Counterions manage metal-to-metal electron transfer: the role of intermolecular interactions in MMET-active [Fe₄Co₄] cubes

Abstract

Unveiling the effect of intermolecular interactions on metal-to-metal electron transfer (MMET) is challenging, but preferentially essential for the engineering of magnetically switchable crystalline materials and devices. Herein, we reported a family of [Fe₄Co₄] cubes sharing the identically cyanide-bridged cubic octanuclear architecture {[Fe(pzTp)(CN)₃]₄[Co(ddpd)]₄}⁴⁺ (pzTp⁻ = tetrakis(pyrazolyl)borate, ddpd = N,N’-dimethyl-N,N’-dipyridin-2-ylpyridine-2,6-diamine) but different counterions with tunable sizes, including BF₄⁻ (1·BF₄), ClO₄⁻ (2·ClO₄), PF₆⁻ (3·PF₆), AsF₆⁻ (4·AsF₆) and SbF₆⁻ (5·SbF₆). All compounds were isomorphic and crystallized in the tetragonal P4̄2₁c space group. Magnetic susceptibility measurements revealed that compound 1·BF₄ with the smallest counterion exhibited the most pronounced MMET behavior, while 5·SbF₆ with the largest counterion completely lost the MMET behavior. By employing both experimental and computational approaches, we demonstrated that the number and strength of intermolecular interactions depend highly on the counterion size. The enhanced interactions impose a strong limiting effect on the octahedral coordination geometry of the cobalt centers, which consequently have a non-negligible influence on the orbital overlap, electrostatic potential, and redox potentials, thereby modulating MMET behavior.

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Introduction

The engineering of magnetically switchable molecules has been a prominent research focus for the past two decades.^1–6 In these molecules, metal-to-metal electron transfer (MMET) induced by external stimuli such as temperature, light, and pressure typically leads to significant alterations in the spin state, charge distribution, and magnetism.^7–16 Additionally, MMET can be coupled with other functional properties, including positive or negative thermal expansion and fluorescence. Therefore, it has vast potential applications in molecule-based high-density memory, switches, and sensors.^17–20 A typical MMET system consists of cyanide-bridged Fe/Co Prussian blue analogues (PBAs), which specifically exhibit thermally/light induced interconversion between the diamagnetic [Fe^II_LS(μ-CN)Co^III_LS] (LS = low spin) and the paramagnetic [Fe^III_LS(μ-CN)Co^II_HS] (HS = high spin) configurations, known as metal-to-metal electron transfer coupled spin transition (ETCST).^21–26

Cyanide-bridged Fe/Co PBAs have been extensively investigated in the context of MMET studies. By meticulously controlling the number, position, and orientation of cyanide-bridged ligands, as well as the denticity and electronic effects of ancillary ligands, a diverse array of Fe/Co MMET molecules with varying dimensionality and nuclearity have been synthesized.^27–38 [Fe₄Co₄] cubic compounds, as representative zero-dimensional PBAs, feature molecular frameworks that serve as fundamental motifs for constructing three-dimensional PBAs. Additionally, these compounds exhibit intramolecular metal-to-metal electron transfer and concomitant spin transition properties, which facilitate the establishment of magneto-structural correlations. In 2008, Holmes, Clérac, and Mathonière et al. reported the first cyanide-bridged [Fe₄Co₄] cube, which exhibited reversible and steep thermally induced ETCST at 250 K as well as the impressively long-lived paramagnetic metal phases at 150 K.³⁹ Recently, Lescouëzec and co-workers reported a family of alkali-inserted [Fe₄Co₄] cubes, denoted as A⊂[Fe₄Co₄] (A⁺ = K⁺, Rb⁺, or Cs⁺).⁴⁰ They found that the interaction between the inserted alkali metal ions and the [Fe₄Co₄] cube framework, along with the structural changes induced by MMET, could significantly influence the stability and relaxation temperature of the photo-induced states. Very recently, Zhang et al. prepared two [Fe₄Co₄] cubes.⁴¹ Due to the elastic frustration originating from competing intermolecular interactions along different directions, the all-alkynyl functionalized [Fe₄Co₄] cubic compound exhibited a thermally induced incomplete MMET behavior. In contrast, the other [Fe₄Co₄] cubic compound, which lacks such competition interactions, demonstrated a complete and sharp MMET behavior. It is evident that the intramolecular MMET and the stability of photo-excited metastable states are significantly influenced by multiple factors, including coordinating ligands, encapsulated ions, and second coordination sphere interactions. Therefore, further investigation into the structure–property relationships in these systems is warranted.

It is considered that intermolecular interactions might be a key factor in regulating MMET behavior.^42–44 Currently, most research approaches focus on decorating different functional groups onto the chelating ligands within the [Fe₄Co₄] cube or adding alkali metals to directly change the metal valence.^{40–42,45–47} We notice that counterions featuring different volume sizes can serve as ideal candidates for purposely tuning intermolecular interactions, effectively eliminating the influence of varying ligand field strength resulting from different chelating ligands on the MMET behavior. However, although counterions can indirectly influence the redox potentials of metal centers through modulation of intermolecular interactions, the dominant mechanism is still unclear and remains to be exploited. To further understand the effect of counterions on intramolecular electron transfer behavior, herein, we designed five new octanuclear [Fe₄Co₄] cubes with the formula {[Fe(pzTp)(CN)₃]₄[Co(ddpd)]₄}·4A⁻·nH₂O (pzTp⁻ = tetrakis(pyrazolyl)borate, ddpd = N,N’-dimethyl-N,N’-dipyridin-2-ylpyridine-2,6-diamine, A⁻ = BF₄⁻ (1·BF₄), ClO₄⁻ (2·ClO₄), PF₆⁻ (3·PF₆), AsF₆⁻ (4·AsF₆), and SbF₆⁻ (5·SbF₆)). The tridentate auxiliary ddpd ligand was selected due to its extended π-conjugation and high symmetry, which facilitate the formation of intermolecular interactions. Our results demonstrated that these five cubes exhibited a quasi-identical [Fe₄Co₄] core with consistent packing modes. As expected, the strength and number of intermolecular interactions between the [Fe₄Co₄] cubes, as well as the interactions between the cubes and counterions, can be systematically tuned by varying the size of the counterions. This provides an ideal platform for exploring the correlations between tunable intermolecular interactions and metal-to-metal electron transfer (MMET) behavior. By employing the experimental and computational approaches, we found that as the number of intermolecular interactions increased, their impact on the local coordination environment of the Co centers and their influence on the redox potential of the Co ions became significant. These interactions hindered the deformation of the CoN₆ coordination sphere and the reduction of the Co center, and resulted in a reduced degree of metal-to-metal electron transfer (MMET) for the complexes 1·BF₄, 2·ClO₄, 3·PF₆, 4·AsF₆, and 5·SbF₆.

