Pentagonal-bipyramidal 4d and 5d complexes with unquenched orbital angular momentum as a unique platform for advanced single-molecule magnets: current state and perspectives

V. S. Mironov *^ab, T. A. Bazhenova ^a, Yu. V. Manakin ^a and E. B. Yagubskii ^a
aInstitute of Problems of Chemical Physics RAS, Federal Research Center of Problems of Chemical Physics and Medical Chemistry RAS, Chernogolovka 142432, Russia. E-mail: mirsa@list.ru
^bShubnikov Institute of Crystallography of Federal Scientific Research Centre “Crystallography and Photonics” RAS, Moscow, Russia

First published on 12th December 2022

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1. Introduction

Molecular nanomagnets have attracted huge interest due to their unique magnetic behavior and forward-looking applications in high-density information storage devices, quantum computing, molecular spintronics, and sensors.^1–11 Molecular nanomagnets are low-dimensional molecular magnetic compounds, single-molecule magnets (SMMs, 0D compounds) and single-chain magnets (SCMs, 1D compounds), featuring strong easy-axis magnetic anisotropy and a large magnetic moment producing together a double-well potential with a spin-reversal energy barrier U_eff, which results in magnetic bistability and slow magnetic relaxation below characteristic blocking temperature T_B. SMMs are the first family of molecular nanomagnets that was discovered in the early 1990s.^1,12,13 Over the last quarter century, a huge number of SMMs with various structures, chemical composition and magnetic properties have been obtained and characterized. Increasing the barrier U_eff and the blocking temperature T_B of SMMs is one of the central goals in this field of research aimed at designing high-performance SMMs that could function as molecular magnetic memory cells at higher temperatures. Originally the search for high U_eff and T_B values was focused on even larger high-spin polynuclear 3d metal complexes based on exchange-coupled high-spin 3d-ions (Mn²⁺, Mn³⁺, Fe³⁺, Ni²⁺ or Cr³⁺) to maximize the total ground-state spin S of the molecule in the hope of increasing the barrier, according to the equation U_eff = |D|S².^12–14 However, maximum achievable barriers of polynuclear 3d-SMMs were strongly limited by low single-ion magnetic anisotropy of high-spin 3d ions with quenched (second-order) orbital angular momentum resulting in small zero-field splitting (ZFS) energy. Besides that, the barrier U_eff = |D|S² is nearly independent of S because the molecular magnetic anisotropy parameter D decreases as S⁻² with the increasing spin S.^15,16

As the research field matures, it has become increasingly apparent that the presence of unquenched first-order orbital angular momentum (which results from the first-order spin–orbit mixing of several close-spaced low-lying orbital states) on magnetic metal ions is a key ingredient in obtaining strong magnetic anisotropy and high SMM characteristics. The most important carriers of the unquenched orbital momentum are f-elements (lanthanide and actinides) and some orbitally degenerate transition-metal complexes. In this respect, lanthanide ions Ln³⁺ are especially attractive as they exhibit very large unquenched orbital momentum, such as L = 5 (Dy³⁺, Tm³⁺) and L = 6 (Ho³⁺, Er³⁺), and have strong spin–orbit coupling which often lead to very high magnetic anisotropy, especially for heavy lanthanide ions (Tb³⁺, Dy³⁺) in highly-axial ligand coordination. The discovery (in 2003) of SMM behavior in double decker mononuclear lanthanide complexes [LnPc₂]⁻ (Ln³⁺ = Tb, Dy, and Ho; Pc = phthalocyanine derivatives)¹⁷ with high barriers initiated a new strategy to develop high-performance SMMs followed by a flurry of research activities that has ultimately resulted in innumerable reports on lanthanide SMMs.^18–24 Considerable effort has been focused on the design of mono-ionic lanthanide SMMs (referenced to as single-ion magnets, SIMs)^25,26 with highly-axial ligand environments that provide a double-well potential with doubly degenerate ground state M_J = ±J and unprecedentedly high energy barrier U_eff resulting from the maximum crystal-field splitting energy of the lowest J-multiplet of Ln³⁺ ions. This situation corresponds to the so-called axial limit of the crystal field that minimizes the transverse magnetic anisotropy (both for the ground and excited spin states) thereby reducing the efficiency of the tunneling mechanism and increasing the barrier and the blocking temperature.^27–32 This has led to recent discovery of high-performance Ln-SIMs in mononuclear pentagonal-bipyramidal,^27–29 hexagonal-bipyramidal³⁰ and linear two-coordinate^31,32 dysprosium complexes with exceptionally high SMM characteristics, such as record values of U_eff = 1541 cm⁻¹ and T_B = 80 K reported for a linear sandwich metallocene complex of dysprosium, [(Cp^iPr5)Dy(Cp*)]⁺ (Cp^iPr5 = penta-iso-propylcyclopentadienyl),³² (Fig. 1).

