Valence tautomerism, non-innocence, and emergent magnetic phenomena in lanthanide-organic tessellations

Abstract

Coordination networks based on lanthanide ions entangle collective magnetic phenomena, otherwise only observed in inorganic 4f materials, and the tunable spatial and electronic structure engineering intrinsic to coordination chemistry. In this review, we discuss the use of 2D-structure-directing linear {Ln^II/IIII₂} nodes to direct the formation of polymeric coordination networks. The equatorial coordination plasticity of {Ln^II/IIII₂} results in broad structural diversity, including previously unobtainable tessellations containing motifs observed in quasicrystalline tilings. The new phases host also magnetic frustration, which is at the origin of enhanced magnetic refrigeration potential. Finally, careful redox matching of Ln node and frontier orbitals of the ligand scaffold has culminated in the discovery of quantitative valence tautomeric conversion in a molecule-based Ln material, opening up new avenues for combining exotic magnetic phenomena with an encoded switch.

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Maja A. Dunstan

Maja A. Dunstan is from Melbourne, Australia, and completed her PhD in the group of Colette Boskovic at the University of Melbourne. In 2022, she joined Kasper S. Pedersen at the Technical University of Copenhagen as a postdoctoral researcher. Her research interests include single-molecule magnetism, neutron spectroscopy, and switchable magnetic materials. Currently, she is working in the field of low-valent lanthanide coordination networks.

Kasper S. Pedersen

Kasper S. Pedersen was born in Allerød, Denmark, and received his PhD from the University of Copenhagen in 2014. After postdoctoral stints in Bordeaux and Montreal, he joined the faculty at the Technical University of Denmark in 2017, and was appointed full professor in 2022. His research spans synthetic and structural inorganic chemistry as well as advanced properties characterization. His current focus is directed toward the discovery of novel metal–organic framework materials with hitherto unknown structural and physical properties, and the development of the field of low/zero-valent metal cluster-based MOFs and the application of 3D electron diffraction techniques.

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1. Introduction

Switchable materials, which exhibit disparate chemical and physical properties across multiple states, are necessary for applications that leverage changes in electronic, magnetic, or optical characteristics. Many such materials exist, both molecule-based and purely inorganic, including those where the electronic state can be manipulated and controlled by a stimulus such as temperature or pressure.¹ These encompass phenomena such as spin-crossover (SCO), between high-spin (hs) and low-spin (ls) tautomers of a transition metal ion complex;² stimulated intramolecular electron transfer between two metal ions; and valence tautomerism (VT), involving stimulated intramolecular electron transfer between a redox-active metal ion and a redox-active ligand (Fig. 1).^3,4 For SCO and VT materials, the vast majority of research has focused on coordination complexes of the 3d metal ions, for which there are known sets of metal ions and ligand scaffolds leading to facile switching by mild stimuli, such as temperature, pressure, and light.

Fig. 1 Valence tautomeric process in an octahedral Co-dioxolene species, with a transition between a Co^III-catecholate and a Co^II-semiquinonate. Occupation of metal 3d (teal/blue) and ligand (pink) valence orbitals shown.

VT transitions have been observed in coordination compounds of Mn,⁵ Fe,^6,7 Co,^8–10 Cu,¹¹ Sn,¹² V,¹³ amongst others, although most widely researched is the Co-dioxolene family of compounds (Fig. 1). Buchanan and Pierpont first observed the molecule-based VT phenomenon in 1980 in [Co(2,2′-bpy)(dbsq)(dbdiox)] (3,5-dbsq = 3,5-di-tert-butyl semiquinone, 3,5-dbdiox = 3,5-di-tert-butyl dioxolene, 2,2′-bpy = 2,2′-bipyridine), which hosts a thermally driven transition between a high-temperature (HT) Co^II-dbsq-dbsq tautomer and a low-temperature (LT) Co^III-dbsq-dbq (dbq = 3,5-di-tert-butyl quinone) tautomer.¹⁴ Progress in the proceeding forty years has led to the observation of VT switching induced by various additional stimuli such as light,^15–17 pressure,^18,19 and X-rays.^16,20 Immobilization of VT complexes on surfaces²¹ or on gold nanoparticles²² has also been achieved for Co-dioxolene systems, with the possibility of now isolating single molecules as molecular switches. For many applications, cooperativity is key, leading to an abrupt SCO or VT transition upon an applied stimulus. In molecular materials, cooperativity in the solid-state bulk material is dictated by the crystal packing, which is difficult or impossible to design for molecular complexes. Instead, incorporation of switchable modules into coordination polymers or metal–organic frameworks (MOFs) is a tactic for engendering cooperativity. For SCO, multidimensional coordination networks have been widely explored since the 1990s, when Kahn et al. demonstrated cooperative, hysteretic SCO switching in Fe^II 1D coordination polymers at room temperature.^23,24 Aside from the possibility of tuning both transition temperature and cooperativity, SCO coordination networks can also host multi-step transitions, where multiple states are accessible.^25,26 These materials also exhibit additional advantages over molecular complexes, for example where guest molecule–framework interactions induce a SCO transition.^27–29 In contrast, examples of VT coordination networks incorporating Co-dioxolene units typically show gradual transitions, with a strong sensitivity to desolvation^30–32 and guest molecule interactions.³³ One notable exception is the 2D coordination network [Mn₂(NITIm)₃]ClO₄ (NITImH = 2-(2-imidazolyl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-3-oxide-1-oxyl), which shows a sharp thermal VT transition at room temperature with a thermal hysteresis of 20 K.³⁴ This observation hints that with a suitable combination of metal ion and ligand scaffold, extended networks exhibiting VT transitions could parallel the robust bistability found in SCO materials. However, for VT materials, unlike SCO materials, the concerted change in electronic structure of both the metal ion and the ligand scaffold may result in a highly correlated state existing in close energetic proximity to a diamagnetic or localised magnetic state. In extended networks, such correlations extend beyond the length scale of the molecule and will be at the origin of novel electronic and magnetic phases.

