Tunable SIM properties in a family of 3D anilato-based lanthanide-MOFs†‡

Noemi Monni§ ^ab, Sourav Dey§ ^a, Víctor García-López ^a, Mariangela Oggianu ^b, José J. Baldoví ^a, Maria Laura Mercuri *^b, Miguel Clemente-León *^a and Eugenio Coronado ^a
aInstituto de Ciencia Molecular (ICMol), Universidad de Valencia, Catedrático José Beltrán 2, 46980 Paterna, Spain. E-mail: miguel.clemente@uv.es
^bDipartimento di Scienze Chimiche e Geologiche, Università degli Studi di Cagliari, Complesso Universitario di Monserrato, 09042 Monserrato, Italy. E-mail: mercuri@unica.it

First published on 16th July 2024

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Introduction

Metal–Organic Frameworks (hereafter MOFs), fascinating crystalline porous materials formed by a suitable combination of metal ions (nodes) with organic ligands (linkers), are promising platforms for a plethora of applications, spanning from fuel storage, CO₂ capture, catalysis to drug delivery, sensing and biomedicine. Indeed lanthanide-based MOFs (Ln–MOFs) have been attracting ever-growing interest in the last few decades because of their intrinsic advantages due to lanthanide coordination versatility and, depending on the lanthanide nature, the possibility to combine both luminescence and magnetic properties in the same crystal lattice, building up multifunctionality. Among magnetic Ln-MOFs, those exhibiting molecular properties, i.e. Single-Molecule Magnet (SMM) behavior, have attracted extensive attention for their potential applications in cutting-edge molecular spintronics and quantum computing devices, since they allow for achieving in principle much higher densities with higher data processing speeds.^1–3 The most used Ln^III ions to construct SMMs are Tb^III, Dy^III, Er^III and Ho^III and particularly, Tb^III and Dy^III are the best candidates, since their electronic structures exhibit large magnetic anisotropy, due to the strong angular dependence of 4f orbitals.^4,5 Recently a second generation of SMM-based MOFs, known as Single Ion Magnet (SIM) MOFs, started to develop rapidly, since the first report of the Ln(bipyNO)₄(TfO)₃ (bipyNO = 4,40-bypyridyl-N,N0-dioxide, TfO = triflate) 3D coordination framework by Coronado, Mínguez Espallargas et al.⁶ SIMs consist of single centres that exhibit slow magnetic relaxation⁷ and, consequently, SIM-MOFs are formed by ordered assemblies of lanthanide ions and different bridging linkers, featuring extended and porous high-dimensional frameworks with tunable magnetic properties. The MOF framework is then used as a challenging scaffold to constrain or tune the local geometries of lanthanide nodes and arrange diverse organic linkers into ordered assemblies, featuring a combination of structural diversity and SMM/SIM behaviour. While a considerable effort has been made to enhance SIM performance, more detailed studies are still required to elucidate the origin of slow relaxation, as well as the influence of the ligand structure and crystal packing on SIM properties. According to the literature, highly symmetrical Dy^III-based SIMs, showing D_4d, D_5h and D_6h coordination geometries, providing reduced electron repulsion around the lanthanide ion and m_J = ±15/2 state stabilization, prevent the quantum tunnelling of magnetization (QTM).^8,9 Therefore, Ln-MOFs, possessing an approximately square-antiprismatic or dodecahedral coordination geometry, have the potential to exhibit SIM behavior. The magnetic relaxation behavior of these SIMs has been shown to be affected by the distortion of the coordination environment, generally due to subtle modifications of the crystal lattice that could be induced by the solvent, ancillary linkers and intermolecular interactions.^10–13 Therefore, the anisotropy of lanthanide ions and their magnetic dynamics are strongly influenced by both the ligand field and coordination geometry.¹⁴ However, it is still a challenge to control the coordination geometry around the lanthanide ions in order to understand how it affects the relaxation mechanism. For this reason, shaping the geometries with properly designed organic linkers has become a successful strategy to achieve SIM-MOFs.

