The Tripodal Ligand’s 4f Complexes: Use in Molecular Magnetism

Abstract

A predictable type of coordination is a key property of tripodal ligands. Homo- and heteroleptic lanthanide complexes with tripodal ligands are a representative class of compounds. However, despite the fact that many of them are paramagnetic, their magnetic behavior is poorly studied. This is because their photophysical and catalytic properties are considered more attractive. In the present review, we try to summarize the available structural information and only a few examples of data on magnetic properties in order to draw some conclusions about the prospect of such ligands in the design of quantum molecular magnets involving lanthanide (Ln) ions. We would also like to catch the reader’s attention to the fact that, despite the consideration of a large part of the currently known Ln compounds with tripodal ligands, this review is not exhaustive. However, our goal is to draw the attention of magnetochemists and theoreticians to a whole niche of air-stable Ln complexes that is still out of their field of vision.

1. Introduction

The rational design of coordination compounds with specific physical properties is a challenging task for synthetic chemists. Chemical engineering can be both highly specialized (improvement of a specific property) and focused on the preparation of polyfunctional materials. The most common objective for material scientists is to tune the electronic properties of a compound. This can be achieved by varying the ligand environment of the central atom, namely the polyhedron geometry and the ligand field strength. The latter is mainly defined by the donor atoms’ composition, whereas the former depends not only on the geometry of the ligand, but also on the predictability of its coordination mode. The organic tripod molecules bearing donor atoms on each of their three legs are the best choice for the chemical design of different complexes with a given geometry. Moreover, the latter can be easily adjusted using the methods of synthetic organic chemistry. Therefore, it is not surprising that tripodal ligands are widely used in various fields of applied coordination chemistry, such as catalysis [1,2,3,4,5,6]; chemo sensing [7,8,9]; photo- [10,11,12] and electroluminescence [11,13,14]; molecular gears and motors construction [15,16]; biomedical applications [17,18,19,20]; and molecular magnetism [12,21,22,23,24].

Although numerous high-spin molecules based on tripodal ligands (including paramagnetic ones [25,26,27,28,29,30,31,32]) and d-metal ions have been studied to date [33,34,35,36,37,38,39,40,41,42], such studies for 4f elements have mainly been focused on synthesis, structural features, and the photophysical properties of the compounds with diamagnetic tripods, often leaving aside the study of their magnetic behavior [10,11,14,18,43,44,45,46,47,48]. The present review is devoted to an analysis of the known lanthanide complexes with tripodal ligands from the point of view of their application in the field of molecular magnetism.

2. Short Theoretical Background

Due to the slow attenuation of magnetization and the existence of magnetic hysteresis of purely molecular origin, single-molecule magnets (SMMs) could offer considerable future applications in the domain of spintronics, quantum computing, and—especially—for use as materials for information storage at the molecular level. There are three main characteristics of SMMs: The first is the effective energy barrier (U_eff), which provides magnetic bistability due to the spin reversal between the two ground states (GS). Highly efficient SMMs are very different in their behavior since large U_eff do not ensure that magnetization is kept at the elevated temperature during the period required for magnetic recording. This is defined by the second characteristic called blocking temperature (T_B), which is a central claim for the implementation of SMMs in practice. Usually, spin–lattice relaxation and quantum tunneling of magnetization (QTM) lead to magnetization disappearance in an SMM. The first is associated with spin–phonon coupling, which can manifest itself through three different mechanisms: Orbach, Raman, and direct. The QTM is a temperature-independent phenomenon. A thermally assisted QTM process on excited states is also possible, and it is through this that relaxation occurs. These processes, phonon-type relaxation and QTM, which have been described in many papers [49,50,51], are closely related to the third SMM characteristic—relaxation time (τ). The U_eff value is ordinarily determined by the Arrhenius dependence of the relaxation time for the Orbach process. For the main SMM characteristic, T_B, the more common definition is that the magnetization blocking temperature is a temperature below which magnetic hysteresis opens. The stronger the SMM coercive field and the higher the residual magnetization in a zero magnetic field, the better magnetic bistability the magnetic material exhibits. In addition, higher U_eff and T_B provide quantized magnetization with satisfactory suppression of spin–lattice relaxation. To date, the achieved blocking temperatures are much lower than room temperature, which limits possible technological applications for the known SMMs [49,50,51,52,53]. Consequently, the quest for SMMs possessing large U_eff and T_B is a crucial issue in molecular magnetism. An important category of SMMs, lanthanide (Ln) single-ion magnets (SIMs—a subclass of SMMs including only mononuclear coordination compounds), are particularly promising due to their huge magnetic moments with immense magnetic anisotropy, which are caused by a large spin–orbit coupling being offered by the unquenched orbital momentum [54,55]. Improved T_B and U_eff are indispensable in terms of realizing their practical applications.

Almost thirty years of transdisciplinary investigations have resulted in SIMs with a record U_eff (up to 2000 K) and a T_B near liquid nitrogen temperature [56,57,58,59]. This is a result of several approaches, which have shown that enhancing the uniaxiality of magnetic anisotropy is crucial for the design of highly performing SIMs [60,61,62,63,64]. The uniaxiality of SIMs can be provided by the corresponding symmetry of the coordination polyhedron. However, despite the similarity in chemical behavior (due to the shielded nature of the f-electrons), Ln³⁺ cations are very different in terms of their electronic properties. This leads to the fact that for ions differing in electronic configurations, their ligand environment must be taken into account along with the crystal field (CF) splitting. Among the lanthanides, the trivalent Tb, Dy, Ho, and Er can produce ground states (GS) with large m_J—if the appropriate CF is provided [65]. This is because the electronic clouds of Ln GS have different shapes. The letters are generally subdivided into prolate and oblate spheroid types [60,66,67,68], which require, respectively, different ligand field organization: axial for Pr, Tb, Dy, and Nd, and equatorial for Pm, Tm, Yb, and Er [60,69]. Thus, to increase the energy barrier U_eff, the symmetry of an Ln³⁺ ion environment along with the ligand field approach (axial or equatorial) are required, depending on the nature of the Ln³⁺ [70,71]. Although this provides an opportunity to design SMMs with ground states that have a large magnetic moment, relaxation often occurs through excited states that have different electron densities. In addition, the energy gap separating the m_J levels (a key parameter for SMM enhancement) is difficult to forecast until a quantitative approach is applied and the mechanisms of relaxation are entirely established.

If strong intermolecular exchange interactions are absent between the mononuclear SIMs (which is precisely the case for lanthanide ions since the magnetic electrons are on a well-screened 4f shell), then the ligand field surrounding the magnetic metal ions leads to the degeneration of the ^2S+1L_J multiplets, resulting in 2J + 1 sublevel m_J. This results in a highly anisotropic ground spin state, which can be explained using quantum mechanics. However, we will not immerse the reader in the mathematical details for all types of magnetic anisotropy, as they can be found in the literature [72,73,74]. Given a fixed molecular structure, uniaxial anisotropy is important to suppress QTM and decrease thermo-assisted magnetic relaxation. In addition, a source of under-barrier QTM is the transversal anisotropy caused by transverse CF, which should be avoided in the design of SIMs. Tong et al. [75] have studied the influence of symmetry on the transverse terms. They conclude that the C_∞v, C_5h/D_5h, S₈/D_4d, and S₁₂/D_6d point group symmetries vanish terms $B_k^q$ (q ≠ 0) of CF for interested Ho³⁺ ions, resulting in the perfect uniaxial anisotropy. Thus, by adjusting the coordination polyhedron symmetry and the ligand environment for a particular lanthanide center, QTM in a single-ion magnet can be overcome.

However, even the most accurate theoretical predictions are not easy to implement in practice since, in order to obtain a coordination polyhedron with a certain symmetry, it is necessary to use ligands with a predictable manner of coordination. Therefore, when designing any SIM, synthetic chemists have to compromise between polyhedra with uniaxial symmetry and a specific choice of ligands to construct magnetic molecules.