The VT transition is an entropically driven process. In Co-dioxolene compounds specifically, the entropy gain in the paramagnetic, HT Co^II-sq˙⁻ form is due to the larger spin state degeneracy leading to a gain in electronic entropy, as well as the longer metal–ligand bond lengths, leading to a higher density of vibrational states and a larger vibrational entropy. The thermal equilibrium is therefore determined by the Gibbs free energy, ΔG = ΔH − TΔS. According to this, the transition will occur when ΔG = 0 and ΔH = T_cΔS, which also defines the critical temperature, T_c.³⁵ Substitution of the dioxolene ligands has allowed for controlled tuning of the ligand redox potential, while careful choice in auxiliary ligand allows for tuning of the Co^II/Co^III redox couple, both directly modifying ΔH.³⁶ In addition, both solvent effects in solution state³⁷ and crystal packing effects³⁸ in the solid state affect the observed transition.

In stark contrast to transition metal ions, the lanthanide (Ln) ions are almost exclusively found as trivalent ions with 4fⁿ electronic configurations and are typically considered redox innocent. For most Ln^III ions, unquenched orbital angular momentum and significant spin–orbit coupling dominate the electronic properties, with the crystal field effect of the ligand scaffold being only weak. One consequence of the unique electronic structure of the Ln^III ions is often large magnetic moments with strong magnetic anisotropy, leading to widespread technological applications in hard magnets (e.g., SmCo₅, Nd₂Fe₁₄B³⁹) or potential future applications of single-molecule magnets.^40–43 Even in the case of negligible magnetic anisotropy, such as for 4f⁷ ions, e.g., Gd^III, the large magnetic moment has led to its use in MRI contrast agents⁴⁴ and in low-temperature magnetocaloric materials.⁴⁵ On the other hand, the weak crystal field interaction with the coordination environment gives rise to sharp, long-lived luminescence, which is used in, e.g., phosphors, sensors, and luminescent thermometers.⁴⁶ As these phenomena are intimately linked to the electronic configuration of the Ln^III ions, any change in oxidation state necessarily leads to a dramatic change in properties. In other words, manipulation of the oxidation state by a VT transition could allow for any of these properties to be switchable by an external stimulus.

In this Feature Article, we discuss the emergence of VT transitions in extended coordination networks based on Ln ions. First, the known redox properties of Ln species are briefly discussed, which are central to fluxional valence phenomena in lanthanide inorganic solid-state materials, as well as VT and intermediate valence tautomerism in molecular Ln materials. We then outline the work we have recently undertaken in the field of Ln-based coordination networks, which includes observation of novel geometric tessellations, slow magnetic relaxation, and enhanced sub-Kelvin magnetic refrigeration. This work culminates in the recent discovery of a samarium–pyrazine framework featuring a thermally activated and complete VT transition.

2. Frozen oxidation states

The lanthanide ions are by far most common in their trivalent state, with notable exceptions to this rule exhibiting either a closed-shell or half-filled 4f configuration: Ce^IV (4f⁰), Eu^II (4f⁷), and Yb^II (4f¹⁴). Despite this redox-inactivity, synthetic efforts, primarily in the last decade, have now resulted in the isolation of Ln^II compounds for all Ln except Pm,^47–50 and Ln^IV coordination compounds for Ce,^51–53 Pr,^54,55 and Tb.^56,57 The implications for coordination chemistry utilising the Ln^III/Ln^II and Ln^IV/Ln^III redox couples have been reviewed by others.^58,59 Of the divalent Ln ions, Sm, Eu, and Yb are most stable towards oxidation to their trivalent state (Table 1), and simple precursors are commercially available. Eu^II, in particular, is widely used in inorganic phosphors, exhibiting tunable 4f⁷ ← 4f⁶5d emission in the visible spectrum.⁶⁰ In the field of molecular magnetism, organometallic complexes of Tb^II and Dy^II have shown promise as improved single-molecule magnets.⁶¹ Synthetically, Ln^II ions are widely used as one-electron reducing agents⁶² or more recently, as catalysts,^63,64 leveraging their large and negative reduction potentials. SmI₂, specifically, is widely used as a versatile, strong one-electron reductant for diverse organic transformations.^65,66

Table 1 Standard reduction potentials (E_1/2vs. NHE) of Ln^III/Ln^II redox couples for selected Ln⁶⁷

	Nd	Sm	Eu	Dy	Tm	Yb
E 1/2(Ln^III/Ln^II)/V	−2.6	−1.5	−0.34	−2.6	−2.2	−1.2

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The possibility to exploit different redox states in molecular systems containing Ln ions is not necessarily limited to the metal centre itself, but could involve the ligand scaffold – a situation of great interest in the field of molecular magnetism. Such resulting radical ligand systems have been a synthetic target in the field of single-molecule magnets (SMMs), compounds which exhibit magnetic bistability at low temperatures.⁶⁸ In such systems, a strong magnetic anisotropy leads to an energy barrier to magnetization reversal and a wide magnetic hysteresis. This field was dominated by 3d-based polynuclear complexes, until Ishikawa et al. reported that the Ln complex [Tb^III(Pc)₂]⁻ (Pc = phthalocyaninate) exhibited the same slow magnetic relaxation as the polynuclear complex-based SMMs.⁶⁹ In the proceeding 20 years, this has led to the discovery of SMMs with record breaking working temperatures.^40–43