To design an extended coordination framework which exhibits SIM behavior, the choice of the organic linker and metal node is crucial. Most importantly the bridging ligand should be capable of constructing an extended framework and it should be a weak magnetic coupler, in order to keep Ln^III ions well isolated.¹⁵ Among the linkers, the anilato derivatives i.e. 3,6-disubstituted-2,5-dihydroxy-1,4-benzoquinones have been successfully exploited as molecular building blocks for constructing Ln^III-based materials. Although these bridging ligands couple (antiferro)magnetically the transition metal nodes,^16,17 they provide a good magnetic isolation of Ln^III metal nodes as a result of the negligible overlap with their 4f orbitals.¹⁵ Since the first report on Ln^III-based anilato complexes,⁴ by Boskovic et al., which consist of two Dy^III-based dimers, [(Tp)₂Dy₂(Cl₂An)]·2CH₂Cl₂ and [(Tp)₂Dy₂((CH₃)₂An)]·1.1CH₂Cl₂ (Tp⁻ = hydrotris(pyrazolyl) borate), showing slow relaxation of magnetization with Orbach and Raman relaxation mechanisms for [(Tp)₂Dy₂(Cl₂An)]·2CH₂Cl₂ (U_eff = 24 K) and a field induced SMM behavior and an Orbach mechanism for [(Tp)₂Dy₂((CH₃)₂An)]·1.1CH₂Cl₂ (U_eff = 47 K), several reports on complexes and 2D/3D anilato-based SMM/SIM CPs/MOFs have been thoroughly described in the literature.^15,18–20 Recently, the unexplored 3,6-N-ditriazolyl-2,5-dihydroxy-1,4-benzoquinone (H₂trz₂An), anilate,²¹ has been used to construct 3D MOFs, due to the coordinative nitrogen of the triazole pendant arms of the anilato moiety.^17,22 Very recently, some of us reported on the synthesis and characterization of neutral polymorphic 3D frameworks, obtained by combining H₂trz₂An and NIR-emitting Er^III ions. These materials exhibit a combination of NIR emission and field-induced slow magnetic relaxation. Remarkably, one of the frameworks is a flexible MOF that undergoes a reversible structural phase transition, due to a dehydration/hydration process leading to pore shrinkage/expansion from a distorted hexagonal 2D to a 3,6-brickwall rectangular 3D structure. Remarkably its structural flexibility provokes a tuning of both luminescence and SIM properties with an improvement of magnetic blocking temperature.²³

By reacting the same H₂trz₂An linker with Dy^III, Tb^III and Ho^III metal nodes, two different series are herein reported, formulated as [Ln₂(trz₂An)₃(H₂O)₄]_n·10H₂O (Ln^III = Dy (1a), Tb (2a), Ho (3a)) and [Ln₂(trz₂An)₃(H₂O)₄]_n·7H₂O (Ln^III = Dy (1b), Tb (2b), Ho (3b)), which are isostructural with the Er^III frameworks and exhibit the same structural flexibility. All compounds were structurally and magnetically characterized, showing SIM behavior in the case of 1a, 1b and 2b. Interestingly, the use of Tb^III in 2b gave rise to the best SIM properties of this family of compounds. On the other hand, although the same structural flexibility in the porous frameworks was obtained for 1a, it did not exhibit the drastic changes in SMM behavior induced by the dehydration observed previously for the Er^III derivative. The ab initio calculations support this behaviour, since 2b shows less mixing between the m_J states of the ground state among all the studied coordination networks. Furthermore, they reveal that the change in the SMM behavior with dehydration relies on the nature of the electron density of the metal center and therefore the choice of the metal center plays a pivotal role in switching the SMM behavior.

Results and discussion

Synthesis

Ln-based magnetic frameworks (1–3a and 1–3b) were obtained by combining Ln(NO₃)₃·xH₂O with H₂trz₂An in a 1:1 ratio, via the hydrothermal method, following the same synthetic strategy reported for the preparation of Er^III-frameworks²³ (Scheme 1). As observed for Er^III, each batch gave two types of crystals which correspond to the two different phases previously reported and formulated as [Ln₂(trz₂An)₃(H₂O)₄]_n·10H₂O (Ln^III = Dy (1a), Tb (2a), Ho (3a)), dark red block crystals, and [Ln₂(trz₂An)₃(H₂O)₄]_n·7H₂O (Ln^III = Dy (1b), Tb (2b), Ho (3b)), orange prismatic crystals. To separate the crystals of the different phases the CH₂Cl₂/CH₂Br₂ solvent mixture in a 0.925/0.975 ratio was used. Interestingly 1–3a MOFs show a reversible structural flexibility. With the removal of water solvent from phase a, by heating the samples at 80 °C or by applying vacuum, the reversible desolvated phase a_des formulated as [Ln₂(trz₂An)₃(H₂O)₂]_n was afforded.

