Rational design of single-molecule magnets: a supramolecular approach

Abstract

Since the discovery that Mn₁₂1212OAc acts as a single-molecule magnet (SMM), an increasing number of transition metal complexes have been demonstrated to behave as SMMs. The signature of a SMM is a slow relaxation of the magnetization at low temperatures accompanied by a magnetic hysteresis. The origin of SMM behaviour is the existence of an appreciable thermal barrier U for spin-reversal called magnetic anisotropy barrier which is related to the combination of a large total spin ground state (S_t) and an easy-axis magnetic anisotropy. The extensive research on Mn₁₂1212OAc and other SMMs has established more prerequisites for a rational development of new SMMs besides the high-spin ground state and the magnetic anisotropy: the symmetry should be at least C₃ to minimize the quantum tunneling of the magnetization through the anisotropy barrier but lower than cubic to avoid the cancellation of the local anisotropies upon projection onto the spin ground state. Based on these prerequisites, we have designed the ligand triplesalen which combines the phloroglucinol bridging unit for high spin ground states by the spin-polarization mechanism with a salen-like ligand environment for single-site magnetic anisotropies by a strong tetragonal ligand field. The C₃ symmetric, trinuclear complexes of the triplesalen ligand (talen^t-Bu₂)⁶⁻ exhibit a strong ligand folding resulting in an overall bowl-shaped molecular structure. This ligand folding preorganizes the axial coordination sites of the metal salen subunits for the complementary binding of three facial nitrogen atoms of a hexacyanometallate unit. This leads to a high driving force for the formation of heptanuclear complexes [M^ttt₆6M^ccc]ⁿ⁺nn+ by the assembly of three molecular building blocks. Attractive van der Waals interactions of the tert-butyl phenyl units of two triplesalen trinuclear building blocks increase the driving force. In this respect, we have been able to synthesize the isostructural series [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+, [Mn^IIIIII₆6Fe^IIIIII]³⁺3+, and [Mn^IIIIII₆6Co^IIIIII]³⁺3+ with [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ being a SMM. A detailed analysis and comparison of the magnetic properties of the three heptanuclear complexes and the tetranuclear half-unit [Mn^IIIIII₃3Cr^IIIIII]³⁺3+ provides significant insight for further optimization of the SMM properties. The modular assembly of the heptanuclear complexes from three molecular building blocks allows the fine-tuning of the molecular and steric properties of each building block without losing the driving force for the formation of the heptanuclear complexes. This possibility of rational improvements of our isostructural series is the main advantage of our supramolecular approach.

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Thorsten Glaser

Thorsten Glaser studied chemistry in Bochum and obtained his Dr. rer. nat. in 1997 with Prof. K. Wieghardt at the Max-Planck-Institut, Mülheim. After postdoctoral work with Professors E. I. Solomon and K. O. Hodgson at Stanford University, he started his independent research in 2000 in Münster with a Liebig fellowship of the Fonds of the Chemical Industry and obtained the venia legendi in 2004. He was awarded the ADUC prize in 2002, the Werner-von-Siemens-Medal in 2004, the Young-Talent-Award of Münster University in 2004, and the “Goldener Brendel” from the students for the best chemistry lecture. In 2005 he declined an offer for a full professorship at Marburg University and accepted an offer for a full professorship at Bielefeld University. Since 2008 he is speaker of the DFG research unit “Nanomagnets”.

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1. Introduction

The broad field of molecular magnetism is concerned with the understanding of the magnetic properties of molecules exhibiting one or more magnetic centers in form of transition metal ions or organic radicals.^1–3 Besides the demand to understand the magnetic properties of a single magnetic center (especially to correlate anisotropic properties to the molecular structure) the study and interpretation of intramolecular and intermolecular interactions between magnetic centers are the main focus of molecular magnetism. In the last two decades, the synthesis and characterization of molecule-based magnetic materials, i.e. compounds with the characteristic features of conventional solid-state magnets but prepared with synthetic tools of molecular chemistry under kinetic control, developed to a contemporary application of molecular magnetism.^4–8 The considerable interest in the synthesis of magnetic materials based on molecular entities with its potential applications in fields like molecular electronics^9,10 started with the observation that [Cp*₂Fe]⁺[TCNE]⁻ exhibits a spontaneous long-range ferromagnetic ordering with a Curie temperature T_C of 4.8 K.^11,12 This 3D long-range magnetic order in a system constructed from molecular building blocks initiated world-wide research activities to prepare quasi-1D, 2D, and 3D molecule-based magnets. Prominent examples with T_C's above room temperature are V(TCNE)₂·y(CH₂Cl₂)¹³ and some members of the family of Prussian Blue analogues like KV^II[Cr^III(CN)₆]¹⁴ or V^II_0.42V^III_0.58[Cr^III(CN)₆]_0.86·2.8H₂O.^15,16 This last class based on the use of hexacyanometallates [M(CN)₆]ⁿ⁻ provides a convenient approach for the design of new interesting materials because the high symmetry of the M–CN–M′ exchange pathway allows the prediction of the nature of the exchange interactions^17–20 by the use of the Goodenough–Kanamori rules.^21–23

Another milestone in the field of molecule-based magnetic materials was the observation that [Mn₁₂O₁₂(OAc)₁₆(OH₂)₄], Mn₁₂1212OAc (Fig. 1a and b),²⁴ exhibits a hysteresis in the magnetization of pure molecular origin^25,26 and has been the first member of a new class of molecule-based magnets called single-molecule magnets²⁷ (SMMs).^28–31 These finite-size molecules possess an energy-barrier U for spin reversal causing a slow relaxation of the magnetization at low temperatures. This magnetic bistability of SMMs promises access to devices for ultimate high-density memory storage and quantum computing.^29,32,33 Since the report that Mn₁₂1212OAc exhibits SMM behaviour, a still increasing number of SMMs have been identified in the effort to enhance the magnetic anisotropy barrier.^34,35

Fig. 1 Molecular structures of (a) and (b) Mn₁₂1212OAc,²⁴ (c) Mn₄4,²⁷ (d) Mn₈₄84,⁴⁹ (e) Mn₁₉19,⁵⁰ (f) Mn₆6.⁵⁶

This article presents a personal account of work in the author's research group over the last years, in which the essence of previous investigations on SMMs has been used as a basis for a rational ligand and complex design of a new family of SMMs based on the ligand triplesalen.

2. Design principles

2.1 The properties of Mn₁₂1212OAc as a guide

Mn₁₂1212OAc consists of 8 Mn^III and 4 Mn^IV ions which couple by exchange interactions to a total spin ground state S_t = 10 of the whole molecule.²⁶ An important property of this spin is its anisotropy, i.e. it has a preferred orientation in the molecular framework that is perpendicular to the approximate molecular plane (Fig. 1a). As a pure spin is magnetically completely isotropic, the anisotropy arises from some orbital angular momentum contribution. This magnetic anisotropy can be phenomenologically described by the so-called zero-field splitting, which is parameterized by an axial zero-field splitting parameter D and a rhombicity E/D. A spin of quantum number S possesses 2S + 1 sublevels of quantum number M_S. In zero magnetic field, these sublevels are degenerate. The effect of an axial zero-field splitting (Ĥ = DŜ_z² − ⅓(S(S + 1))) is schematically shown in Fig. 2a for an S_t = 10 spin with negative D. The M_S sublevels split with M_S = ±S lying energetically lowest. This corresponds to the preferred orientation of the spin perpendicular to the molecular plane, while other orientations correspond to the M_S states of lower absolute value, which lie energetically higher. This is also called an easy-axis magnetic anisotropy. A positive D corresponds to a preferred orientation of the spin in the molecular plane associated with the M_S = 0 (or ±1/2 for non-integer spins) being lowest in energy. This is referred to as an easy-plane anisotropy.