Further improving the performance of Ln-SMMs via coupling of electronic spins in polynuclear assemblies, akin to the strategy pursued for the 3d metal ion complexes, has been of limited success. The problem is rooted in the shielded nature of the 4f orbitals, that hinders any strong magnetic interaction between Ln ions in a given material. Ligand-based radicals often possess significant electronic spin densities at the ligating atom, thereby promoting the strong magnetic interactions in Ln-radical systems. Notable examples include the N₂³⁻-bridged Ln dinuclear complexes, which show some of the highest hysteresis temperatures and, notably, extremely large magnetic coercivities.^70–72 The group of Murugesu recently published tetranuclear complexes, [(Cp*₂Ln^III)₄(tz˙⁻)₄] (Cp* = pentamethylcyclopentadienide), consisting of Cp*₂Ln^III units bridged by tetrazine (tz˙⁻) anion radical ligands. Here, strong magnetic exchange coupling leads to a large coercive field of H_coer = 3 T at 1.8 K.⁷³ Switching to a pyrazine anion radical ligand (pyz˙⁻), the related family of compounds [(Cp*₂Ln^III)₄(pyz˙⁻)₄] could be obtained.⁷⁴ Here, a coercive field of 6.5 T is observed for the Dy analogue. The extraordinary properties stem from strong Ln-radical magnetic exchange coupling, combined with a strongly axial crystal field at each Dy^III ion. Despite the potential of such scenarios for generating novel magnetic phases in coordination networks, these are yet to be discovered.

3. Redox isomerism and related phenomena in lanthanide materials

3.1 The dawn of VT transitions in lanthanide materials

Divalent Ln ions were first widely observed in inorganic solids. Perhaps unsurprisingly, valence change transitions have therefore been observed in intermetallics, chalcogenides, and oxides for all the common Ln^II ions. These transitions are typically characterised by (partial) electron transfer from the localised 4f orbitals to a conduction band, formally corresponding to an increase in the Ln oxidation state. Conceptually, this situation is analogous to the previously discussed VT transition, while commonly referred to as a valence change transition or valence instability. The first observation in 1912 of such a transition was in metallic Ce.⁷⁵ Herein, Ce exhibits a temperature- and pressure-dependent change in oxidation state from Ce^III to an intermediate valence Ce^3.6+ phase, due to the promotion of 4f electrons to the s–d conduction band.^75–78 Alloying with Th yields Ce_1−xTh_x phases exhibiting thermally driven VT transitions, allowing for tuning of the transition temperature and pressure, with a cooperativity governed by the Th content (Fig. 2(a)).⁷⁹ Similarly, in samarium monosulfide, a pressure-induced (0.65 GPa) VT transition promotes an electron from Sm^II to the conduction band, giving a formal oxidation state of near 2.6+ in the “golden” intermediate-valence phase (Fig. 2(b)).^80,81 This transition is accompanied by a dramatic change in the physical properties, reflected in the semiconductor-to-metal transition. Even larger pressures lead to a complete transition to Sm^III, resulting in a metallic, correlated heavy fermion phase.⁸² Chemical alloying of SmS with Y, Eu, Gd, or Yb leads to a shift in the temperature and pressure at which the valence transition occurs, analogous to the shift in the thermally induced transition in Ce_1−xTh_x alloys.^83–85 For example, Sm_1−xY_xS stabilises the golden phase due to the “chemical pressure” from the dopant, and by x = 0.2, the intermediate valence state is observed at ambient pressure and room temperature.⁸⁶

Fig. 2 (a) Temperature-dependent magnetic susceptibility (χ) in Ce_1−xTh_x alloys exhibiting thermally induced valence transitions. Reproduced with permission from EDP Sciences (1976).⁷⁹ (b) Phase diagram of SmS, showing temperature- and pressure-dependent valence change transitions. Reproduced from Springer Nature (2017).⁸⁷ (c) Temperature dependence of the unit cell volume of Sm_2.75C₆₀, demonstrating the large negative thermal expansion driven by the valence change transition. Reproduced with permission from Springer Nature (2003).⁸⁸

Lanthanide fullerides similarly exhibit VT transitions stimulated by temperature or pressure. In these compounds, Ln ions are intercalated between fulleride anions. Due to the molecular nature of the fullerides, the electron-accepting state is not necessarily the conduction-band, but could be of isolated, molecular origin. At room temperature, Sm_2.75C₆₀ is intermediate valence, with a Sm valence of 2.3+.⁸⁸ Upon decreasing temperature, a VT transition at 32 K leads to a localised Sm^II state, accompanied by a negative thermal expansion due to the increased ionic radius (Fig. 2(c)). Here, the electronic driving force for the VT transition is the thermal population of the low-lying t_1u level of C₆₀ upon heating, leading to an overall decrease in occupation of the Sm 4f orbitals. An analogous VT transition is observed in the Yb congener, Yb_2.75C₆₀, with a higher transition temperature of 60 K.⁸⁹ A room-temperature, pressure-induced (4 GPa) VT transition is also observed for Sm_2.75C₆₀, which leads to the more intuitively expected increase in valency to Sm^III, driven by the smaller radius of the higher oxidation state ion.⁹⁰ Indeed, VT transitions are now widespread in inorganic solids, in particular in intermetallics.^91–95 Herein, the VT transitions are accompanied by stark changes in structural, electronic, magnetic, and optical properties.