Crystal structures

Compounds 1–3a and 1–3b crystallize in the triclinic space group P. They are isostructural with the previously reported Er^III compounds.²³ Their structures were solved by single crystal X-ray diffraction (see Tables S2 to S9 in the ESI‡). They consist of 3D neutral coordination frameworks formed by Ln^III ions connected by trz₂An bridging linkers. The Ln^III ions are ennea-coordinated with a {NO₈} coordination sphere arising from two oxygens of three bidentate trz₂An anilates, the N4 atom of one trz₂An and two coordinated water molecules (see figures in Tables S4 and S7 in the ESI‡). The Ln^III ions are linked to three neighboring ions through the oxygens of three trz₂An anilates, coordinating in bis-bidentate mode. This leads to layers with a (6,3) topology forming six-membered rings with distorted hexagonal cavities in 1–3a and rectangular six-membered cavities, which adopt a brick-wall structure, in 1–3b (see Scheme 1). Ln^III nodes of the same layer are connected to Ln^III nodes of other layers, through the N4 atom of the two pending triazolyl arms of one of the three trz₂An linkers.

Polycrystalline samples of 1a, 2a and 3a were placed under vacuum in a Schlenk tube and then sealed in a glove box to study if vacuum could induce changes in the crystal structure. As observed with the Er^III compound, a reversible structural change was observed leading to new phases 1a_des, 2a_des and 3a_des (Fig. 1). Furthermore, when 1a_des, 2a_des and 3a_des were released in air, the samples were rehydrated forming again the 1a, 2a and 3a phases as shown by PXRD measurements (Fig. 1). This proves that the dehydration/hydration process is fully reversible, as well as the induced structural change. PXRD data suggest that the structures of 1–3a_des are isostructural to the dehydrated compound obtained with Er^III of the formula [Er₂(trz₂An)₃(H₂O)₂]_n·2H₂O.

This rehydrated phase exhibits a drastic change from the distorted hexagonal 2D network found in 1a, 2a and 3a to a distorted 3,6-brickwall rectangular structure related to the loss of one of the two coordination water molecules of the Ln^III ion, which shows, in these dehydrated compounds, a {NO₇} coordination sphere arising from six oxygens of three bidentate trz₂An linkers, the N4 atom of one trz₂An linker and one coordinated water molecule.²³

This structural change induces a decrease in the pore sizes. Thus, the distorted hexagonal cavities of 1–3a compounds show maximum diagonal Ln^III–Ln^III distances of 22.1 Å and minimum Ln^III–Ln^III distances between atoms of opposite sides of 9.4 Å (1a), while the 3,6-brickwall rectangular structures of 1–3a_des show the shortest Ln^III–Ln^III distances (maximum diagonal ones of 20.2 Å and minimum ones between atoms of opposite sides of 7.0 Å in the previously reported isostructural Er^III derivative²³).

As previously demonstrated, the new phase 1–3a_des can be obtained by dehydration under very mild conditions in a reversible way. Thus, the initial structure can be recovered by placing the dehydrated crystals in air, indicating a reversible structural phase transition between a hexagonal and a rectangular cavity, which has been already observed in other flexible MOFs.²⁴