In mononuclear 3d-complexes, unquenched orbital angular momentum (L ≠ 0) combined with the strong axial limit of magnetic anisotropy occurs in linear two-coordinate 3d⁷ complexes of Fe⁺ and Co²⁺, which demonstrate the best SMM performance among transition metal compounds, [Fe(C(SiMe₃)₃)₂]⁻ (U_eff = 226 cm⁻¹),³³ [(sIPr)CoNDmp] (U_eff = 413 cm⁻¹; sIPr = 1,3-bis(2′,6′-diisopropylphenyl)-4,5-dihydro-imidazol-2-ylidene, NDmp = 2,6-dimesitylphenyl imide)³⁴ and Co(C(SiMe₂ONaph)₃)₂ (U_eff = 450 cm⁻¹; Naph = 1-naphthyl).³⁵

These breakthrough results for 4f- and 3d-based SIMs vividly demonstrate the crucial role of unquenched orbital angular momentum and the importance of high axial symmetry of the coordination geometry in designing high-performance SMMs. At the same time, despite the impressive progress reached for Ln-SMMs, it is relevant to highlight significant limitations in the further movement towards even higher barriers and blocking temperatures in 4f-SMMs. First, it is important to note that the aforementioned record values of U_eff and T_B were obtained exclusively in mononuclear lanthanide complexes, which still cannot be considered as true high-temperature SMMs because a single magnetic ion does not provide long magnetic relaxation times, even at temperatures well below the formally high blocking temperature T_B. Thus, in the record 4f-SIM [(Cp^iPr5)Dy(Cp*)]⁺ with T_B = 80 K, long relaxation times (τ > 100 s) occur only below ∼30 K; at low temperatures, the maximum relaxation time is just few hours.³² An even more important issue is that the barrier U_eff in lanthanide SIMs is controlled solely by the crystal-field splitting energy of the lowest J-multiplet of the Ln³⁺ ion, which is generally rather small (few hundred cm⁻¹) and rarely exceeds 1000 cm⁻¹.³⁶ Therefore, although theoretical calculations predict higher barriers in Ln-SMMs with very short metal–ligand bonds,³⁷ it is generally difficult to expect that the barriers of mononuclear SMM lanthanides can be significantly higher than the current record barrier of U_eff = 1541 cm⁻¹,³² which is already close to the maximum achievable crystal-field splitting energy for the ground J-multiplet. In other words, the axial limit of the strong crystal-field has been reached for Ln-SIMs.^29–32

As for mononuclear high-spin 3d-SIMs with the axial ligand field,^33–35,38 the maximum value of their U_eff barriers is strongly limited by the total spin–orbit splitting energy of the ground orbital doublet (M_L = ±L, L ≤ 3), which is less than ∼1000 cm⁻¹;^33–35 the largest known barrier for 3d-SIMs is 450 cm⁻¹.³⁵ This implies that the prospects of mononuclear 3d-complexes as high-performance SMMs are even less favorable as compared to those of 4f-SIMs.

Nevertheless, monometallic 4f and 3d SIMs continue to intensively develop using various approaches toward better SMM performance; modern trends in this field were reviewed in ref. 39. Among them are various synthetic schemes employing new apical ligands and equatorial macrocyclic ligands with the aim to increase the gap between the ground and excited CF states and to improve axial symmetry of magnetic anisotropy due to the larger ratio of axial to equatorial ligand donor strength. New efficient theoretical approaches to model relaxation mechanisms in monometallic Ln-based SMMs were recently developed in ref. 39d.