Fig. 2 Schematic representation of the anisotropy barrier in SMMs: (a) effect of a negative zero-field splitting parameter on a S_t = 10 spin manifold; (b) magnetization of the sample by application of an external magnetic field (Zeeman effect); (c) frozen magnetized sample showing a slow relaxation of the magnetization over the anisotropy barrier after turning off the external magnetic field; (d) quantum tunneling of the magnetization through the anisotropy barrier for magnetic fields leading to interacting M_S substates at the same energy. Note that the representation as potentials is only a guide to the eyes. The basic representation is energy as a function of the M_S quantum number.

The effect of the application of an external magnetic field is illustrated in Fig. 2b. The states with negative M_S values become energetically stabilized while the substates with positive M_S values become energetically destabilized (Zeeman effect). This leads to a preferred population of the M_S = −10 substate corresponding to a preferred orientation of the microscopic magnetic moments [small mu, Greek, vector] in the direction of the external magnetic field. The effect is a magnetization of the macroscopic sample. This phenomenon occurs in any paramagnetic sample. By switching off the external magnetic field the unperturbed energies (Fig. 2a) are restored. While a paramagnetic system relaxes very fast (≪1 s, dependent on temperature)³⁶ to the unmagnetized equilibrium initial state, this relaxation of the magnetization is slow in a SMM due to the anisotropy barrier schematized in Fig. 2c. This energy barrier (D_St·S_t² for integer spins, D_St·(S_t² − 1/4) for non-integer spins) for spin reversal originates from a ground state with large total spin S_t and large magnetic anisotropy of the easy-axis type. In Mn₁₂1212OAc, the S_t = 10 spin ground state has a zero-field splitting D_St=10 ≈ −0.5 cm⁻¹, which results in an anisotropy barrier of ∼50 cm⁻¹.^25,30 In simple words, the microscopic magnetic moments are frozen in a non-randomized assembly so that a macroscopic magnetization remains without an external magnetic field. Thermally, the direction of the magnetization can only be reversed by a pathway over the top of the energy barrier.³¹ In this respect, the anisotropy barrier represents an activation energy for the magnetization reversal. Below some temperature, the relaxation is slow enough to be probed by experimental techniques with regard to the specific time scales of the techniques.

2.2 Recent highlights past Mn₁₂1212OAc

Since the discovery of the fascinating SMM behavior of Mn₁₂1212OAc, a lot of synthetic efforts have been devoted to the preparation of new molecules with an increased anisotropy barrier and fascinating new structural motives have been reported. Besides the serendipitous approaches,³⁷ the majority of work is based on synthetic approaches to increase the anisotropy barrier by increasing the total spin ground state S_t while providing some source of magnetic anisotropy.^{29,34,35,38–40} Here, only some very selective examples can be presented.

2.2.1 Mn₁₂12OR . The acetate ligands in Mn₁₂1212OAc (Fig. 1a and b) can be substituted by other carboxylates and other ligands, allowing a manipulation of the electronic and magnetic properties of Mn₁₂12 and its interaction with the environment.⁴¹ While all derivatives of Mn₁₂12OR seem to have the S_t = 10 spin ground state,³¹ the anisotropy barrier varies. For example, Mn₁₂12OCOCH₂2Br has an anisotropy barrier U^eff = 80.4 K.⁴² There have been careful crystallographic, spectroscopic, and magnetic studies on several Mn₁₂12OR derivates and solvates, which identify disorder in the organic groups and/or solvent molecules of crystallization that introduces a rhombic component in the magnetic anisotropy.^43–46 This opens a non-thermal relaxation pathway and a decrease of the anisotropy barrier (see Section 2.5). Another kind of chemical manipulation of Mn₁₂1212OAc is its successive reduction. While the reduced species still show SMM behavior, the anisotropy barrier decreases with reduction, which has been attributed to the exchange of anisotropic Mn^III ions by isotropic Mn^II ions.⁴¹

2.2.2 Mn₄4 . A second large class of SMMs with interesting properties are the [Mn^III₃Mn^IV(μ₃-O)₃(μ-X)]⁶⁺, Mn₄4, cubane complexes (Fig. 1c).^27,47 This Mn₄4 family exhibits a S_t = 9/2 ground state. The symmetry of these cubane complexes is C_3v. By an electrochemical synthetic procedure, a cubane Mn₄4 complex of reduced symmetry (C_S) could be prepared.⁴⁸ Interestingly, this complex exhibits a faster magnetization relaxation in comparison to its C_3v analogs despite having a higher D_St value. This has been ascribed to the greater rhombicity E/D, which leads to the conclusion that for the improvement of SMMs, ‘it is important to not just increase S and/or D, but also keep E as small as possible to minimize the quantum tunneling of the magnetization rates through the barrier’.⁴⁸

2.2.3 Mn₈₄84 . Oxidation of Mn₁₂1212OAc with [MnO₄]⁻ under selected conditions results in a complex referred to as a Mn₈₄84 torus (Fig. 1d), which must be regarded as the largest SMM yet reported.⁴⁹ This large molecule has a diameter of ∼4.2 nm, a height of ∼1.2 nm and an inner free space with a diameter of ∼1.9 nm. All Mn ions seem to be in the +III oxidation state and the ground state has been evaluated to be S_t = 6.

2.2.4 Mn₁₉19 and Mn₁₈18Dy. Another record has been obtained with the complex Mn₁₉19 (Fig. 1e), which comprises 12 Mn^III and 7 Mn^II ions.⁵⁰ All 19 Mn ions couple ferromagnetically to the record S_t = 83/2 spin ground state. Despite this large spin, Mn₁₉19 does not exhibit SMM behavior, which has been ascribed to a very small positive D.⁵¹Mn₁₉19 can be considered as two Mn₉9 subunits bridged by an additional Mn^II ion. This supramolecular assembly allowed the targeted replacement of the central Mn^II by a Dy^III ion in order to introduce magnetic anisotropy.^52,53 Indeed, this Mn₁₈18Dy complex exhibits SMM behavior.

2.2.5 Mn₆6 . A real improvement of the anisotropy barrier has been achieved in a family of complexes abbreviated Mn₆6 (Fig. 1f). These complexes are built by reacting manganese(II) acetate under basic conditions with differently substituted salicylaldoxime ligands.^54–59 One derivative of these Mn₆6 complexes exhibits the record anisotropy barrier U^eff = 86.4 K and a blocking temperature of ∼4.5 K, ‘finally breaking the long-standing record held by the Mn₁₂12 family of molecules’.⁵⁶

2.3 High spin ground states

The height of the anisotropy barrier U clearly defines two necessary requirements to be considered for the development of new SMMs: a high spin ground state S_t combined with a strong magnetic anisotropy D_St of the easy-axis type. Unfortunately, an important result from the study of exchange interactions between paramagnetic metal ions transmitted through bridging ligands (superexchange) is that the predominant coupling is of antiferromagnetic nature. This observation is well understood on the basis of several levels of theory and is mainly attributed to the overlap of magnetic orbitals (orbitals containing an unpaired electron) (1st Goodenough–Kanamori rule)^21–23 and the onset of chemical bonding, i.e. the pairing of electrons in the resulting bonding molecular orbitals.¹

Thus, the need for high spin ground states S_t to rationally develop new SMMs requires synthetic strategies to building blocks, which either enforce ferromagnetic interactions and/or predictable antiferromagnetic couplings resulting in ferrimagnetic arrangements of the spins. This objective was already formulated by the late Olivier Kahn: ‘The normal trend for the molecular state is the pairing of electrons […] with a cancellation of the electron spins. The design of a molecule-based magnet requires that this trend be successfully opposed’.⁶⁰

In order to establish synthetic recipes for parallel spin alignments we are exploring three different strategies: (1) the double exchange mechanism^61–63 in face-sharing octahedra,^64–67 (2) the use of orthogonal magnetic orbitals (2nd Goodenough–Kanamori rule),^{21–23,68,69} and (3) the spin-polarization mechanism^70–74 in m-phenylene-bridged complexes, which is the strategy employed in this project. We have recently summarized the principle aspects and the application of the spin-polarization mechanism⁷⁵ so that only the main concept of this simple, heuristic phenomenon will be recapitulated here.