Magnetic properties

Solid state, dc magnetic susceptibility measurements were carried out in the temperature range of 2–300 K, under an applied magnetic field of 0.1 T, for 1–3a and 1–3b. As in Er^III-MOF, phase a, it was necessary to protect the sample with H₂O since the vacuum of the squid chamber (∼2–3 mbar) caused desolvation and the formation of 1–3a_des, even in the presence of eicosane. The χ_MT values at 300 K of 14.0 (1a), 13.9 (1a_des), 13.7 (1b), 11.7 (2a), 11.7 (2a_des), 11.3 (2b), 13.8 (3a), 13.8 (3a_des) and 13.7 (3b) cm³ K mol⁻¹, are in agreement with that expected for each non-interacting Ln^III ion (⁷F₆ for Tb^III, ⁶H_15/2 for Dy^III and ⁵I₈ for Ho^III), as shown in Fig. 2–4 and S5–7, S9–11 and S13–15.‡ The field dependence of magnetization was also measured in the 2–8 K temperature range by varying the magnetic field up to 5 T (Fig. S17–S25‡). A sharp increase in magnetization was observed for Tb and Dy compounds at low magnetic fields but saturation was not observed at higher magnetic fields. On the other hand, the reduced magnetization curves at the different temperatures do not coincide (Fig. S17–25‡). These two facts suggest significant anisotropy. Finally, hysteresis of magnetization was not found in these compounds.

The dynamic magnetic properties were studied by susceptibility measurements performed with an alternating magnetic field (AC susceptibility). In the absence of a magnetic field, no signal in the out-of-phase molar susceptibility (χ′′) was observed. When magnetic dc fields of 0.1 T were applied, strong frequency-dependent peaks in both the in-phase molar susceptibility (χ′) and χ′′ appeared in 1a, 1a_des, 1b and 2b with clear maxima of χ′′ below 4 K for 1a and 1a_des, 6 K for 1b and 14 K for 2b (Fig. 5–8 and S26‡). This indicates that the four compounds present a field-induced slow relaxation of magnetization.

The χ′ and χ′′ peaks of 1a measured in contact with eicosane (1a_des) present a small shift to higher temperatures of ca. 0.2 K with respect to those measured in contact with water 1a (Fig. 8 and S26‡). This suggests that the magnetic behavior of 1a is not as sensitive to desolvation as that of its correspondent Er^III-based MOF, as shown in Fig. 8.

To further investigate the observed magnetic behaviour of coordination networks 1–3 (both a and b) and the effect of dehydration in complex 1a, we performed ab initio CASSCF/RASSI-SO/SINGLE_ANISO calculations using the MOLCAS 8.2 package.²⁵ Calculations were performed on a fragment of the MOF that contains one metal centre, keeping the coordination environment unchanged. The computed g factors of Kramers doublet 1 (KD1) (g_xx = 0.140, g_yy = 0.244, g_zz = 18.777 for 1a, g_xx = 0.002, g_yy = 0.006, g_zz = 19.328 for 1a_des and g_xx = 0.021, g_yy = 0.041, g_zz = 19.547 for 1b) indicates a significant transverse magnetic anisotropy in all isomers of complex 1 (see Tables S11–S13‡) which explains the field induced SIM behaviour in these complexes. The magnetic anisotropy axis of KD1 in all these isomers is oriented along the –trz₂An ligand to minimize the electrostatic repulsion with the oblate electron density (see Fig. 9 and S6, S7‡). The ground KD is found to possess a dominant contribution from m_J = |±15/2〉, whereas a significant mixing of m_J = |±13/2〉 with other m_J states in the first excited KD leads to magnetization relaxation in 1a, 1a_des and 1bvia this KD (see Fig. 9 and S5–S7‡).

This leads to the U_cal values of 71.6, 139.1 and 102.6 cm⁻¹ in 1a, 1a_des and 1b, respectively. The computed magnetic susceptibility of the three derivatives is found to be in line with the experimental results (see Fig. 2 and S5–S7‡). We determined the relative donor strength by computing LoProp charges.²⁶ We can observe that removing one water molecule from the equatorial position of 1a increases the axiality which is also reflected in the slight increase of the LoProp charge of the coordinated atoms at the axial position (see Table S14 and Fig. S8‡). Therefore, it quenches the quantum tunneling of magnetization (QTM) and increases the U_cal value in 1a_des compared to that in 1a. This is also in agreement with the experimental result where improvement in magnetic properties is observed in 1a_des compared to those in 1a. In comparison with the Er analogue, the change in magnetic properties from 1a to 1a_des is not drastic. This can be ascribed to the nature of electron density, the m_J = |±15/2〉 oblate in nature in Dy(III) while being prolate in Er^III. The removal of the water molecule from the equatorial position strongly affects the electronic structure of Er(III) compared to that of Dy(III). Furthermore, the increment of U_cal and quenching of QTM from 1a to 1b can be again explained by analysing the LoProp charge of the equatorial atoms, which decreases, whereas in the axial atoms it increases (see Table S14 and Fig. S8‡). Then, we computed the crystal field parameters (CFPs) using Stevens Hamiltonian, , where B^q_k represents the CFPs and Õ^q_k represents the Stevens operator.²⁶ The negative value of the B⁰₂ crystal field parameter explains strong axiality in all the coordination networks (see Table S15‡) and the value of B⁰₂ increases from 1a to 1a_des, which agrees well with the increase of axiality after dehydration of 1a (Table S15‡). To explain the relaxation of magnetization, molecular vibrations also play a key role.²⁷ In this regard, the octacoordinated system presents less active vibrations due to the loss of a water molecule. However, the actual effect will depend on the level of resonance of those molecular vibrations with the electronic energy levels.