Results and discussion

Structural characterization

Single crystal X-ray diffraction (SCXRD) data were collected on crystals of 1·BF₄, 2·ClO₄, 3·PF₆, 4·AsF₆, and 5·SbF₆ at both 120 K and 400 K (Tables S1 and S2). Powder X-ray diffraction (PXRD) patterns match well with their SCXRD simulations, thereby confirming the phase purity of the bulk crystalline products (Fig. S28). Compounds 1·BF₄, 2·ClO₄, 3·PF₆, 4·AsF₆, and 5·SbF₆ all crystallize in the tetragonal P4̄2₁c space group, remaining unchanged at all temperatures, which indicates that they have similar molecular packings. Furthermore, these compounds manifested similar macroscopic morphologies, presenting as dark green block crystals. The asymmetric units of 1·BF₄, 2·ClO₄, 3·PF₆, 4·AsF₆, and 5·SbF₆ exhibit a similar structural arrangement. Each [Fe₄Co₄] cubic unit consists of a cyanide-bridged cubic cation of {[Fe(pzTp)(CN)₃]₄[Co(ddpd)]₄}⁴⁺, along with four counterions. This configuration ensures that all Co or Fe atoms are positioned in identical chemical environments. As illustrated in Fig. 1, four iron ions and four cobalt ions, alternately located at the corners of the cube, are linked along the edges by twelve cyanide groups. Each iron ion is capped by one pzTp⁻, affording a [FeC₃N₃] coordination environment; each cobalt ion is capped by one auxiliary ddpd ligand, forming a [CoN₆] coordination environment.

Fig. 1 Molecular structures of 1·BF₄, 2·ClO₄, 3·PF₆, 4·AsF₆, and 5·SbF₆ at 120 K. Color code: Co^III_HS, pink; Fe^II from [(pzTp)Fe(CN)₃]²⁻, green; N, blue; C, gray; F, purple; B, orange; O, red; Cl, maroon; P, olive; As, cyan; and Sb, navy. Hydrogen atoms and lattice solvent molecules are omitted for clarity.

For 1·BF₄, the average Co–N bond length at 120 K is 1.917 Å, which is similar to the values previously observed for Co^III_LS ions in the relevant molecular cubes (Table S4). The average distances of Fe–C and Fe–N are 1.883 Å and 1.995 Å, respectively, which are also consistent with those for the previously reported complexes containing [(pzTp)Fe^II(CN)₃]²⁻ units (Table S6).⁴¹ These structural results indicate that in the low-temperature phase (LT phase), compound 1·BF₄ is in the diamagnetic [Fe^II_LS(μ-CN)Co^III_LS] state. As the temperature increased to 400 K, the average Co–N bond length of 1·BF₄ in the high-temperature phase (HT phase) extended to 1.936 Å. However, it is still far shorter than typical Co–N bond lengths observed in Co^II_HS complexes. Structural distortions could be evaluated by calculating the octahedral distortion parameters Σ and the continuous shape measures (CShM). The octahedral distortion parameters around the Co centers (Σ_Co and CShM_Co) for 1·BF₄, 2·ClO₄, 3·PF₆, 4·AsF₆, and 5·SbF₆ were analyzed and are shown in Table 1. In the LT phase, the Σ_Co and CShM_Co of 1·BF₄ are 32.26° and 0.219, respectively, while in the HT phase, the values of Σ_Co and CShM_Co increase to 41.39° and 0.296. The above results indicate that in the HT phase, compound 1·BF₄ exists as a mixture of diamagnetic [Fe^II_LS(μ-CN)Co^III_LS] and paramagnetic [Fe^III_LS(μ-CN)Co^II_HS] states.

Table 1 Structural parameters around the Co centers for 1·BF₄, 2·ClO₄, 3·PF₆, 4·AsF₆, and 5·SbF₆

Compounds	Σ ^120 KCo	Σ ^400 KCo	CShM^120 KCo^b	CShM^400 KCo
a Σ Co (°): the sum of |90° − α| for the 12 cis N–Co–N angles around the cobalt atom. b CShMCo: the continuous shape measurement relative to the ideal octahedron of the Co centers; zero value means the ideal octahedron geometry.
1·BF4	32.26	41.39	0.219	0.296
2·ClO4	25.11	40.53	0.159	0.321
3·PF6	40.97	46.09	0.342	0.400
4·AsF6	32.76	33.90	0.275	0.281
5·SbF6	38.18	34.21	0.282	0.260