3.2 Valence instabilities and nebulous oxidation states

In molecular Ln materials, observation of VT transitions is extremely limited. In 2009, Fedushkin et al. reported the observation of an in-solution VT transition in [(dpp-bian)Yb(dme)(μ-Br)]₂ (dpp-bian = 1,2-bis[(2,6-diisopropylphenyl)imino]-acenaphthene; dme = dimethoxyethane).⁹⁶ Here, a HT tautomer was observed to interconvert with a LT tautomer above room temperature. This was followed in 2012 by the observation of a VT transition in the compound [(dpp-bian)Yb(dme)(μ-Cl)]₂ (Fig. 3(a)) in the solid state.⁹⁷ Single-crystal X-ray diffraction allowed the authors to conclude that one half of the dimer undergoes a VT transition–i.e. a LT-{Yb^III₂(bian²⁻)₂} ⇄ HT-{Yb^IIIYb^II(bian²⁻)(bian˙⁻)} conversion (Fig. 3(b)). For this compound, only a single polymorph undergoes the VT transition, which hints that the tautomerism is particularly dependent on steric effects. This year, a gradual VT transition in the related, monomeric complex [(Ar^BIG-bian)Yb{(C(S)NMe₂)(dme)] (Ar^BIG-bian = 1,2-bis[(2,6-dibenzhydryl-4-methylphenyl)imino]acenaphthene) was reported.⁹⁸ Herein, the HT phase (350 K) of a 1 : 1 mixture of {Yb^III(bian²⁻)} and Yb^II(bian˙⁻)}, gradually transitions to a 3 : 1 mixture in the LT phase (100 K). The presence of four crystallographically independent molecules in the unit cell, only one of which transitions, showcases, again, the sensitivity of the VT transition to minute structural differences.

Fig. 3 (a) Molecular complex of [{(dpp-bian)Yb(dme)(μ-Cl)}₂].⁹⁷ Isopropyl groups and H-atoms are omitted for clarity. (b) Magnetic moment with temperature for several single-crystals of [{(dpp-bian)Yb(dme)(μ-Cl)}₂]. Reproduced with permission from Wiley (2012).⁹⁷

Changes in local coordination environment due to chemical pressure can also induce VT transitions in Ln molecular complexes. When functionalised Ln(Pc)₂ complexes, Ce{(15C5)₄Pc}₂⁹⁹ and Eu{(BuO)₈Pc}₂¹⁰⁰ are introduced into a Langmuir air/water monolayer, they undergo an electron transfer from one ligand to the metal, undergoing Ce^IV{Pc²⁻}₂ ⇄ Ce^III{(Pc²⁻)(Pc˙⁻)} and Eu^III{(Pc²⁻)(Pc˙⁻)} ⇄ Eu^II{Pc˙⁻}₂ transitions, respectively. For Ce{(15C5)₄Pc}₂, the surface pressure could be tuned to yield different tautomers. In Ce(Pc)₂, the same tautomerism could be induced by deposition on a gold surface, which induces a 45° twist between the Pc^2−/˙⁻ ligands, triggering the transition.¹⁰¹

Pairing Ln ions with other redox-active ligands such as 2,2′-bipyridine (2,2′-bpy) ligands has led to the observation of intermediate valency.¹⁰² Here, close energetic proximity of ligand and Ln valence states lead to multi-configurational ground states, where the formal valence of both the Ln ion and the ligand are non-integer. The Yb(Cp*)₂L systems, where L are derivatives of 2,2′-bpy, are particularly well studied examples of intermediate valency in molecules. Within this family, a phenomenon termed intermediate valence tautomerism (IVT) is exhibited by (Cp*)₂Yb(4,4′-Me₂-2,2′-bpy) (Fig. 4(a)).^103,104 In this compound, magnetometry and Yb L₃-edge X-ray absorption near-edge structure (XANES) spectra are consistent with a hysteretic valence transition between two distinct intermediate valence tautomers (Fig. 4(b)). Intermediate valence tautomerism is now well established in both purely inorganic solids and molecular Ln complexes, whilst remaining elusive in coordination networks of any kind.

Fig. 4 (a) Structure of (Cp*)₂Yb(4,4′-Me₂-2,2′-bpy).¹⁰⁴ (b) f-hole occupancy (n_f) determined by fitting of XANES spectra across the thermal intermediate valence transition. Reprinted with permission from ref. 103. Copyright 2010 American Chemical Society.

4. Tiling valence, tautomerism & magnetism

4.1 Inspiration from transition metal tessellations

Coordination networks extending into one, two, or three dimensions conceptually reside between extended inorganic solids and molecular coordination complexes, thereby benefitting from the designable molecular properties and by physical properties tied to long-range correlations. This is well exemplified by the family of compounds spurred from the discovery of the 2D network CrCl₂(pyz)₂ (Fig. 5). The reducing nature of Cr^II leads to an electronic ground state approximated by the formulation Cr^III{(pyz⁰)(pyz˙⁻)}.¹⁰⁵ Strong metal–radical magnetic interactions and significant π–d conjugation lead to ferrimagnetic ordering at relatively high temperatures (55 K) and one of the highest observed electrical conductivities in a coordination compound.