Therefore, the analysis of currently known molecular mononuclear complexes containing tripodal ter- and tetradentate ligands is aimed at drawing the attention of the scientific community to the use of such ligands in the design of Ln complexes with uniaxial anisotropy. To date, approaches based on the shape of 4f electron clouds (oblate or prolate) have been developed to select the most suitable Ln-ions for an appropriate ligand field for both the ground state and the excited levels of the central atom [60,76,77,78].

3. Lanthanide Complexes with Tripodal Ligands

3.1. Complexes with Pyrazolyl-Bearing Tripodal Ligand

3.1.1. Complexes with Tris(Pyrazolyl)Borates Tripodal Ligands

The first and most studied coordinative tripods were the scorpionate ligands, hydro-tris(pyrazolyl)borates, first obtained by S. Trofimenko [33,35]. The coordination chemistry of these negatively charged ligands mainly includes d-metal complexes [37,79,80]. In the chemistry of coordination-capacious f-elements, scorpionates are often used as capping ligands that additionally compensate for the positive charge of Ln [81,82,83,84,85,86]. In the area of molecular magnetism, the bulky hydro-tris(pyrazolyl)-borates (TPzB) are commonly employed as a capping ligand to reduce intermolecular magnetic interactions and protect the air-sensitive radical cites [87]. A number of 3d ion-based SMMs and SCMs (single-chain magnets) [88,89] have been obtained using this approach. Unfortunately, very few Ln-TPzB complexes have been magnetically studied. Among them, there are three Dy³⁺ compounds: a purely homoleptic [Dy(Tp^Me₂)₂]I (1), a heteroleptic (Me₄N)[DyCl₃(Tp^Me₂)] (2) (Tp^Me₂ = tris(3,5-dimethylpyrazolyl)borate), and a mixed-type complex [Dy(Tp^Me₂)₂][DyCl₃(Tp^Me₂)]·CH₂Cl₂ (3) [90]. The Dy³⁺ ions are six-coordinated for all three complexes (Figure 1). The [Dy(Tp^Me₂)₂]⁺ cation in 3 adopts a bent sandwich-type structure with a B–Dy–B angle of 169.57(3)° [90]. In the cationic part, the Dy³⁺ center is surrounded only by N-atoms of two Tp^Me₂, while in the anionic part, the coordination sphere of Dy³⁺ consists of the three nitrogen atoms from one tripod and the three chloride ions. The structural shape analysis has shown that the Dy center in cation 3 is in an elongated trigonal antiprismatic coordination environment (Figure 1) [90]. Such a geometry has been previously found for the divalent lanthanides [44,46,91].

The complex 2 contains the separate [DyCl₃(Tp^Me₂)]⁻ anion, which is alike to that of the complex 3 but it has Me₄N+ as a cation. Compound 1 is isomorphous to the Sm³⁺ analogue reported earlier [44]. It contains well-isolated [Dy(Tp^Me₂)₂]⁺ and iodide ions. The cation in 1 is placed in a 2/m symmetry element representing a mirror plane passing through two of the pyrazolyl rings [90]. It is worthy of note that the Dy center in 1 has a similar geometry comparatively to those of compound 3, but it has the following key dissimilarities: the two independent Dy–N bond distances, 2.376(2) and 2.430(3) Å, are longer compared to those of 3; due to the crystallographic symmetry, the two planes defined by the nitrogen donor atoms of each tripod are parallel, whereas in 3, the angle between the planes is 10.53(2)°; both the Tp^Me₂–Dy–Tp^Me₂ and B–Dy–B angles in 1 (178.64(2)° and 180.00(2)°), are broader than those of 3 (173.05(2)° and 169.57(2)°), indicating that cation 1 reveals a more dense and linear structure than the cation in 3. In conclusion, the isolated [DyCl₃(Tp^Me₂)]⁻ is in an alike trigonal antiprismatic coordination environment with very similar bond distances and angles for the compounds 2 and 3 [90].

Magnetic studies have shown that complex 1 displays an energy barrier U_eff of 13.5 K with τ₀ = 1.6 × 10⁻⁶ s under a 0.08 T applied field, while 3 is an SIM with U_eff = 80.7 K and τ₀ = 6.2 × 10⁻⁷ s under a zero applied field [90]. The results of the first principle CASSCF + RASSI-SO calculations correspond well with the experimental magnetic measurements for 3 and 1, indicating the presence of an intermolecular dipolar interaction of (zJ = −0.1 cm⁻¹) in 3 [90]. The absence of SMM behavior in 1 and 2 under a zero dc field supports the conclusion that the slow magnetic relaxation observed for 1 is a result of minor changes in the coordination geometry of the Dy³⁺ ion, and/or intermolecular dipolar interactions between the anionic and cationic moieties [90]. The QTM probability of a ground state for Kramers doublets is described by the crystal field (CF, B_k^q) parameters. QTM is prevailing when the non-axial terms (for which q ≠ 0 and k = 2, 4, and 6) are larger compared to the axial ones (for which q = 0 and k =2, 4, and 6). For all the Dy³⁺ ions in 1–3, there is significant transverse anisotropy and fast QTM relaxation [90]. The cationic Dy1 units in 1 and 3, however, have a relatively small temperature assisted-QTM in the first excited states. This can assist magnetization relaxation via the first excited states when a dc field is applied [90].

From the point of view of the design of high-performance SIMs, it is worth paying special attention to the recent publication by Hao Qi et al. [92], which is devoted to the synthesis of the Eu(II) compounds with bulky tris-pyrazolyl-borates. First of all, it should be noted that the obtained three complexes are stable under ordinary conditions and can be sublimated. Both of these properties are very important for practical applications. When extending the synthesis procedure chosen by the authors to magneto-anisotropic Ln ions, it would be interesting to test these compounds for SMM behavior. The complexes Eu(Tp^Ph,Me)₂, Eu(Tp^Ph)₂, and Eu(Tp^Ph2)₂ are all hexa-coordinated, with six N atoms from pyrazole hetero-cycles. Eu(Tp^Ph)₂ is isomorphous to the known compounds Sm(Tp^Ph)₂ and Yb(Tp^Ph)₂ [44]. The molecular structure of Eu(Tp^Ph2)₂ differs from that of Eu(Tp^Ph,Me)₂ and Eu(Tp^Ph)₂. Due to the substituent changes, the structure symmetry of the compounds rises in the following order Eu(Tp^Ph,Me)₂ → Eu(Tp^Ph)₂ → Eu(Tp^Ph2)₂. The latter has a higher symmetry of D_3d, while the others possess a “bent sandwich-like” structure known for other Ln(II) ions [91,93,94,95,96,97,98]. The complex Eu(Tp^Ph)₂ (4) adopts an ideal trigonal antiprismatic (D_3d symmetry) molecular structure with a linear B–Eu–B fragment (Figure 1).

The D_3d single-point group with a C₃ axis is a subgroup of D_6h, which is effective enough to induce strong magnetic axiality in the Ln complexes [99,100,101,102]. However, trigonal antiprismatic complexes are underexplored in the field of molecular magnetism. This is especially true for the stable Ln²⁺ complexes of type 4. However, one must take into account the ground state electronic configuration of the central ion when choosing a lanthanide for such studies. This is because the Ln²⁺ ions can have two types electronic configurations: 4fⁿ⁺¹5d⁰6s⁰ (for Nd, Sm, Eu, Dy, Tm, and Yb) and 4fⁿ5d¹6s⁰ (for La, Ce, Pr, and Gd) [103]. The letters should be avoided in the design of new, performant SIMs due to the presence of an unpaired electron at the 5d level.

