrium is more challenging through the method of guest molecule loss, which also exerts a greater influence on the elastic frustration of the framework compared to altering the type and ratio of the immersed solvent.

In conclusion, a strategy for guest-manipulated slow spin equilibrium in two-step SCO behavior is proposed to achieve bidirectional modulation of the untouched region between one-step incomplete (HS_0.5LS_0.5↔HS) and two-step complete (LS↔HS_0.5LS_0.5↔HS) SCO behaviors in such Hofmann-type MOFs. The SCO properties of the framework stuffed with H₂O versus D₂O states for variant scan rate-dependent slow spin equilibrium exclude the effect of the size of the guest molecule. The ranking of H₂O, D₂O, and CH₃OH guest molecules regarding the degree of SCO completeness is summarized, while the PXRD data for different guest-saturated states indicate the contraction/expansion of the framework. This also impacts the elastic frustration of the framework structure, consistent with its effect on the spin equilibrium of Fe2. The SC-XRD data for 1·3H₂O·3/2CH₃OH (the guest-saturated sample with a 5:5 H₂O-CH₃OH ratio) reveal that CH₃OH molecules preferentially replace H₂O molecules in the central part of the pore cavities while the overall framework does not change significantly. Even though the potential mechanisms controlling these slow spin equilibria have not been fully established, it is evident that guest molecules can achieve detailed regulation of the slow spin equilibrium in guest-saturated states through host-guest interactions. This provides novel insights and methods for designing new SCO material systems and for rationally modeling theoretical calculations of SCO textures.

Synthesis of [Fe ^II (prentrz) ₂ Pd ^II (CN) ₄ ]·guest (1·guest) and guest exchange. The pristine crystals of 1·guest were synthesized by the method of slow diffusion reported previously.^[56] The samples in the guest-saturated state with H₂O-CH₃OH (10:0, 8:2, 5:5, 2:8), H₂O-D₂O (5:5), and D₂O-CH₃OH (10:0, 8:2) ratios were obtained by guest exchange through immersion of the as-synthesized samples in respectively pure mixture solutions (10 mL) for 3 times.

Single-Crystal X-ray Diffraction (SC-XRD) Measurements. The crystal data for the guest-saturated state 1·3H₂O·3/2CH₃OH were recorded at 293, 190, 150, 130, 120, and 85 K, respectively, with a Bruker/ARINAX MD2 diffractometer equipped with a MarCCD-300 detector (λ = 0.77484 Å) at the BL17B beamline station of the Shanghai Synchrotron Radiation Facility (SSRF). A total of 360 frames were collected using ω-scans with the 1^o oscillation angle, spanning from 0 to 360^o, an exposure time of 0.50 s per frame, and a detector distance of 90 mm. The BlueIce software was used to collect data. The dataset was collected on the beamline configured with a single-axis goniometer, which enabled phi-scans. However, the orientation of the small-molecule crystal and its low symmetry presented challenges in capturing 100% of reflections within this setup. Unit cell parameters were refined and data reduction was carried out using the HKL3000 software.^[64]

All the structures were determined using direct methods and subsequently refined through full-matrix least-squares techniques on F² using the SHELX program.^[65] Non-hydrogen atoms underwent anisotropic refinement, whereas hydrogen atoms were placed in geometrically idealized positions and refined with isotropic displacement parameters.

Powder X-ray diffraction (PXRD) Measurements. The PXRD data were recorded on a Bruker D8 ADVANCE diffractometer with Cu Kα radiation at room temperature. The samples immersed in solutions with H₂O-CH₃OH (10:0, 8:2, 5:5), H₂O-D₂O (5:5), and D₂O-CH₃OH (10:0, 8:2) ratios were loaded on the glass sample table with a circular groove (diameter ~ 2 cm, thickness ~ 1 mm). After flattening and compacting the samples, two drops of the solution with the corresponding ratio were added to the sample surface, and then the glass sample table including samples was coated with a PE film to keep the guest-overload state during the measurement.

Magnetic Measurements. The measurements of variable-temperature magnetic susceptibilities

were performed on a Quantum Design MPMS XL-7 magnetometer working in the range of 2–400 K with 10, 5, 2, 1, 0.5, 0.25, and 0.1 K min^–1 sweeping rate under the 5000 Oe magnetic field.