It is well established in organic chemistry^76,77 that the m-phenylene linkage of organic radicals and carbenes leads to ferromagnetic interactions, while in the corresponding o- and p-phenylene linkages the interaction is antiferromagnetic (Scheme 1, left). Application of many-electron MO theory provides an alternation of the sign of the spin-density at the atoms in the bridging unit.⁷⁸ This is illustrated in Scheme 1, right and provides the opportunity to develop high spin organic radicals and carbenes on the back of an envelope as the nature of the interaction – ferromagnetic or antiferromagnetic – only depends on the number of atoms between the paramagnetic centers.⁷⁹

Scheme 1

This concept has been applied to transition metal complexes by using various types of bridging ligands based on heteroaromatic systems,^80–83trithiocyanuric acid,⁸⁴resorcinol,^85,86 and di- and trioxamato benzene systems.^87–90 One trinuclear complex using 1,3,5-trihydroxybenzene (phloroglucinol) as a bridging ligand was reported which exhibits ferromagnetic interactions between three (Tp*)Mo^VOCl fragments.⁹¹ Our approach was to use phloroglucinol to establish ferromagnetic interactions between paramagnetic 3d ions, as their local spin can be up to S_i = 5/2, which is difficult to achieve with 4d or 5d metal ions due to their intrinsic preference for low-spin electronic configurations. However, we realized by painful failures in a whole series of synthetic approaches that the preparation of trinuclear complexes of 3d metal ions bridged by the parent phloroglucinol is hindered due to too low stabilities. To overcome this problem we have attached pendant arms with additional coordinating groups in the 2,4,6-positions of phloroglucinol, thereby enhancing the stability by the chelate effect. In this respect, the use of the tris-imine ligand H₃L (Scheme 2a) allowed the preparation of the trinuclear complexes [L(Cu^II(bpy))₃](BF₄)₃ and [L(Cu^II(sal))₃] (Hsal = salicylaldehyde), which exhibit ferromagnetic couplings with J = +1.96 cm⁻¹ and J = +3.31 cm⁻¹, respectively (all J values are given according to the HDvV-Hamiltonian in the form H = −2 JS₁S₂).⁹² Thus, the phloroglucinol bridging unit propagates ferromagnetic couplings in trinuclear Cu^II complexes, while the magnitude of the coupling is relatively small.

Scheme 2

2.4 Magnetic anisotropy

The main challenge in the preparation of SMMs with increased anisotropy barriers is the realization of both a high spin ground state S_t and a sizable magnetic anisotropy D_St in one molecule. The magnetic anisotropy of the ground state (D_St) of polynuclear transition metal complexes has its main contribution usually from the projection of the single-site anisotropies (D_i) onto the spin ground state S_t. Dipolar and anisotropic interactions usually yield only minor contributions.^93–95 Thus, the local magnetic moments should possess some source of anisotropy. The magnetic moment arising from a pure spin angular momentum is not coupled to the molecular framework and exhibits no magnetic anisotropy. The magnetic anisotropy results from a certain amount of orbital angular momentum in the magnetic moment. Transition metal ions with a formal T ground state possess an in-state first-order orbital angular momentum,⁹⁶ so that the application of the pure spin-Hamiltonian is not indicated. However, this first-order orbital angular momentum gives rise to very strong magnetic anisotropies. Transition metal ions with formal A, B, or E ground states do not possess a first-order orbital angular momentum but some orbital angular momentum may arise from the mixing of the excited states into the ground state by second-order spin–orbit coupling. This leads to the anisotropy of the spin ground state which is parameterized in the spin-Hamiltonian by the zero-field splitting D.⁹⁷

Spin–orbit coupling is a relativistic effect and scales with Z⁴. Thus, 4d and 5d metal ions exhibit stronger magnetic anisotropies than 3d metal ions. However, 4d and 5d metal ions are, besides some spectacular exceptions, in a low-spin configuration with small spin quantum numbers S_i. Lanthanide and actinide ions may also possess strong magnetic anisotropies. There is an increasing number of SMMs containing lanthanide ions^98–102 and there are even mononuclear complexes of therbium, which exhibit a slow relaxation of the magnetization as SMMs.^103–105 The drawback of the use of lanthanide ions is that they exhibit only weak exchange couplings due to the buried nature of their magnetic f orbitals and thus their low covalencies.

In summary, the main problem in a rational design of SMMs is the lack of metal ions, which combine strong magnetic anisotropies with high local spin states and strong exchange couplings. In this respect, the use of 3d metal ions is not a natural choice but a compromise between high local spin states combined with reasonably strong exchange couplings, while the magnetic anisotropies are usually small.

As magnetic anisotropy is a complicated property, the perturbational treatment in ligand-field theory is educational and valuable for the synthetic coordination chemist to obtain some recipes for introducing magnetic anisotropy. The origin of the magnetic anisotropy of Mn^III ions, which is the main source of anisotropy in Mn₁₂1212OAc, should illustrate how the careful choice of the ligand environment may provide access to appreciable magnetic anisotropy even for 3d ions. Mn^III is a d⁴ ion and the free ion has a ⁵D ground state. This state is split in an octahedral ligand field (O_h) into a ⁵E_2g ground state and a ⁵T_2g excited state (Scheme 2b). The ⁵E_2g ground state in pure O_h symmetry is magnetically completely isotropic. The well-known magnetic anisotropy of Mn^III ions can be explained by ligand-field theory through the incorporation of two perturbations.^106–108 The ⁵E_2g ground state in O_h symmetry is Jahn–Teller active and Mn^III complexes usually exhibit a tetragonal elongation, which results in a symmetry reduction to D_4h. This leads to a ⁵B_1g ground state (Scheme 2b), which is still magnetically completely isotropic. Spin–orbit coupling mixes the excited ⁵E_2g and ⁵B_2g states into the ground state, which results in a splitting of the ⁵B_1g ground state. This splitting is phenomenologically described by the zero-field splitting (Scheme 2b). Second-order perturbation theory provides that this splitting is proportional to the splitting Δ of the ⁵T_2g state induced only by the symmetry reduction from O_h to D_4h.^107,109 Thus, the stronger the tetragonal symmetry reduction, the stronger the splitting of the ⁵B_1g state and the zero-field splitting. Therefore, the use of a ligand, which introduces a strong tetragonal component into the ligand field, should maximize the magnetic anisotropy.

Besides the careful consideration of the local magnetic anisotropies, there are also some symmetry constraints for the relative orientation of the metal ions. Since zero-field splittings are tensor quantities, the projection of the single-site zero-field splittings onto the spin ground state may vanish as the metal ion arrangement approaches a cubic symmetry.⁹³

2.5 Quantum tunnelling and its consequences

The fascinating properties and the still ongoing interest in the study of Mn₁₂1212OAc are not only due to the slow relaxation of the magnetization, but also to the presence of quantum effects.^110–113 While the height of the anisotropy barrier U is related to the thermal pathway for spin reversal, there is also a non-thermal pathway for spin reversal through the anisotropy barrier by a quantum mechanical tunnelling of the magnetization (Fig. 1d). This tunnelling mechanism is directly related to the rhombic component (Ĥ = E(Ŝ_x² − Ŝ_y²))³⁰ of the magnetic anisotropy which vanishes for complexes with at least a threefold axis (see Sections 2.2.1 and 2.2.2). This provides another prerequisite to improve the properties of SMMs by the minimization of the quantum mechanical magnetization tunneling, which provides an alternative pathway for spin-reversal and thus the loss of information.