This article discusses an alternative avenue for the development of high-performance SMMs, which is based on the idea of efficient integration of the extremely strong magnetic anisotropy of several magnetic ions with unquenched orbital angular momentum (L ≠ 0) through exchange interactions in a polynuclear SMM cluster. The highly challenging problem here is the optimal choice of mononuclear metal complexes with L ≠ 0 and development of synthetic routes for their assembly into polynuclear spin structures to ensure strong magnetic coupling between spin centers with the aim to produce maximum molecular magnetic anisotropy of strictly axial symmetry. After a comparative review of anisotropic magnetic properties of various mononuclear complexes with unquenched orbital angular momentum, we show that the pentagonal-bipyramidal (PBP) 4d³ and 5d³ complexes of second and third row transition metals are especially promising as magnetically anisotropic building blocks for the design of high-performance polynuclear SMMs.

In contrast to polynuclear 3d-SMMs, where the overall magnetic anisotropy originates from the single-ion ZFS anisotropy of individual exchange-coupled high-spin 3d ions, in these systems magnetic anisotropy of a SMM results from pair-ion magnetic contributions associated with anisotropic exchange interactions produced by low-spin (S = 1/2) 4d³/5d³ PBP complexes exhibiting no ZFS anisotropy (that occurs only at S > 1/2, see Fig. 4 below). More specifically, this approach exploits a unique property of orbitally-degenerate PBP 4d³ and 5d³ complexes to form highly anisotropic spin coupling with high-spin 3d ions, which is described by the anisotropic spin Hamiltonian −J_zS^z_4dS^z_3d − J_xy(S^x_4dS^x_3d + S^y_4dS^y_3d) of strictly uniaxial symmetry;^40–43 remarkably, uniaxial character of anisotropic 4d/5d–3d exchange coupling does not depend on the symmetry of the local geometry of the exchange-coupled metal centers.⁴² The latter fact considerably facilitates the attainment of high axiality of the molecular magnetic anisotropy of a SMM cluster, as it largely removes the requirement for a polynuclear SMM molecule to have the structural axial symmetry. In mixed heterometallic 4d/5d–3d clusters based on these complexes with a properly organized structure and composition, uniaxial Ising-type spin coupling (with |J_z| > |J_xy|) forms a double-well potential with a barrier U_eff, whose value is controlled by anisotropic exchange parameters J_z, J_xy and by the number of the 4d/5d–3d exchange-coupled pairs in the magnetic cluster (see below Fig. 3 and 4).^42,43

In this article, we overview the current state-of-the-art in this field of research and consider some ideas and approaches for efficient scaling up the barrier U_eff and blocking temperature T_B in polynuclear SMMs based on PBP 4d and 5d complexes by enhancing the exchange parameters, as well as by increasing the nuclearity of the SMM cluster.^41–43 In addition to the known heptacyanide PBP complexes [Mo^III(CN)₇]⁴⁻⁴⁴ and [Re^IV(CN)₇]³⁻,⁴⁵ we present a novel class of PBP 4d and 5d complexes [M^III(L5)X₂] with unquenched orbital angular momentum involving planar pentadentate Schiff-base ligands L5 in the equatorial plane and two apical ligands X; we show that these complexes are a unique, very efficient platform for high-performance single-molecule magnets. General principles of control of the composition, geometry, and topology of heterometallic 4d/5d–3d clusters aimed at achieving highest SMM characteristics are considered. Some specific synthetic routes for practical implementation of this approach are also discussed.

2. Mononuclear metal complexes with unquenched orbital angular momentum as building blocks for efficient polynuclear SMMs: a comparative overview