The magnetic test samples are divided into two production methods according to the full-sealed and semi-sealed conditions as follows:

The full-sealed method involved high-temperature sintering of a quartz tube containing guest-exchange samples. The as-synthesized samples were placed at the bottom of the quartz tube, and guest exchange was performed as the same method described above. After the exchange, the excess solutions were thoroughly removed. The sample was then vacuum-sealed while being frozen in liquid nitrogen. During this process, a handheld gas torch was used to sinter and seal the quartz tube approximately 3 cm above the samples. The sealed quartz tube containing the samples was subsequently fixed for magnetic testing.

The semi-sealed method involved wrapping the guest-exchange samples with a PE film. The samples were placed in the center of the PE film (3 × 3 cm²), followed by the addition of two drops of the corresponding pure mixture solutions, then quickly wrapped and folded. Absorbent cotton was used to soak up the excess solution around the sample, which was subsequently wrapped with an additional layer of PE film. The samples were loaded into the SQUID chamber at 250 K.

Acknowledgments

This work was funded by the National Natural Science Foundation of China (Grants 92161123, 21971078). We thank Zi-Shuo Yao and Jun Tao at Beijing Institute of Technology for the technical support of magnetic measurements. The SC-XRD data was collected at BL17B beamline of the National Center for Protein Sciences at Shanghai Synchrotron Radiation Facility.

Author contributions

J.-P.X. proposed the idea, and designed the research. J.-P.X., Y.C., and Y.-T.Y performed syntheses and measurements. J.-P.X. and Y.C. performed the magnetic and SC-XRD measurement. Y.-T.Y performed the PXRD measurements. J.-P.X., X.L. and B.L. supervised the research. J.-P.X., Y.C. and B.L. wrote the manuscript. All authors discussed the results and commented on the manuscript.

Additional information

Supplementary Information is available in the online version of the paper.

Corresponding author: Correspondence and requests for materials should be addressed to [email protected] (J.-P.X); [email protected] (B.L.).

Competing financial interests

The authors declare no competing interests.

Data availability

The data supporting the findings of this study are available within the article and its Supplementary Information. The crystallographic data for The X-ray crystallographic coordinates for structures reported in this study have been deposited at the Cambridge Crystallographic Data Centre (CCDC) under deposition numbers CCDC: 2357594 (the guest-saturated state 1·3H₂O·3/2CH₃OH at 293 K), 2357595 (the guest-saturated state 1·3H₂O·3/2CH₃OH at 190 K), 2350745 (the guest-saturated state 1·3H₂O·3/2CH₃OH at 150 K), 2350741 (the guest-saturated state 1·3H₂O·3/2CH₃OH at 130 K), 2357603 (the guest-saturated state 1·3H₂O·3/2CH₃OH at 120 K), and 2357613 (the guest-saturated state 1·3H₂O·3/2CH₃OH at 85 K). These data can be obtained free of charge via http://www.ccdc.cam.ac.uk/data_request/cif.

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Table of Contents: A strategy for guest-manipulated slow spin equilibrium of SCO behaviour is proposed to achieve different degrees of spin equilibrium within a Hofmann-type framework at the same temperature scan rate. This approach enables bidirectional modulation of the unexplored region between one-step incomplete (HS_0.5LS_0.5«HS) and two-step complete (LS«HS_0.5LS_0.5«HS) SCO behaviors. The guest-saturated states are achieved using both full-sealed and semi-sealed methods, with the slow spin equilibrium controlled from difficult to thermally overcome to fully overcome by modulating the mixing ratios and types of CH₃OH, H₂O, and D₂O in the immersed solvents.
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theguestsaturatedstateat120K.cif
theguestsaturatedstateat130K.cif
theguestsaturatedstateat150K.cif
theguestsaturatedstateat190K.cif
theguestsaturatedstateat293K.cif
theguestsaturatedstateat85K.cif

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Entanglement of Spin Transition and Elastic Interactions: Manipulating the Slow Spin Equilibrium by Guest-Mediated Fine-Tuning Elastic Frustration

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