2.6 Combination into a hybrid ligand

In summary, a rational design of a SMM requires not only a high spin ground state combined with a significant magnetic anisotropy of the easy axis type, but should also imply considerations of the topology of the metal ion arrangement. The overall molecular symmetry should be at least trigonal to minimize the quantum tunneling but lower than cubic to avoid an isotropic system. Such a control is difficult to achieve with small flexible ligands of low directionality. The use of the concepts of supramolecular chemistry (i.e. association of molecular building blocks based on (i) preorganization and topological constraints to increase binding power and (ii) complementarity to determine molecular recognition)^114–116 should provide an ansatz for a rational design of SMMs. An advantage of this modular approach is that the molecular building blocks can be fine-tuned by steric and electronic controls while the driving forces to assemble the whole chemical entity are still present (see, e.g., the variation from Mn₁₉19 to Mn₁₈18Dy in Section 2.2.4). It is important to point out that rational design should not be misinterpreted such that structural parameters (bond distances, angles, torsion angles) or the extent of Jahn–Teller distortions can be exactly predetermined or changed into values, which would result in better magnetic properties.

In this respect, we have tried a ligand and complex design based on all these requirements for SMMs. We thought to combine the phloroglucinol bridging unit A with the coordination environment of a salen ligand B into the C₃ symmetric ligand triplesalen C (Scheme 2c). The design of the triplesalen ligand has been based on the following concepts: in order to ensure high spin ground states, we have chosen the phloroglucinol bridging unit A, which is able to transmit ferromagnetic interactions in trinuclear Cu^II complexes by the spin-polarization mechanism (see Section 2.3). We have chosen a salen-like coordination environment because the salen ligand B is known to establish pronounced magnetic anisotropies by its strong ligand field in the basal plane (see Section 2.4).^94,106,108 A well studied example is the Jacobsen catalyst [(salen′)Mn^IIICl] (H₂salen′ = (R,R)-N,N′-bis(3,5-di-tert-butylsalicylidene)-1,2-cyclohexanediamine) which is a Mn^III (S = 2) species with a zero-field splitting of D ≈ −2.5 cm⁻¹.^108,117,118 In this respect, it is interesting to note that already dimeric Mn^III salen complexes behave as SMMs.^119–121 Furthermore, the trigonal symmetry provided by the triplesalen ligand should result in highly axial anisotropies with small to zero rhombic components and thus reduced tunneling through the anisotropy barrier (see Section 2.5).

3. Ligand synthesis

Symmetrical salen ligands are very common and can easily be prepared by one pot condensation reactions of one diamine with two identical aldehyde or ketone derivatives. However, the targeted triplesalen ligand C contains three unsymmetrically substituted ethylene diamine units making the synthesis not trivial. The controlled synthesis of unsymmetrical salen ligands (not a mixture of symmetrical and unsymmetrical compounds) containing two different aldehyde or ketone derivatives must involve in a first step the isolation of a mono-condensated ethylene diamine, a so-called salen half-unit.^122–126 This intermediate would provide the opportunity for the synthesis of the desired unsymmetrical salen ligand by the reaction of the remaining amine with the other aldehyde or ketone derivative. However, a salen half-unit is not always accessible¹²³ and mainly requires a differentiation of the reactivity of the two amine functions.¹²⁷ Another important aspect to consider is that an aldimine is usually easy to prepare but not very stable. On the other hand, the preparation of a ketimine requires harsher conditions but it exhibits a higher stability.¹²⁸ Therefore, in a stepwise procedure, the generation of the more stable ketimine half-unit in the first step and the subsequent reaction with an aldehyde is a promising sequence.

Two reaction routes are in principle feasible for the preparation of the targeted triplesalen ligand C (Scheme 3). Route A requires the synthesis of a ketimine salen half-unit E in the first step which reacts in the second step with the trisaldehyde derivative of phloroglucinol D. Route B requires the synthesis of a triplesalen ketimine half-unit G which reacts in the second step with a salicylaldehyde derivative F.

Scheme 3

Thus, the key step in the synthesis of a triplesalen ligand C is the preparation of a half-unit, either E or G. Several methods for the preparation and isolation of derivatives of the parent salen half-unit E are described in the literature.^{124,125,127,129,130} We applied several of these methods for the synthesis of a triplesalen ligand and obtained various new compounds.¹³¹ The successful synthesis of a triplesalen ligand is based on an observation of Elias and coworkers.¹²⁷ They reported that the sterically more crowded amine function of diamine I (Scheme 4) does not react with ketones to form ketimines, but only with aldehydes to form aldimines. On the other hand, the less crowded amine function does react with aldehydes as well as with ketones to form imines. Thus, the reaction of the diamine I with the triketone H affords chemoselectively the triplesalen ketimine half-unit J. In the second step, this triple ketimine J reacts with a simple salicylaldehyde to yield the desired triplesalen (Scheme 4).¹³² This stepwise protocol allows the use of variously substituted salicylaldehydes in the second step and the ligands H₆talen, H₆talen^t-Bu₂, and H₆talen^NO₂ have been reported.¹³³ Besides these triplesalen ligands, a chiral version using the chiral diaminetrans-1,2-cyclohexanediamine,^134,135 a triplesalophen ligand,¹³⁶ and a triplesalacen ligand have been realized.¹³⁷

Scheme 4

4. Properties of trinuclear triplesalen complexes

The trinucleating tris(tetradentate) triplesalen ligands H₆talen^X₂ are capable to coordinate three transition metal ions. In a series of trinuclear nickel triplesalen complexes we have shown that variation of the terminal substituents in the triplesalen ligands provides a control of the electronic communication between the metal–salen subunits.¹³³ The corresponding trinuclear copper triplesalen complexes all exhibit ferromagnetic interactions with S_t = 3/2 spin ground states.^138,139EPR spectra display a ten line hyperfine splitting pattern due to the coupling of the total electron spin with three Cu nuclear spins.¹³⁸ DFT calculations demonstrate that the spin-density on adjacent carbon atoms of the central benzene ring alters in the quartet ground state in accordance with the spin-polarization mechanism.^138,139 The V^IV ions in the trinuclear vanadyl complex [(talen^t-Bu₂)(V^IV=O)₃] also reveal weak but ferromagnetic interactions.¹⁴⁰

A common feature of the complexes with the tert-butyl derivative (talen^t-Bu₂)⁶⁻ is a severe ligand folding leading to an overall bowl-shaped structure. Interestingly, there is a driving force for two of these bowl-shaped trinuclear complexes to dimerize to disk-shaped hexanuclear assemblies. The interior of this dimer can be filled with non-covalently bound solvent molecules as observed in the complex [(talen^t-Bu₂)Cu₃] (Fig. 3a–c).¹³⁹ The interior can also be filled with covalently bound molecules which bridge the metal ions of the individual trinuclear triplesalen complexes as in [{(talen^t-Bu₂)Mn₃(MeOH)}₂(μ₂-OAc)₃]³⁺ (Fig. 3d). In this complex, two trinuclear Mn^III triplesalen complexes are bridged by three acetates resulting in an overall hexanuclear Mn^III₆ complex.¹⁴¹ The driving force for dimerization seems to be so strong that entities are stabilized inside, which are not commonly detected as free species. The Fe^III ions in the trinuclear Fe^III triplesalen complex [(talen^t-Bu₂){Fe^III(MeOH)(H₂O)}₃]³⁺ are hexa-coordinate with one methanol molecule and one water molecule in the apical positions. The methanol molecules are placed inside the bowl (Fig. 3e). Two [(talen^t-Bu₂){Fe^III(MeOH)(H₂O)}₃]³⁺ units dimerize and encapsulate the uncommon [Cl⋯H⋯Cl]⁻ species by interaction of the chloride ions with the coordinated methanol molecules (Fig. 3e).¹⁴² Another example is the stabilization of an unprecedented [V₃O₉]³⁻ unit between two [(talen^t-Bu₂){Mn(MeOH)}₃]³⁺ building blocks (Fig. 3f).¹⁴³