Subsequently, we computed the electronic and magnetic properties of coordination networks 2a, 2a_des and 2b. The calculations reveal significant tunnel splitting (∇_tun) in the ground pseudo-Kramers doublet (pKD) of 2a while a negligible ∇_tun is observed in 2a_des and 2b (see Tables S16 and 17 in the ESI‡). The strong ∇_tun in 2a is correlated with the larger and smaller LoProp charges in the equatorial coordinated atoms compared to that in 2b (see Fig. S12 and Table S18‡), which is also reflected in the computed CF parameters (Table S19‡). This explains the absence and presence of SMM behavior in 2a and 2b, respectively. The computed magnetic susceptibility in all the isomers of 2 are found to be in good agreement with the experimental result (Fig. 3 and S9–11‡). However, the strong ∇_tun in the first excited pKD of 2b reinforces the relaxation of the magnetization, leading to U_cal = 141 cm⁻¹ (see Fig. S11‡). This value of U_cal is largely overestimated compared to that of U_eff, which can be ascribed to the metal–ligand covalency, dipolar coupling and dynamic correlation that have not been included in our calculations. Compared to 1a, 1a_des and 1b, the compound 2b shows less mixing among m_J states. This results in effective quenching of ∇_tun, and therefore, it displays the best SMM characteristics among all the coordination networks studied here.

Finally, to investigate the possibility of SMM behavior, we extended our simulations to coordination networks 3a, 3a_des and 3b. Although the computed magnetic susceptibility of all coordination networks is found to be in good agreement with the experimental result (Fig. 4 and S13–15‡), the ground pKDs possess strong m_J mixing that yields significant ∇_tun, which explains the absence of SMM behavior in these coordination networks (Tables S20–23‡).

Between, 3a, 3a_des and 3b, a smaller ∇_tun is observed in 3a due to smaller equatorial and larger axial LoProp charges of the coordinated atoms compared to 3a_des and 3b (Fig. S16 and Table S22‡), which is also reflected in the computed CF parameters (Table S23‡).

The relaxation times (τ) of 1a_des, 1b and 2b were determined from the maximum of χ′′ at a given frequency (τ = 1/2πν) and from the Debye model. They were fitted to the Arrhenius expression for a thermally activated process (Orbach, τ = τ₀exp(U_eff/k_BT)) leading to τ₀ = 5.4 × 10⁻⁸ s and U_eff = 17.5 K for 1a_des, τ₀ = 1.2 × 10⁻⁸ s and U_eff = 25.7 K for 1b, and τ₀ = 2.0 × 10⁻⁶ s and U_eff = 16.4 K at 0.1 T for 2b. However, the plots of τ vs. 1/T deviate from linearity at low temperatures for 1a_des and 2b indicating the coexistence of multiple relaxation pathways as observed in the Er^III frameworks previously reported²³ and other anilate-based lanthanide coordination networks (see Fig. S27‡). The general model where the first, second, third and fourth terms include quantum tunneling, direct, Raman and Orbach relaxation processes, respectively, was applied.