3.1.2. Complexes of Tris(3,5-dimethylpyrazolyl)methane

The next group of tripods is a family of trispyrazolylmethane derivatives. In contrast to their boron-containing congener, tris(3,5-dimethylpyrazolyl)borate anion, trispyrazolylmethane terdentate ligands are neutral in most currently known compounds [Ln(TPM)(anion)₃] (TPM = tris(3,5-dimethylpyrazolyl)methane). For the first time, air-stable lanthanide complexes with TPM were obtained in 2007 by Sella et al. [45]. The six-coordinated compounds [Ln(TPM)Cl₃](CH₃CN)₂ were prepared in an acetonitrile solution for Ln³⁺ = Y, Ce, Nd, Sm, Gd, and Yb. The crystal structure was reported only for the Y³⁺ ion. The molecular structure of [Y(TPM)Cl₃](CH₃CN)₂ (5) is shown in Figure 2.

Long et al. [24] have since studied the isostructural of the yttrium congener complexes for Tb³⁺, Dy³⁺, and Er³⁺ with the same composition. The compounds crystallize in the space group P2₁/n with two solvent molecules. A SHAPE [104] analysis revealed that the coordination environment of Ln³⁺-ions is a distorted octahedron.

The isomorphous [Ln(TPM)(OArMe₂)₃](thf)₃ (Ln = Y, Nd, Sm, and ArMe₂ = Ph-2,6-Me₂) were obtained in a concentrated THF solution at −30 °C. These complexes crystallize in the space group P-1 with three solvent molecules. The molecular structure of the [Sm(TPM)(OArMe₂)₃](thf)₃ (6) is shown in Figure 2. In all three compounds, each six-coordinated Ln-ion is in a trigonal antiprismatic coordination environment (C₃ symmetry) composed of one smaller triangle (formed by nitrogen atoms) and a larger one that has the OAr^Me₂ groups in its vertices. This is clearly seen by comparing the ∠(N–Ln–N) and ∠(X–Ln–X) angles (∼70 vs. 100–108°). It should be noted that in the [Ln(TPM)(OAr^Me2)₃] compounds, the Ln–N distances (2.565(5) Å) are longer than those in 5 (2.459(5) Å), suggesting that the binding of the TPM tripod is subtle to modifications in the steric demand of the adjacent ligands in the Ln coordination sphere. Compared with the six-coordinate compounds comprising the isosteric but anionic Tp^Me2 tripods, the average M–N distance is also noticeably longer (2.44(1) and 2.443(7) Å) in [Sm(Tp^Me2)]₂BPh₄ and [Sm(Tp^Me2)₂]I [44], which is consistent with the weaker Ln interaction with a neutral ligand.

The molecular structure of seven-coordinate [Sm(TPM)Cl₃(thf)]·thf (7) is presented in Figure 2. By contrast to the unsolvated six-coordinate complex 5, 7 contains one thf ligand, which can probably be accommodated due to the larger coordination sphere of the Sm-ion than that of Y. The two studied [Ln(TPM)(OTf)₃(thf)] complexes are isomorphous due to almost the same ionic radii of Y³⁺ and Ho³⁺. The molecular structure for the latter, (8), is demonstrated in Figure 2. The coordination sphere of the triflate or chloride complexes [Ln(TPM)(X)₃(thf)] may be described differently. Firstly, a trigonal antiprism is defined by one tripod and three anionic ligands (X = Cl or OTf), with a thf-ligand lying on the C₃ axis passing through the top of the tripod and the triangular face defined by the anions. Secondly, a tricapped trigonal pyramid has three N atoms of the TPM lying in the triangular base, with the thf oxygen defining the apex [45]. As in the case of the six-coordinate compounds, the triangles defined by nitrogen are smaller than those defined by the three anionic ligands.

Much later, the three isomorphous complexes [Ln(TPM)(NO₃)₃]·MeCN (Ln³⁺ = Tb, Dy, and Er) were synthesized and studied, which crystallize in the P2₁/n space group with one heteroleptic [Ln(TPM)(NO₃)₃] complex in the asymmetric unit [24]. The molecular structure of the complex [Ln(TPM)(NO₃)₃]·MeCN (9) is presented in Figure 2. The coordination sphere of 9 is composed of three nitrogens from the tripodal ligand and six oxygens from bidentate nitrate anions. The Tb–N distances ranging from 2.482(2) to 2.530(2) Å are slightly longer than the Tb–O ones (2.416(2)–2.458(2) Å). The analysis of the nine-coordinate polyhedron by the SHAPE software indicates that the geometry of the lanthanide site could be best described as a spherical tricapped trigonal prism [24].

Magnetic studies for the TPM coordination compounds were performed only for the two types of anionic co-ligands (chloride and triflate) for the three Ln³⁺ ions: Tb, Dy, and Er, which are congeners of the compounds 5 and 8. For these complexes, the room temperature χT values correspond well to the theoretical ones predicted for a single Ln³⁺ ion consuming the free ion approximation. A temperature decrease induces a negative deviation of χT for all the compounds, reflecting the depopulation of the m_J states [24]. The magnetization for both series does not saturate even at a field of 7 T, witnessing the pronounced magnetic anisotropy for all six complexes. Field-induced slow magnetic relaxation was observed for all nitrate compounds and only for the Er congener of 5. Based on these studies, the authors argue that the manifestation of a field-induced slow magnetization relaxation is greatly reliant on the anion’s nature. While nitrate moieties appear to be suitable to stabilize the oblate electronic density of Dy³⁺, chloride ions generate an equatorial crystal field, allowing the slow relaxation of prolate Er³⁺ ions [24].

3.1.3. Complexes of Anionic Tripodal Ligand: Tris(3,5-dimethylpyrazolyl)-methanide

The electronic analog of tris(3,5-dimethylpyrazolyl)borate anion is a deprotonated TPM: tris(3,5-dimethylpyrazolyl)-methanide (TPM*). Only a few Ln complexes of TPM* are known to date [105]. Among them, the three complexes with diamagnetic central Ln³⁺ ions [Ln(TPM*)Cl₃][Li(thf)₄] (Ln = Sc, Y (10), Lu) were synthesized and structurally characterized. The molecular structure of [Y(TPM*)Cl₃][Li(thf)₄] (10) is shown in Figure 2. All complex anions have C₃ symmetry, and each metal ion is surrounded by three N atoms of the TPM* ligand and three chloride anions, which form a distorted octahedron polyhedron that is also found for 5, despite the different space groups: P2₁/n and R₃ for 5 and 10, respectively. It should be emphasized that the Y–N bond lengths of 2.425(5) Å for [Y(TPM*)Cl₃]⁻ (in 10) are somewhat shorter compared to those in the anions [Y(TPM)Cl₃]⁻ and [Tb(TPM)Cl₃]⁻ 2.459(2) Å [45], and 2.472(3)–2.490(3) Å [24]), but are closer to those of 2.425(6) Å for DyCl₃(Tp^Me₂)]⁻ [90]. This makes sense since the tripodal ligand in both the latter and in 10 has a negative charge, while the tripod in the complexes with longer Ln-N bonds is neutral.

To our great regret, we could not find a single publication describing the magnetic properties of methanide-containing complexes of paramagnetic lanthanides.

3.2. Complexes with the Pyridyl-Bearing Tripodal Ligands

Pyridine-containing tripodal ligands have been described earlier [1]. Moreover, a diversity of bridgehead atoms such as nitrogen, carbon, and phosphorus [106], as well as other elements: Si [107], As [108], Al and In [109], Sn [110,111], Pb [112], and B [113] have been included to alter the properties of the coordination metal complexes, both in terms of polyhedral geometry and to tune the electronic structure.

Strangely enough, the structurally characterized lanthanide complexes of the tris(2-pyridyl)methane have not yet been obtained. Only a small group of exotic organometallic complexes based on tris(2-pyridyl)metalates that are unstable under normal conditions have been obtained and structurally characterized. This family of Ln complexes will be briefly discussed in the next subparagraph of the review.