As discussed above, the presence of the unquenched orbital angular momentum on magnetic metal ions incorporated in a SMM is the most important and necessary condition to obtain extremely strong magnetic anisotropy and high energy barriers. Another essential condition is to ensure the axial limit of the magnetic anisotropy of a high-spin molecule, in which the transverse magnetic anisotropy becomes vanishingly small. In this regime, strong axiality of magnetic anisotropy suppresses the quantum tunneling of magnetization (QTM) in the magnetic relaxation process, both in the ground and exited spin states ±M_S, thereby raising the effective energy barrier U_eff to the upper spin energy levels with M_S = 0 or ±1/2.^19–21 In this respect, record SMM characteristics of single-ion lanthanide complexes convincingly show how high the barrier U_eff and blocking temperature T_B can be when both of these conditions are met.^30–32 However, in passing from mononuclear to polynuclear SMMs, a challenging problem arises, which is how to efficiently convert the unquenched orbital angular momentum of individual metal ions into the maximum barrier and blocking temperature of the whole SMM molecule. Magnetic anisotropy of individual spin centers should be combined into the overall magnetic anisotropy of a polynuclear SMM cluster through exchange interactions, which have to be sufficiently strong to ensure efficient combining of the local magnetic anisotropies of metal ions. Therefore, the most appropriate magnetic building blocks for assembling advanced polynuclear SMMs should be sought among mononuclear metal complexes that meet two basic conditions:

(a) The complex must provide strong exchange interactions with other spin centers;

(b) The complex should have uniaxial local magnetic anisotropy resulting from its unquenched orbital angular momentum.

Below we provide a comparative review of various mononuclear 4f, 3d, 4d and 5d complexes with unquenched orbital momentum aimed at evaluating their correspondence to the given conditions.

2.1. 4f complexes

As described previously, most of the lanthanide ions exhibit strong single-ion magnetic anisotropy arising from large unquenched orbital momentum and strong spin–orbit coupling. At the same time, exchange interactions of Ln³⁺ ions with other spin centers are generally weak due to the core-like nature of 4f electrons. Particularly, Ln–Ln exchange interactions via superexchange pathways through ordinary (diamagnetic) bridging ligands are almost invariably weak (|J| < 1 cm⁻¹ typically).^46–50 As a consequence, in polynuclear lanthanide complexes, weak exchange interactions of 4f electrons are unable to integrate the local magnetic anisotropy of individual Ln³⁺ ions into the overall magnetic anisotropy of a Ln-cluster, as it happens in polynuclear 3d SMM clusters such as Mn₁₂Ac. In fact, magnetic behavior of polynuclear Ln assemblies is often described as a series of non-interacting single-ion Ln-SMMs.^51,52

Far stronger magnetic couplings are required to increase U_eff and T_B values, because weak or moderate spin couplings can lead to exchange-coupled spin states lying below the energy levels arising from the single-ion anisotropy. These spin states can be active as intermediate states in Orbach relaxation processes giving rise to short-cutting the energy barrier. More pronounced exchange interactions are operative in mixed 4f–3d polynuclear complexes (few wavenumbers),^53–56 but they are still insufficient to considerably increase SMM characteristics resulting from single-ion magnetic anisotropy of individual lanthanide ions. Overall, such strong exchange couplings of Ln³⁺ ions are extremely difficult to achieve.

Considerably stronger exchange interactions of Ln³⁺ ions (some tens of cm⁻¹) can occur in lanthanide complexes with organic radicals. Undoubtedly, the Ln-radical approach is a promising strategy toward better Ln-SMMs, but so far, considerable success in this field has been achieved only for lanthanide dimers, namely, for N₂³⁻-radical-bridged binuclear lanthanide complexes, [{[(Me₃Si)₂N]₂(THF)Tb}₂(μ-η²:η²-N₂)] (U_eff = 227 cm⁻¹, T_B = 14 K)¹⁹ and for the endo-fullerene complexes Tb₂@C79N (U_eff/k_B = 757 K, T_B = 24 K) and Tb₂@C80(CH₂Ph) (U_eff/k_B = 799 K, T_B = 27 K).⁵⁷ Quite recently, extremely strong ferromagnetic spin coupling between 4f electrons through delocalized singly occupied σ-bonding 5d_z² molecular orbital (J = +387 cm⁻¹ for Ln = Gd) has been reported for mixed-valence dimers (Cp^iPr5)₂Ln₂I₃ (Ln = Gd, Tb, Dy).⁵⁸ This results in exceptionally high SMM performance, U_eff = 1631 cm⁻¹, T_B = 72 K (Ln = Dy) and U_eff = 1383 cm⁻¹, T_B = 65 K (Ln = Tb).