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Similar to 1·BF₄, the Co–N bond lengths in the LS phase are 1.926 Å for 2·ClO₄, 1.925 Å for 4·AsF₆, and 1.934 Å for 5·SbF₆, and the Σ_Co and CShM_Co are 25.11° and 0.159 for 2·ClO₄, 32.76° and 0.275 for 4·AsF₆, and 38.18° and 0.282 for 5·SbF₆, which are also characteristic of the previously reported Co^III_LS. The Co–NC angles in all five cubic compounds do not exhibit any significant variations (Fig. S12; the Co–NC angles are all around 175°). It is because the extensive intermolecular interactions present in each compound generate compact packings that preclude substantial distortion of the Co–NC angle. In addition, the average Fe–CN–Co edge lengths are 4.92 Å for 1·BF₄, 4.92 Å for 2·ClO₄, 4.91 Å for 4·AsF₆, and 4.92 Å for 5·SbF₆, which align well with the expected value for Fe^II–CN–Co^III linkages (approximately 4.91 Å). In analogous [Fe₄Co₄] cubic frameworks, the incorporation of high-spin Co(II) ions generally leads to an elongation of the Fe–CN–Co edge length.^40,47,48 Notably, in 3·PF₆, the measured average Fe–CN–Co edge length (4.95 Å) is larger than that observed in the other four cubes, indicating the presence of HS Co^II species within 3·PF₆. In addition, in the LT phase, 3·PF₆ has a Co–N bond length of 1.950 Å, which is longer than the Co–N bond lengths of the remaining four compounds, and the values of Σ_Co and CShM_Co are also larger than those of the remaining four compounds, suggesting that 3·PF₆ is in a mixture state rather than the fully diamagnetic [Fe^II_LS(μ-CN)Co^III_LS] state. It is worth noting that the Σ_Co and CShM_Co of 2·ClO₄ and 3·PF₆ also increase during the transition from the LT phase to the HT phase, following the same trend as 1·BF₄. However, for 4·AsF₆ and 5·SbF₆, the values of Σ_Co and CShM_Co for the HT phase are almost constant or even smaller compared to those of the LT phase, which indicates that 1·BF₄, 2·ClO₄, and 3·PF₆ may have MMET behavior while 4·AsF₆ and 5·SbF₆ do not.

Magnetic properties

Variable temperature susceptibility measurements were conducted to probe the ETCST property. As depicted in Fig. 2, compounds 1·BF₄, 2·ClO₄, 3·PF₆, 4·AsF₆, and 5·SbF₆ all exhibited temperature dependence of susceptibilities but with significant differences. At 120 K, the χT (χ = molar susceptibility) values were 0.49 cm³ mol⁻¹ K, 0.49 cm³ mol⁻¹ K, 0.63 cm³ mol⁻¹ K, and 0.73 cm³ mol⁻¹ K for 1·BF₄, 2·ClO₄, 4·AsF₆, and 5·SbF₆, respectively, close to the theoretical values for four LS Fe^II (S = 0) ions and four LS Co^III (S = 0) ions, implying that they were in the diamagnetic [Fe^II_LS(μ-CN)Co^III_LS] state in the LT phase. The slightly positive χT value might be due to a small amount of residual paramagnetic state. Exceptionally, the χT value was 2.41 cm³ mol⁻¹ K for 3·PF₆ at 120 K, which was higher than the χT values of the other four compounds. This suggested that 3·PF₆ was in a mixed state in the LT phase. These findings are consistent with the results obtained from bond length data and the octahedral distortion parameters in the LT phase. As the temperature was further reduced from 120 K, the χT values of all five compounds showed a slight decrease, which could be attributed to the effect of intermolecular antiferromagnetic interactions of the remaining paramagnetic metal centers or the zero-field splitting of the HS Co ions. As the temperature increased from 120 to 400 K, the χT values of 1·BF₄, 2·ClO₄, and 3·PF₆ showed a steady increase at 250 K, 310 K, and 360 K, respectively. Then, their χT values reached 1.25 cm³ mol⁻¹ K, 0.94 cm³ mol⁻¹ K, and 2.51 cm³ mol⁻¹ K at 400 K. These observations indicate that thermally induced desolvation triggers structural reorganization and subsequently promotes the incomplete MMET. For compounds 4·AsF₆ and 5·SbF₆, their χT values were essentially unchanged, indicating that they do not undergo electron transfer. It should be noted that, for all compounds, the MMET process is not reversible after heating to 400 K (Fig. S6), which is associated with the loss of crystallized solvent molecules. This phenomenon is similar to observations in previously reported FeCo molecular switches.^40,46–48

Fig. 2 Temperature-dependent susceptibilities of 1·BF₄, 2·ClO₄, 3·PF₆, 4·AsF₆, and 5·SbF₆ under the scan rate of 2 K min⁻¹. The presented magnetic susceptibility corresponds to the full [Fe₄Co₄] cubic unit.

Variable-temperature infrared studies and dielectric properties

To further probe the MMET property, variable-temperature infrared (VT-IR) spectra were collected for the solid samples of 1·BF₄, 2·ClO₄, 3·PF₆, 4·AsF₆, and 5·SbF₆. For compound 1·BF₄ (Fig. 3), three cyano stretching bands (ν_CN) were observed at 2111, 2125, and 2144 cm⁻¹ at 250 K. Upon increasing the temperature to 400 K, all bands shifted to slightly lower wavenumbers and significantly decreased in intensity, which can be assigned to the characteristic cyanide stretches (ν_CN) for the [(pzTp)Fe^II(CN)₃]²⁻ units in the bridging mode, suggesting the diamagnetic [Fe^II_LS(μ-CN)Co^III_LS] state in the LT phase.^{31,35,49–54} Similarly, the same characteristic cyanide stretching bands were observed for 2·ClO₄ (2126 and 2146 cm⁻¹), 3·PF₆ (2113, 2125 and 2145 cm⁻¹), 4·AsF₆ (2146 and 2126 cm⁻¹), and 5·SbF₆ (2147 and 2125 cm⁻¹) at 300 K, and these shifted to slightly lower wavenumbers at 400 K. Notably, similar to compound 1·BF₄, these ν_CN bands in compounds 2·ClO₄ and 3·PF₆ also exhibited a significant decrease in intensity with increasing temperature. This observation suggests a continuous decrease in the population of the diamagnetic [Fe^II_LS(μ-CN)Co^III_LS] component. In contrast, the absorption bands of 4·AsF₆ and 5·SbF₆ did not change with temperature variations, indicating that the MMET process did not occur. This observation also agrees with the aforementioned results. As depicted in Fig. S2 and S3, compounds 1·BF₄ and 2·ClO₄ exhibited an additional absorption band around 2174 cm⁻¹, which can be assigned to the bridging ν_CN absorptions of Fe^III_LS–C≡N–Co^II_HS in the HT phase.