τ−1 = τQTM−1 + AH2T + CTn + τ0−1exp(−Ueff/KBT)\

Correct fitting of 2b was obtained using Raman and Orbach relaxation processes with values comparable to those found for other anilate-based Ln^III compounds with C = 81.7 s⁻¹ K^−3.2, τ₀ = 1.0 10⁻⁶ s and U_eff = 30.5 K.^28–31 The calculated value of n (3.2) is smaller than the ideal value of 9 found for Raman processes. This suggests that these Raman-like relaxations are attributed to acoustic and optical vibrations.³² In the case of 1a_des, a reasonable fitting using Raman and Orbach relaxation processes could not be obtained. This was obtained by combining direct and Orbach relaxation processes with AH² = 3541.7 s⁻¹, τ₀ = 3.5 10⁻¹⁰ s and U_eff = 32.8 K (Fig. S28‡).

The variable-frequency AC data at different temperatures of 1a_des, 1b and 2b show a single relaxation with maxima at 960 Hz (1a_des), 65 Hz (1b) and 210 Hz (2b) at 2 K (see Fig. S30–33‡). The Cole–Cole plots (χ′′ vs. χ′) of the three samples confirm the presence of a single relaxation process (Fig. S29‡). Thus, at fixed temperatures between 2.0 and 5.0 K for 1a_des, 2.0 and 4.0 for 1b and 2.0 and 7.5 K for 2b, semi-circular plots were obtained and fitted using a generalized Debye model, yielding an α parameter in the ranges of 0.12–0.42 (1a_des), 0.21–0.25 (1b) and 0.06–0.33 (2b). This indicates narrow distributions of the relaxation processes.

Conclusions

The H₂trz₂An anilate derivative, bearing a triazole pendant arm at the 3,6 position of the anilato core, has been used for the first time in combination with Dy^III, Tb^III and Ho^III nodes to afford 1–3a and 1–3b 3D frameworks, formed by 2D layers with a (6,3) topology, connected through the triazolyl pendant groups of the anilato linkers. These compounds are isostructural to the previously reported Er^III frameworks.²³ Remarkably, 1–3a are MOFs showing flexibility as the Er^III-MOF (phase a), with analogous reversible drastic structural changes to a less porous 3D structure, after partial dehydration under very mild conditions. The use of these three metals enables optimization of the SIM properties. Magnetic characterization reveals a field-induced SIM behaviour for 1a, 1a_des and 1b Dy^III compounds and for the 2b Tb^III compound, which, to the best of our knowledge, is the first Tb^III–anilate-based coordination polymer that exhibits SIM behaviour. Conversely, the SIM properties of 1a are much less sensitive to the removal of water molecules than those of the previously reported Er^III-MOF. Interestingly, the blocking temperature of the Tb^III compound is higher than those of Er^III and Dy^III compounds, showing the best SIM properties within this series. Remarkably theoretical calculations evidenced that 2b, compared to 1a, 1a_des and 1b, shows less mixing among m_J states, resulting in effective quenching of ∇_tun, and therefore the best SIM properties among all coordination networks herein studied. Furthermore, they reveal that the choice of the metal center plays a crucial role in switching the SMM behavior, since the dehydration process depends on the electron density nature of the metal center. Finally, retention of the flexibility and porosity of this family of compounds with different lanthanide ions paves the way for the preparation of other members of this family of coordination polymers/MOFs with other NIR emitting metal ions such as Nd^III and Yb^III, which could allow a fine tuning of other properties such as luminescence by the reversible dehydration/rehydration process. Further optimization of SIM properties could also be achieved by diluting the paramagnetic Tb^III nodes with diamagnetic ions such as Eu^III.

Experimental section

General remarks

The lanthanide precursors, NaOH in pellets and the solvents used were purchased from AlfaAesar and Exacta Optech and used without further purification. The synthesis of the ligand H₂trz₂An was performed as reported in the literature.²¹ Elemental analyses (C, H, and N) were performed with a CE Instruments EA 1110 CHNS. FT-IR spectra were collected using a Bruker Equinox 55 spectrometer on KBr pellets.