Fig. 3 Molecular structures of (a), (b) and (c) [(talen^t-Bu₂)Cu₃],¹³⁹ (d) [{(talen^t-Bu₂)Mn₃(MeOH)}₂(μ₂-OAc)₃]³⁺,¹⁴¹ (e) [{(talen^t-Bu₂){Fe^III(MeOH)(H₂O)}₃}₂(ClHCl)]³⁺,¹⁴² (f) [{(talen^t-Bu₂){Mn(MeOH)}₃}₂(V₃O₉)]³⁺.¹⁴³

5. Heptanuclear complexes [Mn^IIIIII₆6M]³⁺3+

5.1 Synthesis and molecular structures

We have been inspired by the well-established chemistry of combining salen complexes with hexacyanometallates as bridging units, which results either in polynuclear complexes or in extended structures of 1D chains, 2D sheets, and 3D networks with interesting magnetic properties.^{17,29,38,39,144–148} However, despite the success of the combination of metal salen units with hexacyanometallates and the highly predictable exchange coupling through a CN⁻ bridge,^17,19,147 the nuclearity and dimensionality of these complexes are difficult to control.

In this respect, we thought that the ligand folding in our trinuclear building blocks [(talen^t-Bu₂){M^t(solv)_n}₃]^m+ preorganizes the three M^t ions for coordination of three facial nitrogen atoms of a hexacyanometallate [M^t(CN)₆]ⁿ⁻. Thus, a hexacyanometallate should bridge two trinuclear triplesalen building blocks in a hexa-connecting fashion (Fig. 4). We anticipated that the heptanuclear complexes [Mn^IIIIII₆6M^IIIIII]³⁺3+ should fulfill all the requirements for SMMs, namely: (i) the triplesalen bridge favors a parallel spin alignment of the three Mn^III ions of a molecular [(talen^t-Bu₂)Mn^III₃]³⁺ building block, (ii) irrespective of the nature of the Mn^III–N≡C–M pathways (ferromagnetic or antiferromagnetic) a high spin ground state of the heptanuclear complex would occur as an efficient ferrimagnetic scheme arises from antiferromagnetic interactions, (iii) the [(salen)Mn^III]⁺ units provide a pronounced single-site magnetic anisotropy, (iv) the C₃ symmetry precludes that the single-site D_is compensate completely by projecting onto S_t, and (v) the molecular C₃ axis enforces E_St = 0 thus minimizing the disturbing tunneling probability.

Fig. 4 Building block approach for the construction of the heptanuclear complexes [M^ccc₆6M^ttt]³⁺3+ (M^t: terminal metal ion of the triplesalen building block; M^c: central metal ion of the hexacyanometallate). The symmetry of the trinuclear triplesalen building blocks is imposed on the molecular structure of the supramolecular assembly.

Our first reaction was that of [(talen^t-Bu₂){Mn^III(solv)_n}₃]³⁺ with [Fe(CN)₆]³⁻. This was inspired by the work of Long et al., who demonstrated that already a trinuclear complex comprised of two Mn^III salen complexes bridged by a central [Fe^III(CN)₆]³⁻ acts as a SMM due to the ferromagnetic S_t = 9/2 spin ground state, the local magnetic anisotropy of the Mn^III salen units, and the linear topology.¹⁴⁹ Miyasaka and Clérac et al. used these trinuclear building blocks to form 1D chains, which exhibit single-chain magnetic (SCM) behavior.¹⁵⁰ Indeed, we obtained the heptanuclear complex [{(talen^t-Bu₂)Mn^III₃}₂{Fe^III(CN)₆}]³⁺, [Mn^IIIIII₆6Fe^IIIIII]³⁺3+, isolated as its [Fe(CN)₆]³⁻ salt.¹⁵¹

The molecular structure of [Mn^IIIIII₆6Fe^IIIIII]³⁺3+ is illustrated in Fig. 5. Two trinuclear Mn^III triplesalen units are bridged by a hexacyanoferrate. The approximate point group of this trication is S₆. Although this was our first (synthesized and completely characterized in 2003) heptanuclear complex [M^ttt₆6M^ccc]ⁿ⁺nn+, it was published only in 2009,¹⁵¹ as the magnetic properties (vide infra) could only be understood and properly analyzed in a fruitful collaboration with Jürgen Schnack at Bielefeld University.

Fig. 5 Molecular structure of [Mn^IIIIII₆6Fe^IIIIII]³⁺3+ in various accentuations.¹⁵¹

In analogy to the synthesis of [Mn^IIIIII₆6Fe^IIIIII]³⁺3+, we reacted [(talen^t-Bu₂){Mn^III(solv)_n}₃]³⁺ with [Cr(CN)₆]³⁻ and isolated the heptanuclear complex [{(talen^t-Bu₂)Mn^III₃}₂{Cr^III(CN)₆}]³⁺, [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+, as its (BPh₄)⁻ salt.¹⁵² In order to simplify the spin coupling scheme and reduce the number of parameters to simulate the magnetic properties, we synthesized the analogous heptanuclear complex [Mn^IIIIII₆6Co^IIIIII]³⁺3+ including a diamagnetic Co^III l.s. ion.¹⁵³ The molecular structures of the heptanuclear complexes [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ and [Mn^IIIIII₆6Co^IIIIII]³⁺3+ are closely related to that of [Mn^IIIIII₆6Fe^IIIIII]³⁺3+.

5.2 Magnetic properties of [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+

The magnetic properties of [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ were the first we analyzed in detail and are therefore discussed here in the beginning. The temperature-dependence of the effective magnetic moment, μ_eff, of [Mn^IIIIII₆6Cr^IIIIII](BPh₄)₃ is typical for a ferrimagnetic coupling scheme with a minimum at 90 K (Fig. 6a) and a maximum of μ_eff = 17.75 μ_B at 5 K. This ferrimagnetic behavior is in accordance with an antiparallel orientation of the central Cr^III spin (S_i = 3/2) with the terminal Mn^III spins (S_i = 2) resulting in a S_t = 21/2 ground state. The variable-temperature and variable-field (VTVH) magnetization measurements with a saturation value at 7 T of 18.4 μ_B in combination with the nesting behavior of the isofield lines (Fig. 6b) demonstrate that [Mn^IIIIII₆6Cr^IIIIII](BPh₄)₃ possesses an anisotropic high spin ground state.¹⁵²

Fig. 6 (a) Temperature-dependence of μ_eff at 0.05 T and (b) VTVH at 1, 4, and 7 T for [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+.¹⁵² The solid line corresponds to a simulation based on parameters provided in the text.

In order to get an estimate of the exchange coupling constants, the temperature-dependence of μ_eff was simulated with a HDvV spin-Hamiltonian by full matrix-diagonalization. The topology of [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ requires a coupling scheme with two different coupling constants: J_Mn–Cr describes the interaction between the central Cr^III (S₇) with each Mn^III (S₁ to S₆) and J_Mn–Mn describes the interaction between two Mn^III belonging to the same trinuclear triplesalen subunit. This results in the Hamiltonian specified in eqn (1).