Fig. 3 Variable temperature solid state infrared spectra of 1·BF₄, 2·ClO₄, 3·PF₆, 4·AsF₆, and 5·SbF₆.

After all samples were heated to remove lattice solvents, IR measurements were performed again (Fig. S1). The absorption bands of all compounds remained unchanged with temperature variations, suggesting that they no longer exhibit MMET behavior after the loss of lattice solvents. In addition, to gain more insight into the mixed-spin LT phase of 3·PF₆, ⁵⁷Fe Mössbauer spectral data were collected. The calculated peak area ratio of the two doublets was 9.42 : 90.58, which means that 3·PF₆ is a mixed-spin state in the LT phase (Fig. S29). Moreover, variable-temperature permittivity measurements were performed in the frequency range of 0.5–1000 kHz from 250 to 380 K for 1·BF₄ and 2·ClO₄. As shown in Fig. S4 and S5, the dielectric constant ε′ (ε* = ε′ − iε′′, where ε′ and ε′′ are the real and imaginary parts of the dielectric constants, respectively) exhibited typical peaks in the temperature range tested, confirming the synergetic transitions of MMET behavior and dielectric properties.

Magneto-structural correlation

Compounds 1·BF₄, 2·ClO₄, 3·PF₆, 4·AsF₆, and 5·SbF₆ have the same spatial packing pattern, yet exhibit completely different MMET behavior due to the presence of different counterions. Since these five complexes are isomorphic, 1·BF₄ is used as an example for the description of the structural details. Given that all compounds contain a considerable amount of lattice solvents, and that they do not form significant hydrogen bonding interactions with [Fe₄Co₄] cubes, our analysis primarily focused on the intermolecular interactions between the cubes and the counterions. To clearly distinguish the arrangement of [Fe₄Co₄] cubes in different planes, we set the bc plane to orange color and the ab plane to blue color. As shown in Fig. 4a, the centers of the nearest four [Fe₄Co₄] cubes in 1·BF₄ in the ab plane are connected by the blue line, which forms a standard square. Similarly, the centers of the four nearest [Fe₄Co₄] cubes in the bc plane are connected by a yellow line, which, together with the blue line, forms a large artificial cuboid. At this point, the three edge lengths of the cuboid are exactly the lengths of the cell parameters (a, b, and c). The cuboid contains 9 [Fe₄Co₄] cubes, with the centers of the eight [Fe₄Co₄] cubes located at the eight vertices of the cuboid, and the 9th [Fe₄Co₄] cube positioned at the center of the cuboid. Given that these compounds are isomorphic, a similar situation exists in 2·ClO₄, 3·PF₆, 4·AsF₆, and 5·SbF₆. In Fig. S7, the intermolecular interactions for 1·BF₄, 2·ClO₄, 3·PF₆, 4·AsF₆, and 5·SbF₆ between these 9 [Fe₄Co₄] cubes are represented. The [Fe₄Co₄] cube at the center interacts with each [Fe₄Co₄] cube at the vertices of the cuboid through C–H⋯π interactions (yellow dashed lines in Fig. 4d and Fig. S8a, S9a, S10a, and S11a). The C–H⋯π interactions are formed by the uppermost pyrazole on the building unit [(pzTp)Fe^II(CN)₃]²⁻ and the pyridine ring on the auxiliary ddpd ligand on the other [Fe₄Co₄] cube. It is worth mentioning that the number of these C–H⋯π interactions remains constant in 1·BF₄, 2·ClO₄, 3·PF₆, 4·AsF₆, and 5·SbF₆.

Fig. 4 (a) Molecular stacking of [Fe₄Co₄] cubes in 1·BF₄ with a/b/c representing the cell parameters. (b) Molecular stacking in the ab-plane for 1·BF₄; the black dashed line represents the presence of intermolecular interactions. (c) Molecular stacking in the bc-plane for 1·BF₄; the black dashed line represents the presence of intermolecular interactions. (d) C–H⋯π interactions between [Fe₄Co₄] cubes and [Fe₄Co₄] cubes (the orange values are the C–H⋯π interaction distance at 120 K, while the grey values are the C–H⋯π interaction distance at 400 K), and C–H⋯F interactions between [Fe₄Co₄] cubes and BF₄⁻ counterions for 1·BF₄ (the blue values are the C–H⋯F interaction distance at 120 K). Color code: Co^III, pink; Fe^II, green; N, blue; C, gray; F, purple; and B, orange. Hydrogen atoms and lattice solvent molecules are omitted for clarity. The intermolecular C–H⋯π interactions are evaluated by yellow dotted lines. The C–H⋯F interactions are evaluated by blue dotted lines. (e) The C–H⋯F interactions between [Fe₄Co₄] cubes and four counterions BF₄⁻ for 1·BF₄ at 120 K. (f) Relationship between cell parameters and the size of counterions at 120 K.