Fig. 5 (a) 2D square tilings formed by MCl₂(pyz)₂. (b) Local coordination environment of M ions. (c) Packing of 2D sheets. Hydrogen atoms are omitted for clarity.¹⁰⁵

Modulation of the Cr^II/Cr^III redox potential through ligand substitution of the trans-chlorido ligands for methanesulfonate yields instead the Cr^II(pyz⁰)₂ redox isomer, which is electrically insulating and exhibits an antiferromagnetic ground state.¹⁰⁶ A postsynthetic reduction of CrCl₂(pyz)₂ leads to formation of Li_0.7Cl_0.7Cr(pyz)₂·0.25 thf (thf = tetrahydrofuran), consisting of layers of Cr^II(pyz˙⁻)₂. Here, the strong metal–radical interactions lead to a massive 0.75 T coercivity at room temperature, rivalling rare-earth based hard magnets.¹⁰⁷ Similar layered 2D sheets to CrCl₂(pyz)₂ can be obtained with Ti and V.¹⁰⁸ TiCl₂(pyz)₂, approximated as Ti^III{(pyz⁰)(pyz˙⁻)}, displays strongly correlated Fermi liquid behaviour, leading to the highest room-temperature electronic conductivity for any metal–organic solid with octahedrally coordinated metal ions. In contrast, the antiferromagnetic insulator VCl₂(pyz)₂ exhibits no electron transfer from the metal to the ligand, leading to a V^II(pyz⁰)₂ redox isomer. These highly correlated, extended materials stand in stark contrast to the vast majority of typical framework materials, which are typically constructed from redox-inactive linkers and metal nodes.

4.2 Innocent Archimedean tessellations

Akin to the MCl₂(pyz)₂ series, trans-dihalido Ln nodes could be similarly expected to structurally direct 2D sheet-like tessellations. Labile solvates of the trans-{Ln^III₂} moieties are readily formed by dissolution of LnI₂ forming what is posited to be trans-LnI₂(CH₃CN)₅ (Ln = Sm, Eu, Yb)¹⁰⁹ in acetonitrile, and trans-LnI₂(thf)₅ (Ln = Nd,¹¹⁰ Sm,¹¹¹ Eu¹¹²) or trans-LnI₂(thf)₄ (Ln = Yb¹¹³) in thf (Fig. 6). Unlike the MCl₂(pyz)₂ tessellations, where octahedral nodes lead to square tilings (Fig. 5), the {Ln^III₂} nodes are pseudo-pentagonal bipyramidal, and as such should engender 2D tilings with five-fold nodes. The proof of principle was achieved through the combination of {Yb^III₂} nodes with ditopic 4,4′-bipyridine (bpy), leading to either 2D sheets, YbI₂(bpy)_5/2, or pseudo-1D ladders, YbI₂(bpy)₂(thf), depending on the reaction solvent (Fig. 7(a) and (b)).¹¹⁴ In YbI₂(bpy)_5/2, irrespective of the close resemblance of the first coordination sphere of Yb to D_5h symmetry–incompatible with periodicity–the flexibility of the bpy ligands results in an elusive, idealized elongated triangular tessellation, consisting of triangular and quadratic motifs. Despite the large and negative reduction potential of the Yb^III/Yb^II redox couple (Table 1), no full or partial electron transfer occurs between Yb^II and bpy, contrasting the observation in, e.g., CrCl₂(pyz)₂ (E_1/2(Cr^III/Cr^II) = −0.42 V). Confirmation of the Yb^II oxidation state in YbI₂(bpy)_5/2 and YbI₂(bpy)₂(thf) is given by their diamagnetism in the entire temperature range of 1.7–273 K. This assignment is further supported by bond length analysis, where the Yb–I bond length is a sensitive measure of the Yb oxidation state (Fig. 8).

Fig. 6 Left to right: Ln^II complexes formed in solution: LnI₂(thf)₅,¹¹¹ LnI₂(CH₃CN)₅,¹⁰⁹ and a Ln^III complex, LnI₂(thf)₅⁺.¹¹⁵ Selected angles shown illustrate the pseudo-pentagonal bipyramidal coordination sphere. Sm–I bond lengths are highlighted to indicate the ca. 6% decrease upon one-electron oxidation.

Fig. 7 Representation of tessellations formed through the combination of trans-{LnI₂} nodes with ditopic pyz and bpy ligands. (a) Elongated triangular net LnI₂(bpy)_5/2.^114,116,117 (b) Pseudo-1D chains of LnI₂(bpy)₂(thf).¹¹⁴ (c) Snub square net of LnI₂(bpy)_5/2.¹¹⁶ (d) Elongated triangular net of LnI₂(pyz)_5/2.¹¹⁷ (e) Pseudo-1D chains of LnI₂(pyz)₃.¹¹⁸ (f) Triangular net of Ln@BaI₂(pyz)₃.¹¹⁹

Fig. 8 Local coordination sphere of LnI₂(bpy)_x, LnI₂(pyz)_x (left), highlighting typical bond angles. Plot of Ln–I bond lengths across the Ln series (right), with groups of Ln^II and Ln^III oxidation states highlighted. For SmI₂(pyz)₃, a HT and LT valence tautomer can be identified.