Synthesis of [Ln₂(trz₂An)₃(H₂O)₄]_n·10H₂O (Ln^III = Dy (1a), Tb (2a), Ho (3a)) and [Ln₂(trz₂An)₃(H₂O)₄]_n·7H₂O (Ln^III = Dy (1b), Tb (2b), Ho (3b))

These series were prepared by using the same synthetic procedure for Er^III compounds.²³ A 5 mL Teflon vial with a mixture of Ln(NO₃)₃·6H₂O (0.05 mmol; 17.4 mg (1), 22.6 mg (2), 18.9 mg (3)), H₂trz₂An (0.05 mmol, 13.7 mg), NaOH (0.1 mmol, 4 mg) and water (5 mL) was heated at 130 °C for 48 hours and then the vial was slowly cooled to room temperature. The heating and cooling rates were 0.92 K min⁻¹ and 0.15 K min⁻¹, respectively. Two different types of crystals were obtained from the same batch, dark red-block crystals (phase a) and orange prismatic crystals (phase b), both of them suitable for single-crystal X-ray diffraction measurements. Their density's difference was exploited to separate them, using a CH₂Cl₂/CH₂Br₂ solvent mixture in a ratio of 0.925/0.975 as reported for the Er^III frameworks. Elemental analysis is reported in Table S1.‡ The results from elemental analysis suggest the absorption of one (phase a) and three (phase b) water molecules after filtering.

Synthesis of [Ln₂(trz₂An)₃(H₂O)₂]_n (Ln = Dy (1a_des), Tb (2a_des), Ho (3a_des))

Polycrystalline powders of 1–3a were placed under vacuum in a vacuum line pump and then sealed in a glove box to obtain the dehydrated phase a_des. Elemental analysis of 1a_des is not shown since it turns to the structure of 1a after two days in air.

X-Ray crystallography

Single crystal X-ray diffraction was performed on 1–3a and 1–3b crystals, which were mounted on a glass fiber using a viscous hydrocarbon oil to coat the single crystal and then transferred directly to the cold nitrogen stream for data collection. X ray data were collected at 120 K for all the samples. Measurements were performed on a Supernova diffractometer equipped with a graphite-monochromated Enhance (Mo) X-ray source (λ = 0.710 73 Å). The program CrysAlisPro, Oxford Diffraction Ltd, was used for unit cell determination and data reduction. Empirical absorption correction was performed using spherical harmonics, implemented in the SCALE3 ABSPACK scaling algorithm. The structures were solved with the ShelXT structure solution program³³ and refined with the SHELXL-2013 program,³⁴ using Olex2.³⁵ Non-hydrogen atoms were refined anisotropically, and hydrogen atoms were placed at calculated positions refined using idealized geometries (riding model) and assigned fixed isotropic displacement parameters. Crystallographic data of all the compounds are summarized in Tables S2 and S3.‡ CCDC 2320542–2320547‡ contain the supplementary crystallographic data for this paper.

All powder X-ray diffraction patterns (PXRD) were obtained using a 0.7 mm glass capillary filled with polycrystalline samples of the compounds and mounted and aligned on an Empyrean PANalytical powder diffractometer, using Cu Kα radiation (λ = 1.541 77 Å). A total of three scans were collected for each compound at room temperature in the 2θ range of 5–40°. Polycrystalline samples of 1–3a were further placed under vacuum in a vacuum line pump and were then opened in the glove box to be sealed in the 0.7 mm glass capillary.

Magnetic measurements

Magnetic measurements were performed with Quantum Design MPMS-XL-5 SQUID and PPMS-9 magnetometers in the 2–300 K temperature range with an applied magnetic field of 0.1 T at a scan rate of 2 K min⁻¹. In the case of 1–3a, it was necessary to protect the sample covering it with H₂O since the vacuum of the squid chamber caused desolvation and the formation of 1–3a_des.

Theoretical calculations

The optimization of the hydrogen positions of the chosen molecular fragment (except 2a, 2a_des and 2b) was performed using the hybrid B3LYP exchange–correlation functional³⁶ (with Grimme-D3 dispersion corrections) with the Gaussian 09 programme package.³⁷ During the optimization, the Dy(III) ion was replaced with diamagnetic Y(III) to facilitate smooth SCF convergence.³⁸ We have employed the Ahlrichs triple-ζ valence plus polarization basis set for oxygen and nitrogen and the 6-31G* basis set for carbon and hydrogen.³⁹ For Y(III), Stuttgart's effective core potential (SDD ECP, 28 core electrons) was used with its corresponding basis set.^40,41 A quadratic convergence method was employed in all our calculations.⁴²