H_HDvV = −2J_Mn–Cr(S₁S₇ + S₂S₇ + S₃S₇ + S₄S₇ + S₅S₇ + S₆S₇) − 2J_Mn–Mn(S₁S₂ + S₂S₃ + S₃S₁ + S₄S₅ + S₅S₆ + S₆S₄) (1)

Only the data above 50 K have been used because we were not able at that time to include zero-field splitting, which has a pronounced influence at lower temperatures. Our best simulation using J_Mn–Cr = −5.0 cm⁻¹, J_Mn–Mn = −1.03 cm⁻¹, and g = 1.98 is shown as a solid line in Fig. 6a. This results in a S_t = 21/2 ground state separated by 2.64 cm⁻¹ from four degenerate S_t = 19 spin states. It is interesting to note that the more rigorous methodology described below for [Mn^IIIIII₆6Fe^IIIIII]³⁺3+ and [Mn^IIIIII₆6Co^IIIIII]³⁺3+ reproduces these coupling constants quite well.¹⁵⁴

Altogether, [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ fulfills all requirements for a SMM. It has a high spin ground state of S_t = 21/2 and the VTVH data indicate relatively strong magnetic anisotropy. Additionally, the molecular symmetry of [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ is approximately C₃. Indeed, ac susceptibility data exhibit a frequency-dependent out-of-phase signal, which is a typical signature for slow relaxation of the magnetization in accordance with [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ being a SMM. Finally, a field-dependent magnetization study on a single-crystal of [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ exhibits hysteresis. Thus, [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ is a SMM and the anisotropy barrier U^eff was determined from the ac measurements to be 25.4 K.¹⁵²

The reaction of [Cr(CN)₆]³⁻ with [(salen)Mn(OH₂)]⁺ results in the formation of a closely related heptanuclear complex [{(salen)Mn^III}₆{Cr(CN)₆}]³⁺ which exhibits also a high spin ferrimagnetic ground state of S_t = 21/2 due to antiferromagnetic interactions.¹⁵⁵ Interestingly, while [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ is a SMM, [{(salen)Mn^III}₆{Cr(CN)₆}]³⁺ is not a SMM.¹⁵⁶ This difference can be related to the overall symmetry of the metal ion arrangements in these two complexes. While the six Mn^III ions in [{(salen)Mn^III}₆{Cr(CN)₆}]³⁺ are surrounding the central Cr^III ion almost octahedrally (Fig. 7a, Mn–Mn distances 7.4 and 7.7 Å), the triplesalen causes a trigonal elongation (Fig. 7b, Mn–Mn distances 6.8 and 8.3 Å). Thus, the local anisotropy tensors in [{(salen)Mn^III}₆{Cr(CN)₆}]³⁺ cancel each other upon projection onto the spin ground state while the trigonal elongation in [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ prevents this cancellation. Additionally, the longer Mn–N^N≡C bond distances of 2.32 Å in [{(salen)Mn^III}₆{Cr(CN)₆}]³⁺ in comparison to 2.18 Å in [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ should result in weaker exchange couplings and thus in a less well separated spin ground state.

Fig. 7 Comparison of the central Mn₆Cr unit in the molecular structures of (a) [{(salen)Mn^III}₆{Cr(CN)₆}]^3+ 148 and (b) [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+.¹⁵²

5.3 Magnetic properties of [Mn^IIIIII₆6Co^IIIIII]³⁺3+

The analysis of the magnetic properties of [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ provided antiferromagnetic exchange couplings (J_Mn–Mn = −1.03 cm⁻¹) between the Mn^III ions of a trinuclear triplesalen building block. As this result was unexpected, a multitude of simulations using a ferromagnetic exchange coupling were performed but these did not reproduce the temperature-dependence of μ_eff. These antiferromagnetic interactions are in contradiction to the expected spin-polarization mechanism through the phloroglucinol backbone and to the experimentally observed ferromagnetic couplings in the trinuclear Cu^II and V^IV complexes (see Section 4). In order to simplify the analysis of the magnetic data and to reduce the exchange pathways, we have synthesized the heptanuclear complex [Mn^IIIIII₆6Co^IIIIII]³⁺3+ with a central diamagnetic Co^III low-spin ion. In collaboration with Jürgen Schnack, we have performed a full-matrix diagonalization of the appropriate spin-Hamiltonian including isotropic HDvV exchange, zero-field splitting, and Zeeman interaction.¹⁵³ A frequently used simplification in such spin-Hamiltonians is a collinearity of the local D-tensors, which is usually not justified. We have incorporated the zero-field splitting for the Mn^III ions including the relative orientations of the individual D-tensors by the angle ϑ of the Jahn–Teller axis with the molecular C₃ axis. The continuous decrease of μ_eff with decreasing temperature (Fig. 8a) indicates dominant antiferromagnetic interactions and the strong nesting behavior of the VTVH magnetization data (Fig. 8b) indicates a strong magnetic anisotropy. Surprisingly, a satisfactory reproduction of the magnetic data required the incorporation not only of an exchange interaction between the Mn^III ions belonging to one triplesalen subunit (J_Mn–Mn) but also of an exchange coupling between Mn^III ions belonging to different triplesalen subunits (J_Mn–Mn′). A satisfactory reproduction of the experimental data has been obtained for the parameter set J_Mn–Mn = −(0.50 ± 0.04) cm⁻¹, J_Mn–Mn′ = +(0.05 ± 0.02) cm⁻¹, and D = −(2.5 ± 0.5) cm⁻¹.¹⁵³

Fig. 8 (a) Temperature-dependence of μ_eff at 0.1 T and (b) VTVH at 1, 4, and 7 T for [Mn^IIIIII₆6Co^IIIIII]³⁺3+.¹⁵³ The solid lines correspond to simulations based on parameters provided in the text.

This detailed analysis manifests that the exchange coupling through the phloroglucinol bridging unit is antiferromagnetic in nature for Mn^III ions despite the ferromagnetic couplings observed in trinuclear Cu^II complexes^92,138,139 and a V^IV=O complex.¹⁴⁰ A crucial parameter for an efficient spin-polarization mechanism through the bridging benzene unit was found to be the amount of spin-density in the p_z^π orbitals of the phenolic oxygen atoms.⁷⁵ This spin-density depends on the metal ion, the remaining coordination sites, and on the ligand folding at the central metal–phenolate bond. Additionally, the trinuclear Mn^III triplesalen building blocks have some degree of freedom to orient the three Mn^III ions for optimal bonding to the facially arranged cyanide nitrogen atoms, which results in different orientations of the magnetic d orbitals relative to the phenolate p orbitals. Our studies on the trinuclear triplesalen complexes indicate that variations in these orientations can have a strong impact on the two different mechanisms, spin-polarization and spin-delocalization,⁷⁵ and thus on the overall exchange interaction of the three Mn^III ions through the phloroglucinol unit.