A similar Archimedean tessellation, i.e., a tiling of different polygons, to that of YbI₂(bpy)_5/2 has previously been observed by scanning tunnelling microscopy in on-surface self-assembled structures of Eu atoms and para-quaterphenyldicarbonitrile.¹²⁰ Herein, several metal–organic Archimedean tessellations were shown to form under near identical conditions suggesting little energetic difference. Notably, the random tessellation of triangles and squares led to the realization of a dodecagonal quasicrystalline phase. The observation of the periodic YbI₂(bpy)_5/2 quasicrystal approximant phase suggests that similar 2D quasicrystalline materials could be designed in bulk, crystalline materials.^121,122 On a separate note, coordination networks incorporating divalent Ln ions instead of the much more common trivalent ions,^123–125 are rare. The spontaneous self-assembly of YbI₂(bpy)_5/2 and YbI₂(bpy)₂(thf) suggests that a wealth of, in coordination chemistry, hitherto unknown tessellations may be readily obtainable.

4.3 Guilty magnetic tilings

In order to leverage the magnetic properties of Ln-based materials, paramagnetic Ln ions were sought. Further, inspired by the burgeoning literature on Ln–radical complexes and their extraordinary magnetic properties, actuation of ligand scaffold non-innocence was pursued. Compared to the less reducing Yb^II, the largely negative reduction potential of, e.g., Dy^II (Table 1) is such that even many common solvents are reduced, making exotic reagents like DyI₂ impractical. Instead of relying on an in situ reduction of the ligand by the Ln^II ion, the solution reaction of trivalent LnI₃ (Ln = Gd, Dy) with a mixture of bpy⁰ and bpy˙⁻, formed simply by Na reduction, yields 2D networks of formula LnI₂(bpy)_5/2, analogous to the previously discussed YbI₂(bpy)_5/2.¹¹⁶ However, for Ln = Gd, Dy, a snub square tiling structure is obtained (Fig. 7(c)), as well as a side-phase of the elongated triangular tiling for Gd (Fig. 7(a)). For both DyI₂(bpy)_5/2 and GdI₂(bpy)_5/2, the Ln–I bond length analyses are consistent with the presence of Ln^III ions (Fig. 8), implying a radical nature of the bpy scaffold and an approximate electronic configuration of Ln^III{(bpy˙⁻)(bpy⁰)_3/2}. The ligand scaffold mixed-valency is reminiscent of the situation encountered in CrCl₂(pyz)₂, however, the absence of any intervalence charge transfer transitions in GdI₂(bpy)_5/2 suggests the presence of weakly electronically coupled bpy fragments and an anticipated poor electrical conductivity.

The magnetometric data for GdI₂(bpy)_5/2 suggest only weak antiferromagnetic Gd^III–bpy˙⁻ exchange interactions, on the order of J = 0.07 cm⁻¹ (JŜ₁Ŝ₂ convention), as often encountered in Ln–radical systems. This number, however, is significantly smaller than those found in the previous discussed molecular complexes.^70–74 In the case of DyI₂(bpy)_5/2, the axial ligand field induced by the anionic trans-iodido ligands combined with a pseudo-D_5d symmetry at the Dy^III centre allows for the observation of slow paramagnetic relaxation in zero applied magnetic field (Fig. 9). However, despite the presence of a small Dy^III–bpy˙⁻ exchange bias, rapid quantum tunnelling of magnetisation is observed.

Fig. 9 In-phase (χ′, left) and out-of-phase (χ′′, right) ac susceptibility data for polycrystalline DyI₂(bpy)_5/2 obtained at selected temperatures and in the absence of a static (dc) magnetic field. Inset: Temperature dependence of the paramagnetic relaxation rate, τ⁻¹, vs. temperature. The solid lines are simulations, yielding an effective energy barrier to magnetization reversal of 63 cm⁻¹ when measured in H_dc = 3 T. Reprinted with permission from ref. 116. Copyright 2021 American Chemical Society.

The isolation of a snub square tiling in a coordination network is exceedingly rare, with only one prior example known in the bulk phase.¹²² The coexistence of both the elongated triangular and snub square tessellation in the case of GdI₂(bpy)_5/2 may suggest similar energies of formation and, thus, provide perspectives for the isolation of intergrown motifs required for quasicrystallinity.