All the ab initio CASSCF/RASSI-SO/SINGLE_ANISO calculations have been performed using the MOLCAS 8.2 programme package considering a fragment of the MOF with only one metal centre.²⁵ We have used Douglas–Kroll–Hess Hamiltonian to take into account the relativistic effect.⁴³ The disk space of our calculations has been reduced using the Cholesky decomposition technique. All the basis sets employed in our calculations have been taken from the ANO-RCC library implemented in the MOLCAS 8.2 programme package.^44,45 We have used the [Dy.ANO-RCC⋯8s7p5d3f2g1 h.] basis set for Dy, [Tb.ANO-RCC⋯8s7p5d3f2g1 h.] basis set for Tb, [O.ANO-RCC⋯3s2p1d.] basis set for O, [N.ANO-RCC⋯3s2p1d.] basis set for N, [C.ANO-RCC⋯3s2p.] basis set for C and [H.ANO-RCC⋯2s.] basis set for H in our calculations. The CAS(8,7), CAS(9,7) and CAS(10,7) active spaces were employed for Tb^III, Dy^III and Ho^III, respectively, in our calculations taking into account all the valence electrons of Dy^III in seven 4f orbitals. We have used only 21 sextets for Dy^III as this has been able to reproduce the experimental observables from the previous studies. We have also computed the energies of 7 septets, 140 quintets and 195 triplets for Tb^III and 35 quintets, 210 triplets and 196 singlets for Ho^III from the CASSCF calculations. The spin-free states (7 septets, 105 quintets and 112 triplets for Tb^III and 35 quintets, 117 triplets and 75 singlets for Ho^III) have been mixed using RASSI-SO⁴⁶ to generate spin orbit coupled states. Finally, the g tensor, blocking barrier, QTM etc. have been extracted from the SINGLE_ANISO module of MOLCAS 8.2.

Author contributions

MLM and NM designed the compounds. MLM and MCL supervised the research project. NM synthesized and characterized the compounds under the supervision of MLM, EC and MCL (structural and magnetic characterization) and with the help of VGL and MO. JJB and SD performed the theoretical calculations and analyzed the magnetic data. MLM, MCL and SD wrote the manuscript. All authors contributed to the final interpretation of the experimental results and critically revised the manuscript. All authors have read and approved the final version of the manuscript.

Data availability

The data supporting this article have been included as part of the ESI.‡

Crystallographic data have been deposited at the CCDC under CCDC 2320542–2320547‡ and can be obtained from https://doi.org/10.1039/x0xx00000x.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Financial support from the EU (ERC Advanced Grant MOL-2D 788222), the Spanish MCIN (Grants PID2020-117264GB-I00 and PID2020-117152RB-I00 funded by MCIN/AEI/10.13039/501100011033 and Unidad de Excelencia María de Maeztu CEX2019-000919-M) and the Generalitat Valenciana (PROMETEO program), is acknowledged. This study forms part of the Advanced Materials programme and was supported by MCIN with funding from the European Union NextGenerationEU (PRTR-C17.I1) and by Generalitat Valenciana. JJB and SD would like to thank EU (Grant No. 2D-SMARTiES ERC-StG-101042680 and Marie Curie Fellowship SpinPhononHyb2D 101107713) and the Plan Gent of Excellence of the Generalitat Valenciana (Grant No. CDEIGENT/2019/022) for the funding. This research was funded in Italy by Fondazione di Sardegna, Convenzione Triennale tra la Fondazione di Sardegna e gli Atenei Sardi, Regione Sardegna, L.R. 7/2007 annualità 2022, project VOC_3D “3D printed optical VOC sensors for indoor air quality evaluation” CUP F73C23001590007. We all thank Alejandra Soriano-Portillo for PXRD measurements and J. M. Martínez-Agudo and G. Agustí for magnetic measurements.

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Footnotes

† This article is dedicated to Prof. Enzo Cadoni for his retirement.

‡ Electronic supplementary information (ESI) available: Elemental analysis, crystallographic tables and figures, PXRD patterns, IR spectra and tables and figures of magnetic characterization and modelling. CCDC 2320542–2320547. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d4qi01549e

§ Both authors contributed equally to this work.

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