Additionally, a detailed analysis of the J_Mn–Mn coupling of the three available heptanuclear complexes [Mn^IIIIII₆6M^IIIIII]³⁺3+ (M=Cr, Fe, Co) indicates that the exchange interaction between the Mn^III ions belonging to the same triplesalen subunit involves not only an exchange pathway through the central phloroglucinol unit but also an exchange pathway through the central metal ion.¹⁵³

5.4 Magnetic properties of [Mn^IIIIII₆6Fe^IIIIII]³⁺3+

The value of μ_eff of [Mn^IIIIII₆6Fe^IIIIII]³⁺3+ decreases monotonically with decreasing temperature (Fig. 9a) indicating dominant antiferromagnetic interactions between the metal ions.¹⁵¹ However, antiferromagnetic interactions between the central Fe^III l.s. ion and the Mn^III ions should result in an increase of μ_eff at lower temperatures due to a ferrimagnetic coupling scheme (see Section 5.2 for [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+). Therefore, the continuous decrease of μ_eff with decreasing temperature was already an indication that the contribution from magnetic anisotropy had a stronger impact on the overall magnetic properties than the exchange interactions. The magnetic data have been analyzed in detail with the methodology described for [Mn^IIIIII₆6Co^IIIIII]³⁺3+. We have been aware that a perfect reproduction of the experimental data with one unique set of parameters is beyond the employed spin-Hamiltonian as other effects like non-negligible orbital effects on the exchange coupling in low-spin Fe^III, the occurrence of intermolecular couplings, and the lower molecular symmetry in the solid state have not been considered. However, a reasonable range of parameters that reproduce both the temperature-dependent magnetization at 1 T and the VTVH magnetization data is given by: J_Mn–Mn = −(0.85 ± 0.15) cm⁻¹, J_Fe–Mn = +(0.70 ± 0.30) cm⁻¹, and D_Mn = −(3.0 ± 0.7) cm⁻¹. The simulation of the 1 T data in Fig. 9b was much more difficult than that of the 4 T and 7 T data. This indicates the presence of intermolecular dipolar interactions between the large magnetic moments of [Mn^IIIIII₆6Fe^IIIIII]³⁺3+. The higher fields of 4 T and 7 T are able to break down these dipolar interactions more efficiently than the 1 T field. This is an important observation as stray fields from neighboring molecules can have the same effect as a rhombic term in the anisotropy with regard to the probability of the tunnelling through the anisotropy barrier. In this respect, even a pure C₃ symmetric complex will always be influenced by its environment in the solid state, even at the large distances found in these heptanuclear complexes.

Fig. 9 (a) Temperature-dependence of μ_eff at 1 T and (b) VTVH at 1, 4, and 7 T for [Mn^IIIIII₆6Fe^IIIIII]³⁺3+.¹⁵¹ The solid lines correspond to simulations based on parameters provided in the text.

ac susceptibility data exhibit no out-of-phase signals above 1.9 K, demonstrating that [Mn^IIIIII₆6Fe^IIIIII]³⁺3+ is not a SMM. It is interesting to compare the magnetic data of [Mn^IIIIII₆6Fe^IIIIII]³⁺3+ to those of [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ in order to obtain insight into why [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ is a SMM and [Mn^IIIIII₆6Fe^IIIIII]³⁺3+ is not a SMM. The coupling of the Mn^III ions with the central Cr^III ion in [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ was found to be J_Cr–Mn = −5.0 cm⁻¹. This results in the stabilization of a high-spin ground state of S_t = 21/2. On the other hand, the small coupling J_Fe–Mn = +0.70 cm⁻¹ in [Mn^IIIIII₆6Fe^IIIIII]³⁺3+ results in a strong mixing of M_S wave functions of various spin states, so that no high spin ground state is stabilized. Thus, the reason for [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ being a SMM and [Mn^IIIIII₆6Fe^IIIIII]³⁺3+ not being a SMM is the large J_Cr–Mn coupling compared to the small J_Fe–Mn coupling.

6. The tetranuclear complex [Mn^IIIIII₃3Cr^IIIIII]³⁺3+ as a half-unit: insight into the driving force for dimerization

In order to obtain more insight into the abstract driving force for dimerization of two trinuclear tripelsalen units, we synthesized as a half-unit of [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ the tetranuclear complex [{(talen^t-Bu₂)Mn^III₃}{(Me₃tacn)Cr(CN)₃}]³⁺, [Mn^IIIIII₃3Cr^IIIIII]³⁺3+ (Fig. 10), by reaction of the trinuclear Mn^III triplesalen complex [(talen^t-Bu₂){Mn^III(solv)_n}₃]³⁺ with [(Me₃tacn)Cr(CN)₃].¹⁵⁷ Several experimental observations indicate that [Mn^IIIIII₃3Cr^IIIIII]³⁺3+ has an overall lower stability than the heptanuclear [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+. Interestingly, this lower stability of [Mn^IIIIII₃3Cr^IIIIII]³⁺3+ is correlated with a significantly longer Mn–N^N≡C bond length of 2.29 Å and a reduced ligand folding at the central phenolate of 35.8° in [Mn^IIIIII₃3Cr^IIIIII]³⁺3+ in comparison to 2.18 Å and 46.7° in [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+, respectively.

Fig. 10 Molecular structure of [Mn^IIIIII₃3Cr^IIIIII]³⁺3+.¹⁵⁷

VTVH and μ_effvs. T magnetic data have been analyzed in detail by full-matrix diagonalization of the appropriate spin-Hamiltonian, consisting of isotropic exchange, zero-field splitting, and Zeeman interaction components. Satisfactory reproduction of the experimental data has been obtained for the parameters J_Mn–Cr = −(0.12 ± 0.04) cm⁻¹, J_Mn–Mn = −(0.70 ± 0.03) cm⁻¹, and D_Mn = −(3.0 ± 0.4) cm⁻¹. These generate a triply-degenerate pseudo S_t = 7/2 spin manifold, which cannot be appropriately described by a giant spin model and which exhibits a weak easy-axis magnetic anisotropy. This is corroborated by the onset of a frequency-dependent χ″ signal at low temperatures, demonstrating a slow relaxation of the magnetization indicative of [Mn^IIIIII₃3Cr^IIIIII]³⁺3+ being a SMM.

The higher driving force for the [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ formation is not only correlated with a shorter Mn–N^N≡C bond length but also with a stronger antiferromagnetic J_Mn–Cr exchange coupling of −5.0 cm⁻¹vs. −0.12 cm⁻¹ in [Mn^IIIIII₃3Cr^IIIIII]³⁺3+. A detailed analysis in conjunction with magnetic properties of complexes with a Mn^III–N≡C–Cr^III exchange pathway found in the literature and a close inspection of the molecular structures of the heptanuclear complexes [M^ttt₆6M^ccc]ⁿ⁺nn+ (see space-filling model of [Mn^IIIIII₆6Fe^IIIIII]³⁺3+ in Fig. 11) identifies some kind of van der Waals-type contacts between the two trinuclear triplesalen building blocks. In this respect, the absence of a second triplesalen subunit in [Mn^IIIIII₃3Cr^IIIIII]³⁺3+ may reduce the driving force for ligand folding. The stronger supramolecular attraction between the two [(talen^t-Bu₂)Mn^III₃]³⁺ subunits in [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ enforces a more substantial bending, which results in shorter Mn–N^N≡C bond lengths and therefore higher Mn–N^N≡C bond strengths. This leads to the observed high driving force for [Mn^IIIIII₆6M^IIIIII]³⁺3+ formation and thus to the strong J_Mn–Cr coupling, which is the origin of [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ being a good SMM.

Fig. 11 Molecular structure of [Mn^IIIIII₆6Fe^IIIIII]³⁺3+ in space-filling representation with the two trinuclear triplesalen building blocks colored individually to illustrate van der Waals interactions between the molecular building blocks.

7. Conclusions and outlook

Based on the extensive work on Mn₁₂1212OAc and other SMMs, we have formulated the requirements for the rational design of new families of SMMs. Besides a high-spin ground state S_t and a strong magnetic anisotropy of the easy-axis type, careful considerations of the overall symmetry of the complexes should be made. The symmetry should be at least C₃ to minimize rhombic components in the anisotropy and therefore the tunnelling probability through the anisotropy barrier, but lower than cubic to avoid a cancellation of the local anisotropies upon projection onto the spin ground state.