3.2.1. Complexes of Tris(2-Pyridyl)Metalates

The most numerous group of the Ln complexes including tris(2-pyridyl)metalates are the coordination compounds of anionic tris(pyridyl)stannate (TPS) [114,115,116,117].

Interactions of [Ln(η⁵-C₅Me₅)₂(OEt₂)] with the lithium complex [LiSn(2-Py-5-Me)₃(thf)] in THF solution using a 1:2 ratio gives sandwich-like [Ln{Sn(2-Py-5-Me)₃}₂] (11) complexes for divalent Ln = Eu and Yb [114]. The formation of 11 displays a more pronounced steric demand of the tripodal stannate ligand than C₅Me₅ groups. This is comparable with similar reactions of tris(pyrazolyl)hydroborates [HB(R₂pz)₃]⁻ (R = H, Me; pz = pyrazolyl) with [Ln(η⁵-C₅Me₅)₂] species giving the analogous Ln^II complexes [Ln(HB(R₂pz)₃)₂] [114].

Both compounds of 11 crystallize in the same space group P2₁2₁2₁ and have very close cell parameters. The molecular structure for the europium complex is shown in Figure 3.

The Ln atoms of 11 are in a distorted octahedral coordination environment formed by six pyridyl nitrogens with a staggered organization of the pyridine rings around the Ln center. The coordination sphere around the Ln center is strongly distorted, and the large size of the Ln atom affords a slight twisting of one of the pyridine rings of each Sn(2-Py-5-Me)₃ ligand unit around its Sn–C_py bond. The non-central location of the Ln atom in the cage is reflected by a bending of the Sn⋅⋅⋅L, n⋅⋅⋅Sn axis with 165.50(1)° and 167.28(13)° for Yb and Eu ions, respectively [114]. The Sn bridgehead atom of the tripod reveals a trigonal pyramidal coordination mode (Figure 3, 11b).

The reaction of [LiSn(2-Py-5-Me)₃(thf)] with [Ln(η⁵-C₅Me₅)₂] precursors resulted in the formation of the first Ln^II sandwich complexes, 12, involving the anionic TPS in a κ³N-coordinating manner and featuring “naked” Sn^II centers, which can be used for the following κ¹Sn-metal coordination (the Eu complex is shown as an example in Figure 3, 12) [114].

The compound 12 crystallizes in the cubic space group Pa3 with Eu²⁺ lying in a special crystallographic position and four molecules in the unit cell. The longer Eu–N (2.611(3) Å) and Eu⋅⋅⋅Sn (3.8874(4) Å) distances are consistent with the larger size of the Eu²⁺ vs. Yb²⁺ cation in 11. The most pertinent feature is the Sn—Li contact of 2.792(12) Å in 12, which is shorter than the covalent Sn—Li bond lengths (2.831–2.897 Å) [118]. An encapsulation of the large Eu²⁺ ion and the additional κ¹Sn coordination of the two inner TPS ligands originate an opening of the tripodal structure (C-Sn-C = 99.6(1)°) compared to both outer TPS frameworks with the “naked” Sn centers (C-Sn-C = 93.6(1)°) [114]. Furthermore, the κ¹Sn binding gives a practically ideal octahedral environment of the Eu²⁺ ion with a linear Sn⋅⋅⋅Eu⋅⋅⋅Sn axis (180.0(1)°).

The room temperature reactions of a trialkylmetalates MAlk₃ (Alk = Me for Al and Et for Ga and In) with the complex [Ln{Sn(2-Py-n-Me)₃}₂] gave the following organometallic species: [Eu{Sn(2-Py-4-Me)₃}₂{GaEt₃}₂] (13), Eu{Sn(2-Py-4-Me)₃}₂{InEt₃}₂] (14), and [Yb{Sn(2-Py-3-Me)₃}₂{AlMe₃}₂] (15) [115]. Compounds 13 and 14 (Figure 3) have similar crystal structures and crystallize in the same space group, C2/c [115]. Eu have a distorted octahedral geometry, which is characteristic for the type 11 compounds described above. In contrast with the complexes 11, the non-central location of the Ln ion in the coordination octahedron of 13 and 14 is much less expressed in the bending of the Sn⋅⋅⋅Eu⋅⋅⋅Sn axis by 176.40(5)° and 172.05(8)° for 13 and 14, respectively. In the solid state, the complex 15 (Figure 3) reveals bonding characteristics similar to those for 13 and 14, but differs in that the Yb ion possesses an almost perfect octahedral environment with a strictly linear Sn⋯Yb⋯Sn axis (180.0°) [115].

Here are a few words about the only sandwich lanthanide complex comprising tris(2-pyridyl)plumbate. The compound [Eu{Pb(2-Py-6-OtBu)₃}₂] (16) has been isolated from a concentrated THF solution [117]. Like 12, complex 16 (Figure 3) crystallizes in the Pa3 space group. The Eu²⁺ ion is coordinated by six nitrogen donor atoms of two tripods with a Eu–N bond length of 2.699(2) Å and a Eu⋅⋅⋅O distance of 4.0215(1) Å, which is greater than those of 2.611(3) and 3.501(3) Å in 12. This is because of the larger radius of the bridgehead ion in the Pb(2-Py-6-OtBu)₃ ligand. Although the cavity of the tripodal ligand offers an almost ideal octahedral coordination sphere for the Eu²⁺ cation, which is well encapsulated and clearly separated from the formally negatively charged Pb bridgehead atoms, compound 16 is not stable in the THF solution [117].

EPR solution studies conducted in ambient conditions for compound 16 in the presence of nitrosobenzene (NOB) have suggested the generation of a radical entity. The X-band EPR spectrum exhibits one broad signal corresponding to a Eu^II 4f⁷ spin system with a value of g₀ = 1.989 ± 0.001 and a line width of ΔB_PP = (31.0 ± 0.1) mT. An identical EPR spectrum was obtained without a spin trap. In addition to a broad signal, the spectrum shows a triplet of multiplets. The well-resolved hyperfine structure is caused by the coupling of the unpaired electron with the ¹⁴N (I = 1) nucleus and three groups of non-equivalent protons of NOB. The spectrum has been well simulated, giving the values g₀ = 2.0057 ± 0.0005 and a₀^N = (1.097 ± 0.005) mT, as well as a₀^H = (0.249 ± 0.005) mT, a₀^H = (0.235 ± 0.005) mT, and a₀^H = (0.089 ± 0.005) mT, respectively [117]. The trapped radical was stable over a period of a few hours. However, no ²⁰⁷Pb hfs coupling could have been observed, indicating a radical adduct formation [117].

The complexes comprising tris(pyridyl)aluminate (TPAl) tripods are completed in this section, and their molecular structures are illustrated in Figure 4.