4.4 Frosty frustrated triangles

The formation of Archimedean tessellations is a robust outcome of the assembly of {LnI₂}^0/+ units with also different ditopic ligands. This is illustrated by the isoreticular EuI₂(bpy)_5/2 and EuI₂(pyz)_5/2, both forming the elongated triangular tessellation (Fig. 7(a) and (d)).¹¹⁷ Switching the long bpy ligand for shorter pyz leads to essentially identical coordination at the Eu centre, although modulates the Eu⋯Eu distances, and thus directly impacts the magnetic interaction strengths. The only weakly reducing nature of Eu^II inhibits any radical character of the ligand scaffold, as confirmed by bond length analysis (Fig. 8), magnetometry, and X-ray absorption spectroscopy. The 4f⁷ electronic configuration of Eu^II leads to the largest possible spin magnetic moment and the absence of an orbital angular momentum results in a vanishingly small magnetic anisotropy. These qualities are tantalizing for the development of Eu^II-based coolant materials for adiabatic demagnetization refrigerators relying on the magnetocaloric effect (MCE).^126,127 The MCE occurs due to the change in magnetic entropy of a material when a magnetic field is applied or removed. When the field is applied, the constituent spins of the magnet align, reducing magnetic entropy, and the system releases heat. When the field is removed, entropy increases as the spin moments randomize, absorbing heat and cooling the material. MCE materials operating in the sub-Kelvin regime are touted as alternatives to traditional ³He cooling used, e.g., for cryogenic applications needed in quantum technology and space exploration. In this temperature window, even weak antiferromagnetic interactions are undesired, as they minimize the ground state spin moment and thus the magnetic entropy. Nevertheless, complete eradication of magnetic interactions between electronic spins is only possible in magnetically highly dilute materials, which concurrently will have an only low cooling capacity. The creation of ideal triangular motifs bypasses this obstacle. An equilateral triangular net with pairwise antiferromagnetic interactions exhibits magnetic frustration, and thereby the absence of long-range magnetic order, and a retention of the magnetic entropy extending into the sub-Kelvin domain. Indeed, EuI₂(pyz)_5/2 fulfills these requirements by featuring triangular motifs with weak antiferromagnetic interactions, on the order of −0.3 cm⁻¹, as suggested by DFT calculations. The specific heat shows a broad maximum in the zero-field c_p between ca. 0.7 and 3 K, attributed to 2D intra-layer fluctuations. However, below 0.5 K, there is the onset of a magnetic phase transition, negating the observation of a magnetocaloric effect below this temperature. Despite this, a sizeable MCE is observed with a maximum isothermal magnetic entropy change of 24.3 J kg⁻¹ K⁻¹ for a 7 T field change and at a high temperature of 3 K. To further improve the MCE at sub-K temperature in Eu^II tessellations, we sought to realize strictly triangular motifs. This situation is fulfilled in the triangular tessellation, featuring 3- or 6-fold symmetric nodes, yet to be observed in a coordination solid. As the ionic radius of Eu^II is slightly too small to accommodate the required six ligands in plane, the larger Ba^II was used. This resultant compound, BaI₂(pyz)₃ (Fig. 7(f)), features sheets with a triangular tessellation, with crystallographic D_3d local symmetry of the Ba site.¹¹⁹ Despite the nonexistence of the Eu^II analogue, performing the synthesis with a mixture of EuI₂ and BaI₂ leads to alloyed networks, Ba_1−xEu_xI₂(pyz)₃, with up to 92% of Eu^II (hereafter denoted as Ba_0.1Eu_0.9I₂(pyz)₃). In the absence (or less than 8%) of templating Ba^II, EuI₂(pyz)₃ is instead formed. Here, a different connectivity is observed, with the smaller Eu^II nodes enjoying a fivefold in-plane coordination (Fig. 7(e)). Structural analysis of Ba_0.1Eu_0.9I₂(pyz)₃ is consistent with an Eu^II oxidation state, and reveals the longest reported unsupported Eu–N bond lengths (2.90 Å). The resultant long Eu⋯Eu distances lead to exceedingly weak exchange interactions, which is reflected by the weak antiferromagnetic J = −0.006 cm⁻¹ obtained from the concerted analysis of magnetometric and heat capacity data obtained down to 0.3 K (Fig. 10(a)). The ensuing magnetic frustration tied to the interactions and the high crystallographic symmetry leads to a magnetocaloric working temperature as low as T = 0.17 K (Fig. 10(b)). This value is remarkably low for a relatively magnetically dense refrigerant and illustrates well how coordination chemistry approaches towards novel MCE materials may challenge the much more established purely inorganic materials.

Fig. 10 (a) The change in magnetic entropy, −ΔS_m, at selected magnetic fields for Ba_0.1Eu_0.9I₂(pyz)₃, as obtained from the experimental c_p and magnetization data, and calculated c_p for J/k_B = −0.008 K and D/k_B = 0.068 K (lines). (b) Demagnetization (0.5 T → 0 T) processes at starting temperatures T₀ = 0.58, 0.47 K, and 0.38 K. Inset: Time-dependence of the temperature at T₀ = 0.38 K following a linear decrease in the magnetic field strength (grey trace). Reproduced from ref. 119.

4.5 Emergence of lanthanide valence swings

As for EuI₂(pyz)₃, the combination of LnI₂ (Ln = Sm, Yb) with pyz leads to the formation of LnI₂(pyz)₃ (Fig. 7(e)), featuring pseudo-1D chains of {LnI₂pyz₂} with interdigitating pendant pyz ligands.¹¹⁸ All data for both EuI₂(pyz)₃ and YbI₂(pyz)₃ are consistent with the presence of a Ln^II ion. For Sm^II, despite the diamagnetic ⁷F₀ ground state, thermal population of the ⁷F₁ state gives rise to a sizable magnetic moment at room temperature (χT ≈ 1.4 cm³ mol⁻¹ K⁻¹), as found in, e.g., Sm^III₂(CH₃CN)₅.¹⁰⁹ For SmI₂(pyz)₃, the room-temperature χT product is commensurate with an Sm^II oxidation state assignment. Upon descending temperature, an abrupt decrease in χT of ∼80% is observed at T ≈ 190 K. Sm–I bond length analysis of the single-crystal X-ray structures of the HT and LT phases suggests the presence of a Sm^II(pyz⁰)₃ HT valence tautomer and a Sm^III{(pyz⁰)₂(pyz˙⁻)} LT valence tautomer (Fig. 8 and 11(a)). As expected for an Sm^II → Sm^III oxidation, a 4% decrease in Ln–I bond lengths is observed and an overall 6% reduction in the unit cell volume. The structural analysis of the LT phase clearly shows the localization of the pyz˙⁻ moieties in a zigzag chain between the Sm^III ions (Fig. 11(a)). Additional evidence of a VT transition is provided by XANES of the HT and LT phases (Fig. 11(c)). The Sm L₃ absorption edge resonance shows a shift of 8 eV, consistent with a quantitative and reversible Sm^II(pyz⁰)₃ ⇄ Sm^III{(pyz⁰)₂(pyz˙⁻)} VT transition, and no indication of intermediate valency. The VT transition is cooperative and has an open thermal hysteresis of 14 K (sweep rate = 0.5 K min⁻¹) and is reversible over at least 100 temperature cycles with only minor loss of conversion (Fig. 11(b)). The electronic ground state of Sm^III, ⁶H_5/2 with g_J = 2/7, results in an almost vanishing magnetic moment. As such, the magnetic moment of the LT phase is dominated by the magnetic moment of pyz˙⁻. The close proximity of the pyz˙⁻ in the zigzag chain results in significant antiferromagnetic radical–radical exchange interactions (J = −76 cm⁻¹). The isomorphism of the LnI₂(pyz)₃ (Ln = Sm, Eu, Yb) series provides the opportunity to tune the VT transition by alloying, as often used in inorganic solids exhibiting VT transitions. Indeed, syntheses involving mixtures of SmI₂ and YbI₂, in any ratio, yield monophasic Sm_1−xYb_xI₂(pyz)₃ solid-solutions. The smaller ionic radius of Yb^II over Sm^II, results in a progressive reduction in the HT unit cell volume with increasing Yb content. Introducing only 10% Yb^II yields an alloy retaining a full VT transition, but at a lower critical temperature (Fig. 12). A further increase in Yb content leads to a further shifting of the VT critical temperature, a softening of the VT transition, and a narrowing of the thermal hysteresis, consistent with decreasing cooperativity. Notably, this is fully analogous to both the situation encountered in SCO coordination polymers, as well as the established Ln valence change transitions in purely inorganic materials. In stark contrast to the purely inorganic solids, however, the VT transition in SmI₂(pyz)₃ and Sm_1−xYb_xI₂(pyz)₃ appears to involve only distinct and integer oxidation states, and in this regard bear closer resemblance to the VT transitions observed in transition metal-based systems.