Furthermore, there is a significant amount of C–H⋯F/C–H⋯O interactions between the [Fe₄Co₄] cubes and the counterions (blue dashed lines in Fig. 4d, e and Fig. S8–S11). The [Fe₄Co₄] cubes form a three-dimensional supramolecular network structure through these intermolecular interactions above. In order to illustrate more clearly the effects of the interactions on the structure, we depicted the [Fe₄Co₄] cube at the center of the cuboid and the two [Fe₄Co₄] cubes located on the c-edge of the cuboid (Fig. 4d). The C–H⋯F interactions with lengths of 3.284 Å and 3.244 Å connected the two [Fe₄Co₄] cubes located in the bc plane. This means that the continuous C–H⋯F interactions can well transfer the supramolecular interactions along the c-axis (Fig. 4c). As mentioned above, each [Fe₄Co₄] cube was accompanied by four counterions. As shown in Fig. 4e, the C–H⋯F interaction distances formed between the four BF₄⁻ ions and the [Fe₄Co₄] cubes were all 3.151 Å. However, the [Fe₄Co₄] cubes are not connected to each other by C–H⋯F interactions in the ab plane, suggesting that the C–H⋯F interactions are discontinuous and unable to transfer the supramolecular interactions along the a or b axes (Fig. 4b). A similar situation has also been observed in 2·ClO₄, 3·PF₆, 4·AsF₆, and 5·SbF₆. Due to steric effects in the crystal packing, larger counterions increase the separation between adjacent cubes along the c-axis, leading to an elongation of the c cell parameter as the counterion size increases (Fig. 4f). Interestingly, the C–H⋯π distance decreases with increasing ionic radius (Fig. S13a), indicating that the C–H⋯π interactions are strengthened as the counterions become larger, with the exception of 5·SbF₆. In parallel, the a and b cell parameters exhibit a similar dependence on the ionic radius, contracting as the C–H⋯π interactions intensify. In addition, a clear positive correlation was observed between the cell volume, crystal density, and the ionic radius of the counterions (Fig. S13b). For 3·PF₆, 4·AsF₆, and 5·SbF₆, the higher crystal densities suggest a more compact packing arrangement, likely arising from stronger intermolecular interactions.

Additionally, compared to 1·BF₄ and 2·ClO₄, the increased number of fluorine atoms in PF₆⁻, AsF₆⁻, and SbF₆⁻ can provide more hydrogen bond acceptors, leading to a higher propensity for hydrogen bond formation with the cubic units. Consequently, the number of intermolecular interactions between counterions and the cubic units in 3·PF₆, 4·AsF₆, and 5·SbF₆ is significantly greater than those in 1·BF₄ and 2·ClO₄ (Fig. S8a, S9a, S10a and S11a). A higher degree of intermolecular interactions leads to enhanced structural confinement and restriction, generating strain that kinetically inhibits structural reorganization caused by thermally induced desolvation. Consequently, the a and b cell parameters of 3·PF₆, 4·AsF₆, and 5·SbF₆ remain almost unchanged even at 400 K compared to those measured at 120 K (Fig. S14). In contrast, for 1·BF₄ and 2·ClO₄, the a and b cell parameters undergo significant changes upon thermally induced desolvation, likely due to the insufficient strain to effectively hinder structural reorganization. Similarly, the variation in the c parameter between 120 K and 400 K is notably larger for 1·BF₄ (0.89 Å) and 2·ClO₄ (0.97 Å) compared to those for 3·PF₆ (0.46 Å), 4·AsF₆ (0.53 Å), and 5·SbF₆ (0.30 Å). Furthermore, the distances of some C–H⋯F/O interactions tend to shorten as the size of the counterions increases, indicating a significant enhancement in intermolecular interactions. These findings suggest that the counterions play a crucial role in modulating both the strength and quantity of intermolecular interactions. Consequently, these interactions induce varying degrees of lattice strain, which restricts structural reorganization associated with the spin transition, thereby modifying the metal centers’ coordination geometry and ultimately affecting the MMET behavior.

To further characterize the intermolecular interactions, Hirshfeld surface analysis⁵⁵ was performed for 1·BF₄, 2·ClO₄, 3·PF₆, 4·AsF₆, and 5·SbF₆ (Fig. 5 and Fig. S15 and S16). The Hirshfeld surfaces revealed a high proportion of close contacts (indicated by red regions) for all compounds, suggesting an extensive intermolecular interaction network within their crystal lattices. The 2D fingerprint plots further revealed the contributions, relative strength, and types of these interactions.⁵⁶ Specifically, for 3·PF₆, 4·AsF₆, and 5·SbF₆, the d_i + d_e values are smaller than those of 1·BF₄ and 2·ClO₄ in both the HT phase and LT phase (Fig. 5f), indicating that the relative strength of C–H⋯F/O interactions in compounds 1·BF₄ and 2·ClO₄ is weaker than that observed in compounds 3·PF₆, 4·AsF₆, and 5·SbF₆. Due to the potential contribution of solvent molecules to the C–H⋯O interactions observed in 2·ClO₄, a focused comparison of C–H⋯F interactions was conducted for 1·BF₄, 3·PF₆, 4·AsF₆, and 5·SbF₆ in the LT phase. Fig. 6 shows that the percentage of the Hirshfeld surface area attributed to C–H⋯F contacts in the LT phase in 1·BF₄ is also lower than those observed in 3·PF₆, 4·AsF₆, and 5·SbF₆. Furthermore, in the HT phase, the contribution of solvent molecules to C–H⋯O interactions is zero for 1·BF₄ through 5·SbF₆. Concurrently, the percentage of the Hirshfeld surface area attributed to C–H⋯F/O contacts in 1·BF₄ and 2·ClO₄ remains lower than those observed in compounds 3·PF₆, 4·AsF₆, and 5·SbF₆, consistent with the trend observed in the LT phase.