As was shown by R. García-Rodríguez et al. [119,120], the complexes of Ln²⁺ with TPAl are air unstable and can only be obtained by employing the sterically hindered tripods-[(Alkyl)Al(2-Py-6-R)₃]⁻, where Alkyl = Et and R = Me or Br. This means that the coordination ability of TPAl can be adjusted by the steric and electronic character of substituents in the sixth position of the pyridyls. While [EtAl(2-py-6-Me)₃]⁻ (17) coordinates strongly to Ln²⁺ ions, [EtAl(2-py-6-Br)₃]⁻ (18) forms much weaker complexes, and [EtAl(2-py-6-CF₃)₃]⁻ does not coordinate at all [120]. Synthetic and structural investigations were essentially devoted to the complexes of two anions—[EtAl(2-Py-6-Me)₃]⁻ and [EtAl(2-Py-6-Br)₃]⁻. The 2:1 ratio reactions of the compound 17 with LnI₂ (Ln = Eu, Yb, and Sm) in thf at room temperature led to the formation of the deep-orange (Eu) or purple (Yb and Sm) solutions after 24 h, which indicates Ln coordination [119,120]. The SC-XRD study confirmed the formation of sandwich complexes: [{Ln(EtAl(2-py-6-Me)₃}₂] (Ln = Sm 18, Eu 19, and Yb 20) and [{Eu(EtAl(2-py-6-Br)₃}₂] (21); see Figure 4. The complexes 18 and 21 crystallize in the P1 space group. The first contains one CH₃C₆H₅ molecule as a solvate upon crystallizing from toluene. The coordination environments formed around Sm or Eu are a slightly elongated octahedron and a trigonal antiprism, respectively, although both compounds have a straight line passing through the bridgehead atoms of the tripods (for Al-Ln-Al, the angle is 180°). The compounds 19 and 20 crystallize in the P4₃2₁2 and P2₁/n space groups, respectively. The molecules of 19 and 20 feature six-coordinate, distorted, octahedral lanthanide ions, with the N–Ln–N angles being approximately 90° and a slightly bent Al–Ln–Al axis (177.17° (19) and 178.23° (20)) [120].

None of the Ln compounds comprising tris(2-pyridyl)metalates have been reported for their magnetic behavior. The next fairly representative group of lanthanide compounds with tripodal ligands are complexes with tris(2-pyridyl)amines.

3.2.2. Complexes of Tris(2-Pyridyl)Amines

The interaction of tris(2-pyridylmethyl)amine (TPA) with the precursors LnHal₃(thf)₄ or Ln(OTf)₃ was investigated in an anhydrous environment and in the presence of water [3,7]. In the absence of water, the succeeding formation of both mono- and bis-(TPA) was detected using a lanthanide/ligand ratio of 1 and 2, respectively. The mono-TPA complexes [Ce(TPA)I₃] (22) [3], [Ln(TPA)Cl₃] (Ln(III) = Eu, Tb, and Lu ([7]), and the bis(tpa) complexes [Ln(TPA)₂]X₃ (X = I, Ln³⁺ = La, Ce, Nd, Lu [3], and Sm [6]; X = OTf), bis(tpa) complexes [Ln(TPA)₂]X₃ (X = I, Ln³⁺ = La, Ce, Nd, Lu [3], and Sm [6]; X = OTf, Eu [3]) were obtained under anhydrous conditions, and their crystal structures were determined.

The complexes [Ln(TPA)Hal₃] (see, as an example the Ce complex (22) in Figure 5) are isomorphous, and they crystalize in the space group P2₁/c without any solvent molecules per each crystal cell. Note that a tripod base and a plane passing through the halide ions are not parallel. The monotripod complexes [Ln(TPA)Cl₃(CH₃OH)]·CH₃OH (23) (Ln³⁺ = La, Nd, and Sm) (Figure 5) were also obtained starting from the corresponding hydrated lanthanide halide [LnCl₃(H₂O)₆] [121]. Nonetheless, the compounds in 23 are not of interest as high-performance SMMs because they do not have monoaxiality.

In contrast, the heteroleptic complexes containing three nitrates and one tripodal tetradentate ligand tris((1H-pyrazol-1-yl)methyl)amine) (TPzMA) are enough axial (Figure 5, 23a) [12]. Their synthesis, structure, and photophysical and magnetic properties of sequence complexes [Ln(TPzMA)(NO₃)₃]·nMeCN (Ln = Eu, Tb, Dy, and Er, n = 0.5; Yb, n = 0) were described [12]. The SCXRD analysis reveals that, among the investigated compounds, the compounds of Eu, Tb, Dy, and Er are isomorphous and crystallize in the triclinic P$\overline{1}$ space group with a single complex molecule and 1/2 of a CH₃CN molecule per asymmetric unit. The structure includes a mononuclear complex in which the Ln³⁺ ion is coordinated by four N atoms from the TPzMA ligand and six oxygen atoms belonging to the three bidentate nitrate anions (Figure 5, 23a). The tripodal ligand is coordinated by the central ion in a symmetrical manner, forming the Ln³⁺ coordination polyhedron together with nitrates, which is better described as a distorted spherocorona [12]. Contrary to its congeners, the Yb complex crystallizes in the monoclinic P2₁/c space group without solvates. Probably, due to the Ln contraction and the fall in intramolecular distances resulting in steric repulsions in the polyhedron, only two nitrate moieties are bidentate and the other one is monodentate, which leads to a muffin geometry of the Yb site with Cs symmetry [12].

The europium, terbium, and dysprosium analogues exhibit a lanthanide-based luminescence, while the dysprosium, erbium, and ytterbium compounds show field-induced slow relaxation of their magnetization involving Raman and direct processes.

The complexes [Ln(TPA)₂]I₃·CH₃CN (Ln = La, Ce, Nd, and Sm) are isostructural to each other (Figure 5, 24) [3,6]. The metal ions are eight-coordinated by the two-tetradentate ligands that wrap around the metal in a pseudo-D₃ symmetric arrangement [3]. All the complexes crystallize as a single enantiomer in the non-centrosymmetric space group P2₁2₁2₁ [3]. The coordination polyhedra are best defined as distorted cubes with a less distorted geometry for Lu [3].

It was not possible to obtain the crystal structure of [Eu(TPA)₂]·3OTf under water-free conditions. The single crystals of [Eu(TPA)₂]·3OTf·CH₃CN·0.3H₂O (25) were obtained in the presence of a ~0.5 equivalent of H₂O. The molecular structure of 25 (Figure 5, 25) is very close to that of the Ln-bis(tpa) iodides. Contrary to the complexes of 24, complex 25 crystallizes in the centrosymmetric space group P2₁/c with two complex molecules per asymmetric unit and a 0.15 molecule of H₂O, which apparently helps with the crystallization [3].

Along with the Ln³⁺ TPA complexes, their congeners of Ln²⁺ were also isolated. Starting from LnI₂, the stable mono- and bis-TPA complexes [Yb(TPA)I₂(MeCN)]·MeCN (26) (Figure 6, 26) and [Ln(TPA)I₂] (Ln²⁺ = Sm and Eu) (27), [Ln(TPA)₂]·2I·0.5MeCM (Ln²⁺ = Sm and Yb) (28) (Figure 6, 28) were prepared and characterized [6]. When the bulk anion NaBPh₄ is added to the previous reaction mixture, a number of compounds with TPA and its methyl analogs were obtained in inert conditions [122]. The compounds [Ln(Me_nTPA)₂](BPh₄)₂ (n = 0–3 reliant on the methylation degree of the six positions of the pyridyl rings of Me_nTPA, when n = 0—Ln²⁺ = Eu, Yb 29 (Figure 6, 29); /n = 2—Ln²⁺ = Eu, Yb (30); and n = 3—Ln²⁺ = Eu (31) (Figure 6, 31)) have been synthesized, and their structural, electrochemical, and photophysical properties have been studied [122].

The complexes 27 [Ln(TPA)₂]·2I crystallize in the monoclinic centrosymmetric P2₁/c space group, while the complexes 28 [Ln(TPA)₂]·2I·0.5CH₃CN crystallize in the non-centrosymmetric monoclinic Cc space group [6]. The complexes 29 crystallize in the monoclinic P2₁/n space group, contrary to 30 and 31, which crystallize in the triclinic P1; space group, with the lowering of symmetry attributed to the presence of the methyl substituents that result in a crystallographic disorder [122]. The Ln²⁺ ion is eight-coordinated in all the sandwich compounds. Continuous shape measures using the software SHAPE 2.1 were employed to determine the geometry of the Ln centers and suggest that the coordination geometry is closest to cubic in all cases [122]. The shape distortion parameters are in the range 0.69–1.53 for the cubic geometry; the further the value is from zero, the greater the distortion from the ideal geometry [122].