Fig. 11 (a) HT and LT valence tautomers of the pseudo-1D chains of {Sm(pyz)₂} in SmI₂(pyz)₃. Local coordination environment of the Sm ions shown on the right. (b) Durability of the VT transition as reflected in the χT data obtained by T cycling between 175 K and 225 K (sweep rate = 2 K min⁻¹). (c) Sm L₃ XANES spectra of polycrystalline SmI₂(pyz)₃ measured at 300 K, at 44 K and again at 300 K. Reproduced from Springer Nature (2024).¹¹⁸

Fig. 12 Magnetic susceptibility-temperature product, χT (μ₀H  =  1.0 T; temperature ramping rate, 0.25 K min⁻¹) of Sm_1−xYb_xI₂(pyz)₃ solid solutions, normalized to the samarium content, 1 − x. The grey surface represents the area spanned by the expected χT product for the LT phase and HT phase. The solid black line represents the 50% molar fraction of the LT  ⇄  HT phase conversion. Inset: Temperature dependence of T_cversus x, with the best linear fit (grey line, T_c (K) = −3.55x + 202). Reproduced from Springer Nature (2024).¹¹⁸

5. Conclusions and outlook

The self-assembly of trans-{LnI₂}^0/+ nodes and ditopic linkers, pyrazine and 4,4′-bipyridine, yields a variety of genuinely new chemical motifs. The robust structure-directing nature of the nodes provide rare opportunities for tailoring symmetries in f-element-based materials. The 2D tessellations escape the periodicity-defying pentagonal nodes by tiling Archimedean patterns, that may verge on even quasicrystallinity. Harnessing a novel templation effect, even hexagonal nodes can be realized. The structural symmetry has decisive implications for the electronic structure and ensuing physical properties. This is exemplified by the spin-frustrated Ba_0.1Eu_0.9I₂(pyz)₃ network, which escapes magnetic order, even when approaching absolute zero temperature. The wide span of Ln^III/Ln^II reduction potentials and the chemical resemblance allows for the design of isostructural materials hosting either Ln^II–ligand(0) or Ln^III–ligand(˙−) linkages. Despite being well-established in purely inorganic materials, stimuli-induced VT transitions linking the Ln^II–ligand(0) or Ln^III–ligand(˙−) states are far from well-established. Sm^II and pyrazine are on the brink of electron transfer. The resultant compound, SmI₂(pyz)₃, is the first coordination solid of the f-block to exhibit an unambiguous and complete VT transition. The phenomenon is robust to structural distortions, although tunable, as illustrated by molecular alloying. The realization of a VT switch in a coordination network opens perspectives for further chemically encoding of cooperative VT events by crystal engineering, as successfully pursued in the field of SCO materials. However, the fundamental advantage to coordination networks featuring VT transitions is the concerted change to the extended electronic structure of the pillaring ligands. Such activation of the otherwise innocent scaffold is currently at the origin of new horizons of metal–organic framework chemistry, such as high electrical conductivity.^128,129 We envision a plethora of magnetoelectrical properties, not currently found in molecular chemistry, could be found in the chemical space of valence-fluctuating lanthanide ions and redox-non-innocent scaffolds, and we do not see any reason why these materials would be limited to the metal ion and ligand combinations discussed in this account.

Author contributions

The manuscript was written by K. S. P. and M. A. D., and both authors have given their consent to the publication of the manuscript.

Data availability statement

No primary research results, software or code have been included and no new data were generated or analysed as part of this review.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

K. S. P. thanks the VILLUM Foundation for a VILLUM Young Investigator+ (42094) grant, the Independent Research Fund Denmark for a DFF-Sapere Aude Starting grant (no. 0165-00073B), and the Carlsberg Foundation for a research infrastructure grant (no. CF17-0637).

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