Extension of the Ln-radical approach from dimers to larger polynuclear radical-bridged lanthanide clusters is an extremely challenging problem. In particular, it is much more difficult to organize strong exchange interactions between Ln³⁺ ions in the entire metal–radical framework of a polynuclear Ln-SMM, as well as to ensure the proper orientation of the local principle magnetic axes of lanthanide ions in order to minimize the transverse magnetic anisotropy. It is also noteworthy that many radicals are chemically unstable.¹⁹ Various approaches to the control of exchange interactions between lanthanide ions in polymetallic Ln-based SMMs have recently been reviewed in ref. 59.

On the whole, therefore, despite strong single-ion magnetic anisotropy, mononuclear lanthanide complexes are not well suited as building blocks for assembling advanced polynuclear SMMs due to very weak exchange interactions, which do not meet the basic condition (a).

2.2. 3d complexes

In contrast to f-block element complexes, in most transition-metal complexes the orbital angular momentum is quenched by a strong ligand field. In this case, unquenched orbital angular momentum can only occur in orbitally degenerate d-complexes, such as [Fe^III(CN)₆]³⁻ and Co²⁺ octahedral complexes. There have been numerous reports on cobalt-based molecular nanomagnets.^60–63 However, these complexes are not especially promising as building blocks for advanced SMMs, since they do not meet the formulated basic conditions (a) and (b); in fact, they exhibit rather low exchange parameters (typically, few tens of cm⁻¹) and often have a low (non-axial) symmetry of the ground-state g-tensor,⁶⁴ which is unfavorable for producing axial magnetic anisotropy of a SMM.

Among mononuclear high-spin 3d complexes, orbital degeneracy of the ground state occurs in linear two-coordinate complexes (Fe⁺ and Fe²⁺,^33,38 Co^2+34,35 and Ni⁺³⁹), trigonal-planar (Fe²⁺),⁶⁵ trigonal-pyramidal (Fe²⁺, Co²⁺, Ni²⁺),^66,67 trigonal-prismatic (Co²⁺),⁶⁸ and pentagonal-bipyramidal (Fe²⁺) complexes.⁶⁹ These complexes often show strong Ising-type magnetic anisotropy with large axial ZFS parameters D resulting from the first-order spin–orbit splitting of the orbitally degenerate ground state.^70–73 As in the case of 4f SIMs, in mononuclear high-spin 3d complexes the enhanced easy-axis magnetic anisotropy and largest energy barriers are obtained for 3d SIMs functioning at the strong axial limit that preserves the orbital angular momentum, minimizes the transverse magnetic anisotropy and suppresses QTM processes. The regime of the strong axial limit is best realized in low-coordinate complexes, especially in two-coordinate 3d⁷ complexes of linear geometry (Fe⁺, Co²⁺) exhibiting double orbital degeneracy with large unquenched orbital momentum (L = 2 or 3); the latter couples parallel to the spin S = 3/2 to produce a |m_J = ±J〉 ground Kramers doublet (where J = L + 3/2) with perfect Ising-type magnetic anisotropy (Fig. 2). This results in the largest barriers among 3d-SMMs, which were reported for the first two-coordinate linear Fe⁺ complex, [Fe(C(SiMe₃)₃)₂]⁻ (L = 2, m_J = ±7/2, U_eff = 226 cm⁻¹),³³ two-coordinate Co²⁺ imido complex [(sIPr)CoNDmp] (L = 2, m_J = ±7/2, U_eff = 413 cm⁻¹)³⁴ and linear dialkyl Co²⁺ complex Co(C(SiMe₂ONaph)₃)₂ (L = 3, m_J = ±9/2, U_eff = 450 cm⁻¹).³⁵ The latter complex refers to the extremely rare case of the maximum achievable orbital angular momentum L = 3 in the ground state of 3d-ions (Fig. 2d).