Unfortunately, for all the above compounds comprising the TPA ligand (both for sandwich and semisandwich), the magnetic properties have not been studied. Only two [Ln(TPA)(Anion)₃] compounds and four [Ln(TPzMA)(NO₃)₃]·complexes have been magnetically characterized [123]. The description of their magnetic behavior concludes the current section of the review.

The two mononuclear seven-coordinated Dy³⁺ complexes—[Dy(TPA)Cl₃] (32) and [Dy(TPA)(OphCl₂NO₂)₃]·0.5CH₂Cl₂ (33) have been synthesized using the neutral TPA ligand and either the strong ligand 2,6-dichloro-4-nitrophenol (Cl₂NO₂PhOH) or the weak ligand field donor Cl⁻ [123]. As in the tri-iodine compounds of type 22, mentioned above, the Dy³⁺ ions in complexes 32 and 33 have seven-coordinated capped octahedral and capped trigonal prismatic coordination geometries, respectively [123]. Magnetic studies have shown that both Dy compounds possess field-induced slow magnetic relaxation. The energy barrier for 33 is higher than that of 32, which is due to the strong ligand field of Cl₂NO₂PhO⁻ vs. Cl⁻, resulting in a larger magnetic anisotropy of 33 compared to 32 [123]. The direction of the magnetic anisotropy axes in both complexes deviates remarkably from the symmetry axis of the capped octahedron (C_3v) and the capped trigonal prismatic (C_2v), which explains the poor performance of the SIM behavior for both complexes [123].

The room-temperature χT values of 12.97, 13.92, 11.54, and 3.20 emu/mol for 23a, respectively, for [Ln(TpzMA)(NO₃)₃]·(Ln = Tb, Dy, Er, and Yb), are in quite good accordance with the theoretical values of 11.82, 14.17, 11.48, and 2.57 emu/mol estimated for a unique Ln³⁺ ion [12]. Upon cooling, all the compounds exhibit the typical decrease in χT caused by the thermal depopulation of the m_J levels, reaching values at 1.8 K of 5.25 and 7.35 [12]. For all the complexes, the absence of saturation for the magnetization curves testifies to the existence of magnetic anisotropy, which is expected for such lanthanide ions [12]. Under a zero dc field, no strong out-of-phase susceptibility (χ″) components were observed for any of the samples, pointing out the occurrence of fast QTM.

Excluding the Tb complex, for which the out-of-phase component remains weak, all other complexes show a strong χ″ component upon applying the dc field. For the Er and Yb compounds, the appearance of a second low-frequency peak was detected at high magnetic fields. This might originate from different relaxation mechanisms actuated by large magnetic fields [12]. Therefore, it appears that the neutral tetradentate TPzMA ligand in association with nitrates and the resulting low symmetry of the lanthanide site do not provide the requirements to maximize the anisotropy for either oblate or prolate lanthanide ions in the zero dc field [12].

4. Complexes with Paramagnetic Ligands

Metal-radical systems are recognized to display better SMM characteristics [124]. For example, an extra unpaired electron transforms (n-Bu)₄N[TbPc₂] (Pc is a dianion of phthalocyanine) into [TbPc₂] (Kramers system), guaranteeing twofold degeneracy of all electronic levels enforced by time reversal symmetry, irrespective of ligand field symmetry [125]. Park et al. [126] stated that higher energy levels strongly depend on the ligand type, molecular symmetry, and overall charge of the molecule. Additionally, ligand distortion and molecular symmetry significantly affect the transverse CF parameters, leading to tunnel splitting. The latter induces QTM. Compared to the anionic complex [TbPc₂]⁻, for the neutral complex, no tunnel splitting was observed for the ground and excited state quasi-doublets [126]. For the anionic complex, tunnel splittings of 0.007, 0.090, and 7.969 cm⁻¹ were observed for the ground, first, and second excited state quasi-doublets. The perceived dissimilarity in the magnetic behavior was attributed to the significant exchange interaction, J_ex of ~7 cm⁻¹, existing in the compound [TbPc₂] compared to the anionic one [126]. Moreover, the axial CF parameter (B₂⁰ = −5.93 vs. −5.05 cm⁻¹) is larger, and the transverse CF parameter (B₂² = 0.3 to 0.4 cm⁻¹ vs. 0.8 to 3.6 cm⁻¹) is small for the latter [126].

The real influence of exchange coupling on magnetic relaxation dynamics was reported by Long et al., who first described the Ln complexes with large T_B values [127]. They obtained a binuclear Tb³⁺ complex [{[(Me₃Si)₂N]₂(THF)Tb}₂(µ-η₂:η₂-N₂)⁻] (TbN₂Tb), in which a large magnetic interaction between Tb³⁺ and the radical was established to quench QTM in the absence of a magnetic field. This SMM relaxed in the thermally activated direct process with (QTM probability B~10⁻⁶) a U_eff = 227 cm⁻¹ and T_B~14 K [127]. Later, the strong coupling of –27 cm⁻¹ was communicated for the Gd congener of TbN₂Tb [128]. For the GdN₂Gd, electronic structure calculations were performed, which clearly demonstrated a direct overlap between the Gd³⁺ 4f orbitals and the π* orbital of the radical [129].

4.1. Complexes of the Tripodal Nitroxyl Radicals

4.1.1. Functionalized by 2-Pyridyl Groups Paramagnetic Tripods and Their Complexes

The stable nitroxyl radicals are widely used in the field of molecular magnetism [130,131,132,133,134,135]. However, till now, only three tripodal nitroxyl radicals functionalized by pyridyl groups (Scheme 1) are known [25,136]. The complexes of 3D metal ions with the radical tripods 34–36 are mostly sandwich types [25,26,27,28,29,30,31,32,137]), while a number of semisandwich Ln complexes (37) have recently been synthesized [138,139] (Figure 7). In contrast to the tetradentate TPA tripods described above, the tripodal oxazolidine radical (Rad) 35 is sterically rigid. Upon coordination, it forms a pyramid with an almost ideal triangle at the face for both monoradical (37) and biradical complexes (38) (Figure 7) [138,140].

4.1.2. Structural Features of the Paramagnetic Tripod Complexes

According to the PRXD study, monoradical complexes [LnRad(NO₃)₃] (37) are isostructural. The crystal structures for the complexes of Ln³⁺ = Dy, Tm, Y, Eu, and Lu are ascertained by SC-RXD experiments. Like their closest relatives, the nitrate complexes of Ln with the diamagnetic tripod TPM (9) and the compounds 37 crystallize in the non-centrosymmetric P2₁/n space group [138]. In these complexes, Rad coordinates to a Ln ion in a tridentate manner via two N atoms of the pyridyl substituents and an O atom of an NO group. The coordination sphere is further complemented by three bidentate nitrates to give an LnO₇N₂ polyhedron [138]. Consistent with the continuous symmetry measures method [104], the polyhedron is best described as a spherical tricapped trigonal prism. The radical donor atoms compose the triangular face of the prism. In addition, the coordinated oxygen atoms of the nitrate ligands also form triangular planes parallel to those of Rad (Figure 7, 37b). Moreover, the centers of all the triangles lie on the same axis passing through a central Ln atom, which bears witness to S₃ symmetry.

The Ln–O bond distances related to the NO moiety vary in a region of 2.34–2.38 Å. The length of the N–O bonds of the nitroxyl group fluctuate in the 1.25–1.28 Å interval. Markedly, all bond lengths and angles of the complexes are in the expected range [138]. The Ln environment is composed of three monodentate anions to give the LnO₅N₄ polyhedron. Unlike nitrate ligands, triflate is bound to Ln only by one donor O atom, and the three CF₃SO₃ ions are located in the equatorial plane of the compounds 38. At first glance, the latter have D_3h pseudo-symmetry since the tripod bases are placed one above the other and the three O atoms from the anionic ligands form a triangle (Figure 7, 38b). However, due to the “sandwich” bending, all the triangles are distorted. The SHAPE analysis [104] gave the polyhedron geometry (Figure 7, 38d) as a spherical capped square antiprism with the point symmetry close to C_4v [140]. It should be noted that the radical’s donor atoms and the two oxygens belonging to the two triflate ligands compose the faces of the antiprism, while an oxygen of the third triflate arranges above the rectangular face (Figure 7, 38b) [140].