Fig. 5 Hirshfeld surface mapped and 2D fingerprint plots of C–H⋯F/C–H⋯O contacts showing the percentages of contacts contributed to the total Hirshfeld surface area of molecules for 1·BF₄ (a), 2·ClO₄ (b), 3·PF₆ (c), 4·AsF₆ (d), and 5·SbF₆ (e) at 120 K and 400 K. (f) Relationship between d_i + d_e and the size of counterions. The smaller the value (d_i + d_e), the stronger the intermolecular interactions.

Fig. 6 Percentages of main contacts contributed to the total Hirshfeld surface area of molecules for 1·BF₄, 2·ClO₄, 3·PF₆, 4·AsF₆, and 5·SbF₆ at 120 K and 400 K.

Hirshfeld surface analysis indicates that intermolecular interactions are predominantly governed by H⋯H, H⋯F, and C⋯H/H⋯C contacts, while H⋯O/O⋯H interactions contribute less. This suggests that lattice solvents exert only a minimal influence on the overall intermolecular interactions within the crystal structure (Fig. 6). The lack of substantial hydrogen bonding interactions between the solvent molecules and the [Fe₄Co₄] cubes likely accounts for this limited impact. Importantly, the H⋯F contacts observed in the Hirshfeld analysis directly correlate with the presence of C–H⋯F hydrogen bonds between the [Fe₄Co₄] cubes and the counterions, which indicates that the introduction of different counterions significantly influences the intermolecular interactions. Furthermore, we cannot neglect the H⋯H contacts that play a role in the short contact contributions, which highlights the importance of van der Waals interactions (C–H⋯H) and dipole–dipole interactions (H⋯H) within the crystal lattice. Given that all compounds have the same packing pattern, the difference in H⋯H contact contributions may arise from the effect of the difference in the C–H⋯F interaction contributions on the overall distribution of contributions. Therefore, Hirshfeld surface analysis confirmed that the introduction of different counterions leads to enhanced intermolecular interactions, primarily C–H⋯F/O contacts, consistent with the crystal structure analysis results. This enhancement can better limit the octahedral coordination geometry of the metal centers, hinder structural reorganization associated with the spin transition, and contribute to structural stability.

Given the distinct electronic state of 3·PF₆ in the LT phase compared to those of the other four compounds, to ensure a more rigorous magneto-structural correlation with minimized variability, the comparative analysis was focused on 1·BF₄, 2·ClO₄, 4·AsF₆, and 5·SbF₆, all of which adopt a pure LS state in the LT phase. We calculated the difference in the distortion parameter Σ_Co (ΔΣ_Co = Σ^{400 K}_Co − Σ^{120 K}_Co) for compounds 1·BF₄, 2·ClO₄, 4·AsF₆, and 5·SbF₆ between 120 K and 400 K. The ΔΣ_Co values for 1·BF₄ (9.13°) and 2·ClO₄ (15.42°) are significantly larger than those observed for 4·AsF₆ (1.14°) and 5·SbF₆ (−3.97°). For compounds 4·AsF₆ and 5·SbF₆, the substantial number of intermolecular interactions between the counterions and the cubic units generates significant lattice strains, which effectively constrain the structure. This constraint drives the Co center's coordination geometry to maintain its original state to the greatest extent possible during the transition from the LT to the HT phase, rather than undergoing further distortion. This is reflected in the small or even negative ΔΣ_Co values. This result manifests the absence of MMET behavior. In addition, the strong intermolecular interactions extending along multiple directions not only increase the structural compactness but also promote more isotropic elastic responses. These isotropic interactions are likely responsible for the gradual MMET behavior observed in 1·BF₄ and 2·ClO₄. Therefore, the key factor governing the MMET behavior is the modulation of intermolecular interactions resulting from counterion substitution. Enhanced intermolecular interactions between counterions and the cubic units act as a kinetic barrier, hindering the structural reorganization associated with the spin transition, thereby keeping the Co centers’ coordination geometry from distorting further and ultimately suppressing the MMET behavior. In essence, the stronger intermolecular interactions between counterions and the cubic units shift the equilibrium towards the LS state, rendering it thermodynamically more stable than the HS state.

Cyclic voltammetry studies

To further investigate the influence of the intermolecular interactions between counterions and the cubic units on MMET behavior, cyclic voltammetry (CV) measurements for 1·BF₄, 2·ClO₄, 3·PF₆, 4·AsF₆, and 5·SbF₆ were performed. This electrochemical method is advantageous for investigating the thermodynamic tendencies and kinetic pathways of electron transfer behavior exhibited by these compounds when subjected to the external stimuli of the electric field. As depicted in Fig. 7, the CV voltammograms for each compound exhibited one reduction wave and two oxidation waves. The reduction wave, as confirmed by linear sweep voltammetry (LSV) measurements (Fig. S20), corresponds to the reduction process from Co^III to Co^II. Based on comparisons with analogous systems reported in the literature,⁴⁰ the oxidation waves observed at approximately 1.2 V and 0.3 V can be assigned to the Fe^II and Co^II oxidation processes, respectively. Firstly, the half-wave potential (E_1/2) of the Co^III/Co^II redox couple was calculated for 1·BF₄, 2·ClO₄, 3·PF₆, 4·AsF₆, and 5·SbF₆, yielding −0.201, −0.206, −0.201, −0.236, and −0.237 V, respectively. Given the distinct electronic state of 3·PF₆, our comparative analysis focused on 1·BF₄, 2·ClO₄, 4·AsF₆ and 5·SbF₆. The E_1/2 values of the Co^III/Co^II redox couple for 4·AsF₆ and 5·SbF₆ are similar and larger than those for 1·BF₄ and 2·ClO₄, indicating that a more negative potential is required to initiate the reduction reaction in 4·AsF₆ and 5·SbF₆. This suggests that the Co^III centers in 1·BF₄ and 2·ClO₄ may exhibit a greater thermodynamic tendency for reduction compared to those in 4·AsF₆ and 5·SbF₆ under these conditions. This observation aligns well with the variable-temperature magnetic susceptibility data, where the absence of MMET behavior within a measurable temperature range for 4·AsF₆ and 5·SbF₆ implies theoretically much higher T_1/2 values compared to those of 1·BF₄ and 2·ClO₄, signifying a greater thermodynamic stability for 4·AsF₆ and 5·SbF₆.