Our approach is based on concepts of supramolecular chemistry including topological constraints, complementarity, preorganization, and molecular recognition, where the prerequisites for SMMs are programmed into a directional polynucleating ligand of low flexibility. In this respect, we have designed the hybrid ligand triplesalen, which combines a phloroglucinol bridging unit to obtain ferromagnetic interactions by the spin-polarization mechanism with a salen-like coordination environment to introduce a strong tetragonal ligand-field component for magnetic anisotropy.

We have shown in a series of trinuclear triplesalen complexes^{132–134,138,139,158} that (i) the C₃ symmetry of the triplesalen ligand is imposed on the complex, (ii) phloroglucinol transmits weak but ferromagnetic interactions between Cu^II and V^IV, and (iii) a severe ligand folding occurs in [(talen^t-Bu₂)M₃], resulting in an overall bowl-shaped molecular structure.^133,139

We have taken advantage of the ligand folding in the triplesalen complexes by reacting two trinuclear Mn^III triplesalen complexes [(talen^t-Bu₂){Mn^III(solv)_n}₃]³⁺ as molecular building blocks with [M(CN)₆]³⁻ as a hexaconnector (Fig. 4) and obtained the isostructural series [Mn^IIIIII₆6Fe^IIIIII]³⁺3+, [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+, and [Mn^IIIIII₆6Co^IIIIII]³⁺3+ with [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ being a SMM.

The analysis of the magnetic properties provides an antiferromagnetic coupling between the Mn^III ions through the phloroglucinol ring, which is especially evident in [Mn^IIIIII₆6Co^IIIIII]³⁺3+ with a central diamagnetic Co^III l.s. ion. The strong antiferromagnetic interaction in [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ between the central Cr^III and the terminal Mn^III ions (J_Cr–Mn = −5.0 cm⁻¹) stabilizes an S_t = 21/2 spin ground state, while the coupling in [Mn^IIIIII₆6Fe^IIIIII]³⁺3+ (J_Fe–Mn = +0.7 cm⁻¹) is too weak to isolate a single spin ground state. Therefore, [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ is a SMM, while [Mn^IIIIII₆6Fe^IIIIII]³⁺3+ is not. Comparison of the properties of [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ and the tetranuclear [Mn^IIIIII₃3Cr^IIIIII]³⁺3+ half-unit established a shortening of the Mn–N^C≡N bond from 2.29 Å in [Mn^IIIIII₃3Cr^IIIIII]³⁺3+ to 2.18 Å in [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ by the attractive van der Waals interactions between the two triplesalen subunits. These attractive forces are thus responsible for the stronger coupling of −5.0 cm⁻¹ in [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ compared to −0.12 cm⁻¹ in [Mn^IIIIII₃3Cr^IIIIII]³⁺3+.

Although [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ is a rationally developed SMM, the question remains as to why the anisotropy barrier is not higher. Our current research identifies several crucial points, which must be improved in order to obtain a higher anisotropy barrier. In this respect, it must be regarded as the main advantage that the modular assembly of the heptanuclear complexes from three molecular building blocks allows the fine-tuning of the molecular and steric properties of each building block without losing the driving force for the formation of the heptanuclear complexes.

We have synthesized, structurally and magnetically characterized an isostructural series of [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ SMMs differing in the counterion and/or the solvent molecules of crystallization.¹⁵⁴ An important parameter, which has strong impact on the magnetic properties, turned out to be the ligand at the sixth coordination site of the Mn^III ions. Mn^III salen units are usually 5- or 6-coordinate with a very flat potential for the coordination of a solvent molecule at the sixth position. However, the presence or absence of a solvent molecule such as methanol or acetonitrile at this position influences the Mn–N^N≡C distance and therefore the coupling constant. We have obtained [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ complexes, where the sixth positions are all occupied by methanol molecules, which results in a good approximation of molecular C₃ symmetry, while others have a mixture of 5-coordinate and 6-coordinate Mn^III ions.

Another structural aspect is the orientation of the neighboring [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ molecules in the crystal structure. The detailed investigation of the magnetic properties indicates that there are intermolecular, dipolar interactions despite the large intermolecular distances. These dipolar fields of neighboring molecules act as stray fields and introduce some rhombic terms in the magnetic anisotropy. As stated already in Section 2.6, rational design does not mean that structural parameters can be varied to a preferred value. In this respect, the nature of the sixth coordination sites of the Mn^III ion and the packing of the molecules in the crystal are difficult to optimize.

Another handle to increase the anisotropy barrier in [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+ is a better stabilization of the spin ground state. An overlap of the spin multiplets leads to a mixing of M_S states belonging to different spin-multiplets. This must be regarded as a source for the effective barrier U^eff being usually smaller than the calculated anisotropy barrier U = D_St·S_t². Therefore, we are trying to optimize the triplesalen ligand backbone in order to increase the contributions of the spin-polarization mechanism over those of the spin-delocalization mechanism. In this respect, we are trying to change the central 1,3,5-trihydroxybenzene bridging unit to a 1,3,5-trimercaptobenzene bridging unit, as metal–sulfur bonds are more covalent leading to stronger spin densities in the sulfur p_z^π orbitals.¹⁵⁹

Another approach to improve the spin-polarization mechanism is based on the observation that the central 1,3,5-trihydroxybenzene unit in our ligands and our complexes has lost a large degree of their aromaticity and a resonance structure corresponding to a radialene-like resonance hybrid has strong contributions.¹⁶⁰ This provides us with a synthetic handle to increase the aromaticity in the central unit by replacing the imine units with amine units.

The projection of magnetic anisotropy tensors onto the spin ground state is maximal for a collinear arrangement of the anisotropy tensors. In this respect, we have synthesized the corresponding triplesalophene ligand, which has a completely sp²-hybridized ligand backbone,¹³⁶ which should enforce a planar trinuclear building block and therefore collinear Mn^III anisotropy tensors. Such planar molecular building blocks should enable the construction of triple-stranded nonanuclear complexes [M^ttt₃3M^ccc₃3M^ttt₃3]ⁿ⁺nn+ or triple-stranded 1D chains.

Besides changing the triplesalen ligand, the driving force for the formation of the heptanuclear assemblies also allows the variation of the terminal metal ions and of the central hexacyanometallate. In this respect, we have been able to synthesize the isostructural complexes [Mn^IIIIII₆6Mn^IIIIII]³⁺3+, [Fe^IIIIII₆6Cr^IIIIII]³⁺3+, [Fe^IIIIII₆6Mn^IIIIII]³⁺3+, [Fe^IIIIII₆6Fe^IIII]²⁺2+, [Mn^IIIIII₆6Fe^IIII]²⁺2+ as well as the 4d homologue [Mn^IIIIII₆6Mo^IIIIII]³⁺3+ and the 5d homologue [Mn^IIIIII₆6Os^IIIIII]³⁺3+. Additionally, we are changing the nature of the terminal donor atoms in triplesalen to stabilize also low-valent metal ions like Co^II or V^III, which might be interesting with respect to the magnetic properties of the heptanuclear complexes. We hope that a single modification or a combination of such modifications will allow us to rationally improve the magnetic properties compared to the existing SMM [Mn^IIIIIIIIIIII₆666Cr^IIIIIIIIIIII]³⁺3+3+3+.

Acknowledgements

I am grateful to all my coworkers on this project whose names can be found in the references. Especially their enthusiasm for this project, despite severe problems in the synthesis of molecules developed on a piece of paper, has been central for the success of this work. This work was supported by the DFG (SFB 424, FOR945 ‘Nanomagnets: from Synthesis via Interactions with Surfaces to Function’), the Fonds der Chemischen Industrie, and Bielefeld University.

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Footnote

† This article is part of the ‘Emerging Investigators’ themed issue for ChemComm.

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