The only two related compounds of complex 38 are the Ln³⁺ complexes with a quasi-tripodal ligand, 1,3,5-trimethyl-triazacyclohexane (Me₃tach), [Pr(Me₃tach)₂(OTf)₃] [141], and HMe₃tach[La(Me₃tach)₂(OTf)₄] [142] (Figure 8). The former is so bent that the three triflates are not evenly distributed in the equatorial plane, while the latter is even capable of housing four triflates. Such a geometrical organization of the Ln coordination sphere is favorable to stabilize the highest m_J ground states for the prolate tripositive lanthanides ions (Pm, Sm, Er, Tm, and Yb). That is why the Dy complex 38, studied by us earlier, does not exhibit slow magnetic relaxation. The most attractive geometry (for prolate-type Ln³⁺) among compounds with this pseudo-tripodal ligand has recently been studied. The only non-bent sandwich complex [La(Me₃tach)₂Cl₃] with three chlorine anionic ligands in an equatorial plane is presented in Figure 9 [142]. However, chloride anions are bulky enough to enter all three of the inner spheres of smaller Ln³⁺ ions, starting with samarium. Nevertheless, the two chlorides can fit quite well in the equatorial plane of the Ln coordination sphere. However, we did not find an example of such a species for any [Ln(tripod)₂Cl₂]⁺.

According to the CCDC database, there are only a few examples of such compounds with bis-tripodal ligands. One of them is the Eu³⁺ complex [Eu^IIICl₂{R)-tppn}]ClO₄ (39) [143], Figure 7. The coordination geometry of 39 is best described as a distorted dodecahedron. The authors point out that the four coordinated pyridyl nitrogens and one from the two chlorine atoms are approximately located on a plane and form a pentagon, the other Cl being coordinated almost perpendicular to this plane. However, from our point of view, it is better to choose a different description of the geometry for compound 39 in order to predict its magnetic behavior. Both Cl anions are best placed in the same plane, as shown in Figure 7, 39b. In this case, the molecule have an axis, which could serve as an axis of magnetic anisotropy. Our preliminary studies have shown that sandwich-type complexes containing two chloride ligands in the equatorial plane of the cationic complex 40 (Figure 7) can also be obtained for the paramagnetic tripod 35 [144].

4.1.3. Magnetic Properties of the Paramagnetic Tripod Complexes

At 300 K, the χT product values are 7.814, 12.210, 14.366, and 7.376 emu K/mol for the 37-type compounds of Gd, Tb, Dy, and Tm, respectively. These values are consistent with the expected ones for the appropriate Ln^III ion plus a radical (8.255, 12.195, 14.545, and 7.525 emu K/mol) [138]. With the temperature lowering, the χT value for all the complexes drops considerably, which can be ascribed to CFS and/or the antiferromagnetic metal-radical interaction. A dominance of the CFS for all Ln except Gd could be assumed, which is magnetically isotropic at the first order. It should be emphasized that the 37-Tm complex, for which the non-magnetic m_J = 0, ground state is stabilized (χT is equal to 0.375 emu K/mol, corresponding to the value of a radical tripod). Furthermore, the important decrease in χT for 37-Gd bears witness to a strong antiferromagnetic (AFM) coupling between the Gd^III ion and the radical. The plot M(H) for the 37-Gd complex is very informative. Considering the low crystal field splitting typical of Gd³⁺, the saturation value of 6 μ_B is consistent with an AFM coupling between a spin S = 7/2 and a radical spin S = ½ (S_tot = 7/2 − 1/2 = 3) [138]. An X-band EPR study was performed on [GdRad(NO₃)₃] in order to obtain precise information about the electronic structure. The spectrum of Gd exhibits several broad transitions. A satisfactory fitting of both the EPR and the static magnetic measurements can be obtained using the following Hamiltonian [138]:

$$\mathcal{H}=b_2^0{\widehat{O}}_2^0+b_2^2{\widehat{O}}_2^2+b_4^0{\widehat{O}}_4^0+j{\widehat{S}}_{Gd}·{\widehat{S}}_{rad}+g_{Gd}{\mu }_B{\widehat{S}}_{Gd}·B+g_{rad}{\mu }_B{\widehat{S}}_{rad}·B$$

where the first three terms parametrize the CFS of the Gd^III ion, the fourth term is the isotropic magnetic coupling between Gd and the radical, and the last two terms are the Zeeman splitting for Gd and the radical, respectively. The finest simulation result was achieved with the values b₂⁰ = 5.2 × 0⁻² cm⁻¹, b₂² = 1.1 × 10⁻² cm⁻¹, b₄⁰ = 3.8 × 10⁻⁴ cm⁻¹, j = +23 cm⁻¹, g_Gd = 2.0023, and g_rad = 1.998. Notably, the value of +23 cm⁻¹ of the isotropic coupling constant is unusually large for gadolinium complexes of organic radicals. For example, for Gd³⁺ hexafluoroacetylacetonate complexes containing one acyclic nitroxyl radical [145,146,147], the |j| value fluctuates between 9.6 and 12.5 cm⁻¹. For the similar compounds, including one nitronyl nitroxyl radical [148,149,150,151,152,153], exchange coupling is also inferior (|j| = 0.77 ÷ 8.35 cm⁻¹). For the Gd complex comprising the congener of Rad TEMPO (TEMPO = 2,2,6,6-tetramethylpiperidin-1-oxyl), the metal–radical interaction is very small (j = 2.43 cm⁻¹) [154]. For the monosemiquinone complex [Gd(HBTp₃)₂SQ], j is equal 11.4 cm⁻¹ [155]. Moreover, the exchange interaction strength for the Gd radical in the [GdRad(NO₃)₃] species is comparable with that of the binuclear Gd complex of the purely inorganic single radical N₂³⁻ obtained in the group of J. Long [128]. The origin of such a strong magnetic exchange interaction in 37 must be ascribed to a favorable metal-to-ligand orbital superposition. In contrast to the most studied complexes with nitronyl and imino nitroxyl radicals, in which the spin density is mainly delocalized over four or three centers (O–N … N–O [156], and N … N–O), in 37, an unpaired electron is shared only between two sites. Consequently, the spin density on the donor oxygen atom in Rad is two times higher than that in the nitronyl nitroxyl radicals. Notably, the exchange interaction is directly related to magnetic orbital overlapping, which depends on the symmetry and donor strength of all ligands [138].

The dynamic magnetic studies were carried out to gather information on magnetization dynamics at low temperatures. A frequency scan at various applied fields for 37 was performed at a temperature of 2 K. The only compound to display a relevant non-zero out-of-phase magnetic susceptibility was 37-Tb. The latter displays slow relaxation, both with and without an externally applied field. In a zero applied field, the relaxation of 37-Tb at 2 K was at the upper edge of accessible frequencies with a relaxation time of ca. 16 μs; for this reason, a temperature study was impossible. When an external magnetic field was applied, the slow relaxation of 37-Tb slowed by several orders of magnitude [138]. The relaxation time best fit was obtained using a combination of quantum tunneling and Orbach processes, giving τ_QT = 12(1) ms, τ₀ = 0.9(3) ns, and ΔE = 57 cm⁻¹ [138].