Fig. 7 Cyclic voltammogram recorded between −1.4 and 1.8 V vs. Ag/AgCl of 1·BF₄, 2·ClO₄, 3·PF₆, 4·AsF₆, and 5·SbF₆ at room temperature at the scan rate of 100 mV s⁻¹. Arrows indicate an open circuit potential along with the direction of the potential sweep.

Furthermore, the reduction peaks observed for 1·BF₄ and 2·ClO₄ around −0.5 V were sharper than those for 4·AsF₆ and 5·SbF₆ around −0.7 V. The peak potential separation (ΔE_p) of the Co^III/Co^II redox couple was smaller for 1·BF₄ (0.546 V) and 2·ClO₄ (0.582 V) compared with those of 4·AsF₆ (0.899 V) and 5·SbF₆ (0.888 V). These observations suggest that the Co^III in 1·BF₄ and 2·ClO₄ can rapidly accept electrons from the electrode surface and undergo electron transfer, a characteristic typically associated with fast electron transfer kinetics. Conversely, the Co^III in 4·AsF₆ and 5·SbF₆ requires a larger activation energy to undergo electron transfer.

Additionally, while the Co^III reduction peaks exhibit comparable intensities across 1·BF₄, 2·ClO₄, 4·AsF₆, and 5·SbF₆, the Co^II oxidation peaks are notably weaker in 1·BF₄ and 2·ClO₄ compared to those in 4·AsF₆ and 5·SbF₆. In contrast, the Fe^II oxidation peaks are significantly more intense in 1·BF₄ and 2·ClO₄ than in 4·AsF₆ and 5·SbF₆. Integrating these electrochemical observations with the magneto-structural correlation analysis results, we tentatively propose that the enhanced intermolecular interactions between the counterions and the cubic units in 4·AsF₆ and 5·SbF₆ impose more significant structural constraints. This, in turn, reduces the extent of orbital overlap (as corroborated by subsequent DFT calculations), thereby progressively hindering the electron transfer pathway. This may be one of the contributing factors to the lower intensity of the Fe^II oxidation peaks observed in 4·AsF₆ and 5·SbF₆.

Theoretical calculations

To further understand how intermolecular interactions affect the MMET behavior, density functional theory (DFT) calculations were performed using the hybrid B3LYP functional based on the LT phase X-ray structures of 1·BF₄ and 5·SbF₆. On the one hand, natural atomic orbital (NAO) analysis was employed to further characterize the atomic orbital contributions to the molecular orbitals potentially involved in electron transfer (Tables S12–S16). As shown in Table 2, NAO analysis reveals a significantly larger orbital overlap integral between the Fe major contributing occupied orbital (MO 824) and Co major contributing unoccupied orbitals (MO 841–844) in 1·BF₄ (0.16) compared to that of 5·SbF₆ (0.13, between orbitals MO 860 and MO 873–876). This enhanced overlap in 1·BF₄ promotes more efficient electronic coupling and thus electron transfer, while the weaker overlap in 5·SbF₆ likely results in a significantly slower electron transfer rate, rendering it undetectable under the experimental conditions.

Table 2 Fe/Co major contributing orbitals, orbital energy, and overlap integral of the norm for 1·BF₄ and 5·SbF₆ at 120 K

Main parameters	1·BF4	5·SbF6
Fe-major contributing occupied orbitals (orbital energy)	MO 824 (−5.58 eV)	MO 860 (−5.76 eV)
Co-major contributing unoccupied orbitals (orbital energy)	MO 841–844 (−1.45 eV)	MO 873–876 (−1.79 eV)
Overlap integral of the norm of the orbitals (a.u.)	0.16	0.13

---

Although the energy differences between the donor and acceptor orbitals are comparable (4.13 eV for 1·BF₄ and 3.97 eV for 5·SbF₆), the difference in overlap likely plays a dominant role in the observed electron transfer behavior. These results suggest that the enhanced intermolecular interactions in 5·SbF₆, arising from the introduction of the larger counterions, may contribute to the attenuation of the overlap between the Fe and Co molecular orbitals, thereby reducing MMET efficiency.

On the other hand, magneto-structural correlation reveals that intermolecular interactions can affect the cobalt centers’ coordination geometry, which in turn affects their electronic structure, redox potential, and also MMET behavior. To gain insight into the influence of intermolecular interactions on the electrostatic structure of the metal centers, the restrained electrostatic potential (RESP) charges,⁵⁷ which provide a qualitative representation of the atomic electrostatic potential, were computed. As shown in Table 3, the RESP charges of both Fe and Co in 1·BF₄ and 5·SbF₆ at 120 K are negative, suggesting significant electron donation from the ancillary ddpd ligands to the metal centers. This can be attributed to the strong σ-donating character of the ddpd ligand, which leads to increased electron density on the metal ions. Notably, the difference in RESP charges between Fe and Co (Δ = −0.369 − (−0.615) = 0.246) in 1·BF₄ was significantly larger than that in 5·SbF₆ (Δ = −0.027 − 0.117 = 0.090). This larger RESP charge difference in 1·BF₄ is consistent with the observed MMET behavior, suggesting a more favorable driving force for electron transfer from Fe^II to Co^III. In contrast, the near-zero RESP charge difference in 5·SbF₆ correlates with the absence of MMET, indicating an insufficient driving force for electron transfer.