The magnetic studies on powder samples of the biradical complex 38 were also fulfilled. The χ_mT-value at 300 K for the 38-Dy compound (14.735 emu K/mol) was slightly smaller than the theoretical one (14.92 emu K/mol) for the non-interacting two radicals and one Dy³⁺ ion (S = 1/2, g = 2.0023, and 0.375 emu K/mol) (4f⁹, S = 5/2, L = 5, J = 15/2, g_J = 4/3, ⁶H_15/2, 14.17 emu K/mol). However, this value corresponds well to those of 14.365 emu K/mol, which were previously obtained for the monoradical complex 37-Dy [138], taking into account the fact that the experimental values for Dy³⁺ in a related coordination environment are somewhat lower than those for a free ion: 13.92–14.00 [12,157]. On cooling, the χ_mT value remains almost unchanged up to 90 K, then steadily falls down to 10 emu K mol⁻¹ at 20 K, and finally drops to 4.803 emu K mol⁻¹ at 2 K. The latter is considerably lower than that for the monoradical analogue (6.50 emu K/mol). Since significant intermolecular exchange interactions in 38-Dy can be excluded, the cause of such behavior could be attributed to the radical–radical coupling, which can reach high values (J_{TEMPO1-TEMPO2}/k_B = −24.9 K) in [Y(hfac)₃(TEMPO)₂]) [158]. Moreover, the metal-to-radical coupling in the [Gd(hfac)₃(TEMPO)₂] complex has been reported to be either positive or negative for the different radicals of the same molecule (J_Gd–TEMPO/k_B = −6.45 and +4.0 K) [158]. Therefore, for a very anisotropic Dy, it is difficult to obtain more information due to the high mixing of the |J,m_J> levels favored by the relatively low-symmetry ligand field in order to elucidate the nature of the exchange interactions in 38-Dy [158].

The temperature dependence of χ_mT for Eu³⁺ compounds is determined by the thermal population of the ⁷F₁ level nearest to the non-magnetic ground level ⁷F₀. The excited ⁷F₁ state, closely sited to the ground state, is already partly populated at room temperature. At 300 K, χ_mT for Eu³⁺ complexes with diamagnetic organic ligands can vary in the range of 1.032–1.386 emu K/mol¹ depending on the ligand field parameters [159]. Therefore, for the complex 38-Eu, the 300 K χ_mT value of 1.778 emu K/mol is reasonable for the two uncoupled radicals and one Eu³⁺ ion, but a value lower than 1.93 emu K/mol was found for the bis-nitronylnitroxide (NN) complex [Eu(NN)₂(NO₃)₃] in a different coordination environment (N₁₀ instead of N₄O₅) [160]. As the temperature decreases, the χ_mT decreases gradually, and, starting from 9 K, drops to 0.348 emu K/mol, which is somewhat higher than that for the [Eu(NN)₂(NO₃)₃] compound (0.24 emu K/mol). No ac signal was observed in either sample in the measurable interval of frequencies (0.1–10,000 Hz).

4.1.4. Rational Design of the Paramagnetic Tripods and Their Complexes

As mentioned above, in the presence of anionic ligands in the equatorial plane, it is better to use prolate Ln ions: Pm, Sm, Er, Tm, and Yb. While for more “magnetic” dysprosium and terbium, the presence of anionic ligands at the equator is strictly contraindicated. Therefore, it is necessary to change the molecular structure of the paramagnetic tripod so that there is no space for anionic ligands or solvent molecules in the Ln coordination sphere. An analysis of the molecular structure of the sandwich complexes with diamagnetic tripods has showed that the low-coordination compounds without anionic ligands are formed in the presence of steric hindrance in a position adjacent to donor tripod atoms, giving propeller-like structures with ideal axiality (see compounds 1, 4, 16, 18, 21, and 31). It should be noted that in most of the bis-tripodal complexes considered in this review, the ligands are symmetrical tripods, in contrast to the radical 35, which consists of two six- and one five-membered hetero-cycles. Moreover, the paramagnetic tripod 35 comprises a bridgehead carbon atom. The other tripods described above are more spatial ligands compared to 35. In complexes with the radical 35, the average value for the side length of the triangular base is about 2.8 Å, while for the non-carbon bridgeheads, it is much larger: 2.9–3.1 for boron and 3.8–4.0 for nitrogen and metallic bridgehead. The larger dimensions to the tripods with hetero-bridgehead atoms “to more deeply set on the head” of the central Ln ion.

On the space filling image of the “burger” 38c (Figure 7), it is clear that two pyridyl substituents of the different oxazolidine radicals 35 are in close proximity, and the shortest contact H…H between them is equal to 2.41 Å. In complex 40, there are also sufficiently close distances between the pyridine rings and the methyl groups of the radical (2.613 and 3.007 Å, Figure 10a). Therefore, if an additional methyl group is located in the fourth position of the pyridyl rings (just near a donor nitrogen atom), then most likely, this will be enough for the paramagnetic tripods to turn relative to each other, resulting in the formation of a propeller-like structure in which there will be no place for additional molecules. In addition to increasing the steric load of the pyridyl substituents, it is necessary to make the paramagnetic tripod more symmetrical about the bridgehead carbon atom.

Such a symmetrization can be performed by going from a five-membered oxazolidine ring to a six-membered oxazinane (41) (Scheme 2a and Figure 10b). The synthesis of such a tripodal radical becomes rather complicated due to commercially unavailable bis(6-methyl-2-pyridyl)methanone and 3-amino-3-methyl-butan-1-ol, the condensation of which yields its diamagnetic precursor.

The other way involves the choice of 1-imidazole as the functional group (instead of pyridine) for oxazolidine nitroxide (Scheme 2b). This is a slightly easier root because the starting aminoalcohol is cheap, but the corresponding bis-ketone must be prepared.

If the use of the hindered tripod 41 is intended to prevent the coordination of hetero-ligands in the equatorial plane, which is favorable for complexes with oblate Ln-ions, then its unhindered congener 42 is better to be used for heteroleptic complexes like 39 and 40 for the prolate lanthanide ion set. The latter can also be chosen for the heteroleptic complexes with the tripod 42.

5. Conclusions

Despite numerous publications on the coordination chemistry and detailed crystallographic information of the lanthanide ions with tripodal ligands, their magnetic behavior has been poorly studied.

In contrast to the complexes of dysprosium and terbium, the coordination compounds of the prolate Pm, Sm, Er, Tm, and Yb are much less investigated. For the prolate ions, unhindered tripods with a shallow fit are more suitable, which makes it possible to ensure equatorial coordination of anionic hetero-ligands. Whereas, the sterically demanding tripods 41 are brilliantly suited for obtaining stable divalent Ln complexes [44,92], which is especially promising for the design of magneto-luminescent materials based on Eu(II) complexes, because their tricationic congener Eu³⁺ has a non-magnetic ground state.

This review of complexes with diamagnetic tripodal ligands was conducted with the hope that physicochemists will pay attention to this family of compounds and make more precise magneto-structural predictions based on CF parameters for the lanthanide ions in the respective ligand environments.

In magnetic terms, mono- and biradical Ln complexes are very interesting, but difficult for theoretical calculations. An important feature of the potential materials is their stability under normal conditions. Complexes with tripodal radicals possess this property. In addition, these paramagnetic tripods have a predictable type of coordination, which is extremely important in the rational design of compounds with desired properties.

The strong magnetic interaction between the radical center and the metal ion has a number of advantages for the design of advanced SIMs. For example, an additional unpaired electron of an organic radical may transform the resulting cationic complex into the Kramers system, while the initial free Ln-ion does not have this feature. In addition, the direct interaction of the unpaired 2p electron of the radical with the 4f shell removes the degeneracy of the energy levels, which can be useful for reducing QTM.

Without theoretical calculations, it is difficult to give precise prescriptions about the structure of a paramagnetic tripod for a particular lanthanide ion. However, we have tried to guess the general trend for the cyclic nitroxyl radicals functionalized by aromatic nitrogen-containing hetero-cycles: pyridine and imidazoline.