Table 3 Mulliken charges and RESP charges of Fe^II and Co^III for 1·BF₄ and 5·SbF₆ at 120 K

Metal	Mulliken charge	Restrained electrostatic potential charge
Fe^II (1·BF4^120 K)	0.325	−0.369
Co^III (1·BF4^120 K)	1.070	−0.615
Fe^II (5·SbF6^120 K)	0.318	−0.027
Co^III (5·SbF6^120 K)	0.810	−0.117

---

Additionally, the electrostatic potential distribution was further analyzed using electrostatic potential maps (Fig. 8).⁵⁸ In 1·BF₄, the nitrogen atom of the cyanide bridge possessed a more negative electrostatic potential than the carbon atom, suggesting a difference that favored electron transfer in the electronic environment along the cyanide bridge. In contrast, the opposite trend was observed in 5·SbF₆, with the nitrogen atom exhibiting a less negative electrostatic potential than the carbon atom. This contrasting electrostatic potential distribution along the cyanide bridge between 1·BF₄ and 5·SbF₆, particularly the difference in the electrostatic potential gradient between the Fe^II and Co^III centers, was consistent with the observed difference in MMET behavior and supported the conclusions drawn from the RESP charge analysis. These theoretical calculations prove that tunable intermolecular interactions can influence the electrostatic structure of the metal centers by affecting their coordination geometry, which consequently influences their redox potentials, thus modulating the MMET behavior.

Fig. 8 Electrostatic potential maps for 1·BF₄ and 5·SbF₆ at 120 K.

Conclusions

In summary, we have synthesized a series of octanuclear [Fe₄Co₄] cubes 1·BF₄, 2·ClO₄, 3·PF₆, 4·AsF₆, and 5·SbF₆, through the self-assembly reaction of divalent Co^II ions, the electron-donating auxiliary ddpd ligand, the tricyanoferrate building unit [(pzTp)Fe^III(CN)₃]⁻, and counterions of varying sizes (BF₄⁻, ClO₄⁻, PF₆⁻, AsF₆⁻, and SbF₆⁻). Variable-temperature magnetic susceptibility measurements revealed a progressive weakening and eventual disappearance of MMET behavior with counterion substitution. For 4·AsF₆ and 5·SbF₆, the increased number and strength of intermolecular interactions formed lattice strain hindering structural reorganization, limiting cobalt coordination sphere distortion, and resulting in a negative shift of the Co^III/Co^II reduction potential. This negative shift, combined with the observed electron density distribution around cobalt centers (reflected by the RESP charge difference and electrostatic potential maps), diminishes the driving force for electron transfer, contributing to the observed inhibition of MMET. Our results suggest that the impact of intermolecular interactions on MMET behavior is not invariably favorable, depending on their strength and quantity. Effective MMET requires a subtle interplay between stabilizing the overall structure through intermolecular interactions and allowing sufficient distortion of the coordination sphere to facilitate efficient electron transfer between the metal centers. These magneto-structural correlations demonstrate that varying the counterions provides an effective strategy for tuning intermolecular interactions, coordination geometry distortion, and consequently the redox properties of the cobalt centers, thereby modulating MMET behavior. This counterion-modulation strategy offers a promising approach for the rational design and assembly of solid-state MMET arrays with tunable and predictable electron transfer properties by precisely controlling the intermolecular interactions and electronic interactions between the metal centers.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information: experimental section of the ddpd ligand, details of the complexes including TGA traces, X-ray single crystal data and structures, PXRD patterns, supplementary Hirshfeld surface data, supplementary VT-IR data and theoretical calculation data. See DOI: https://doi.org/10.1039/d5qi01982f.

CCDC 2415150–2415159 contain the supplementary crystallographic data for this paper.^59a–j

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grants 22222103, 22025101, 22173015, and 22103009), the Fundamental Research Funds for the Central Universities (DUT22LAB₆06), the Liaoning Binhai Laboratory (LBLE-2023-02), and the “Excellence Co-innovation Program” International Exchange Fund Project (DUTIO-ZG-202505). We acknowledge Dr Qiang Liu and Jingyi Xiao from the Instrumental Analysis Center, Dalian University of Technology, for their assistance with magnetic measurements.

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59. (a) CCDC 2415150: Experimental Crystal Structure Determination, 2025,  DOI:10.5517/ccdc.csd.cc2m252z; (b) CCDC 2415151: Experimental Crystal Structure Determination, 2025,  DOI:10.5517/ccdc.csd.cc2m2530; (c) CCDC 2415152: Experimental Crystal Structure Determination, 2025,  DOI:10.5517/ccdc.csd.cc2m2541; (d) CCDC 2415153: Experimental Crystal Structure Determination, 2025,  DOI:10.5517/ccdc.csd.cc2m2552; (e) CCDC 2415154: Experimental Crystal Structure Determination, 2025,  DOI:10.5517/ccdc.csd.cc2m2563; (f) CCDC 2415155: Experimental Crystal Structure Determination, 2025,  DOI:10.5517/ccdc.csd.cc2m2574; (g) CCDC 2415156: Experimental Crystal Structure Determination, 2025,  DOI:10.5517/ccdc.csd.cc2m2585; (h) CCDC 2415157: Experimental Crystal Structure Determination, 2025,  DOI:10.5517/ccdc.csd.cc2m2596; (i) CCDC 2415158: Experimental Crystal Structure Determination, 2025,  DOI:10.5517/ccdc.csd.cc2m25b7; (j) CCDC 2415159: Experimental Crystal Structure Determination, 2025,  DOI:10.5517/ccdc.csd.cc2m25c8.

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