Nonetheless, even with exceptionally strong Ising-type magnetic anisotropy, none of these high-spin 3d-complexes can be applied as efficient building blocks for constructing advanced polynuclear SMMs, primarily due to their structural lability tending to lift orbital degeneracy and to quench the orbital momentum (especially in linear two-coordinate complexes). Another disadvantage is the absence of available coordination positions capable of producing strong spin coupling with other attached magnetic ions without distortion of high axial symmetry around the 3d ion. More generally, in many other highly symmetric 3d complexes, the orbital degeneracy of the ground state lifts due to distortions of the coordination sphere caused by the unsymmetrical ligand field and the Jahn–Teller effect.⁷⁰ Because of the relatively weak spin–orbit coupling of 3d electrons, lifting the orbital degeneracy of a mononuclear 3d complex quenches easily its orbital angular momentum. As a result, the strong first-order magnetic anisotropy transforms into the ordinary second-order ZFS magnetic anisotropy. In particular, this is the case for high-spin pentagonal-bipyramidal 3d complexes, none of which features true unquenched orbital angular momentum.⁷³

2.3. 4d and 5d complexes

Compared to 3d metal ions, 4d and 5d ions are characterized by larger radial extension of valence orbitals (following the trend 5d > 4d ≫ 3d) and by considerably larger spin–orbit coupling (SOC) parameters. They are of particular interest as building units for SMMs due to stronger exchange interactions resulting from the diffuse nature of the 4d and 5d orbitals, which better overlap with the ligand's orbitals;⁷⁴ one more advantage is that the larger SOC of 4d and 5d ions ultimately leads to the larger magnetic anisotropy.⁷⁵

Bulk of mononuclear 4d and 5d complexes have a low-spin ground state (S = 1/2 or S = 0 for odd and even number of d-electrons, respectively) due to stronger ligand fields and reduced electron repulsion energy (quantified by lower Racah parameters B and C) resulting from the diffuse nature of their d orbitals.⁷⁵ High-spin ground state (S > 1/2) can only occur in some highly symmetric d² and d³ complexes with degenerate lower d orbitals, which are singly occupied by electrons with parallel spins. The best-known examples are pentagonal-bipyramidal d² complexes [Mo^IVCl₂(DAPBH)] (H₂DAPBH = 1,1′-(pyridine-2,6-diyl)bis(ethan-1-yl-1-ylidene))dibenzohydrazine⁷⁶ and W^IV(CN)₇²⁻⁷⁷ with S = 1, as well as a number of octahedral d³ complexes (S = 3/2), such as [Mo^III(CN)₆]³⁻,⁷⁸ [Mo^IIICl₆]³⁻,⁷⁹ [Re^IVF₆]²⁻,⁸⁰ [Re^IVCl₄(CN)₂]²⁻,⁸¹ [Re^IVF₄(CN)₂]²⁻.⁸² These complexes exhibit a non-degenerate (spin-only) ground orbital state characterized by large ZFS energies with the axial parameter D reaching a value of 330 cm⁻¹, as is the case in W^IV(CN)₇²⁻.⁷⁷ Enhanced ZFS energies are caused by the considerably stronger SOC in heavy transition metal ions, especially in 5d ions. Applications of these complexes in SMMs are described in the literature.^75,83

Currently, only a limited number of orbitally degenerate 4d and 5d complexes with unquenched orbital angular momentum are known. In fact, there are three groups of 4d and 5d complexes featuring true first-order unquenched orbital momentum, (i) octahedral hexacyanide complexes [Ru^III(CN)₆]³⁻⁸⁴ and [Os^III(CN)₆]^3−85,86 with triple orbital degeneracy (L = 1), (ii) pentagonal-bipyramidal complexes [Mo^III(CN)₇]⁴⁻,⁴⁴ [Re^IV(CN)₇]⁴⁻,⁴⁵ and [Mo^IIICl₂(DAPBH)]⁻⁸⁷ with double orbital degeneracy (M_L = ±1) and (iii) trigonal-pyramidal d³ complexes of Mo and W based on tris-amido amine ligands (double degeneracy).^88,89 All these complexes reveal a low-spin ground state (S = 1/2) exhibiting no single-ion ZFS magnetic anisotropy, which is inherent in high-spin ions (S > 1/2). In this case, single-ion magnetic anisotropy is only viewable in anisotropic g-tensor and anisotropic magnetic susceptibility, or may even be absent, as occurs in magnetically isotropic [Ru^III(CN)₆]³⁻⁸⁴ and [Os^III(CN)₆]^3−85,86 octahedral complexes. However, from the point of view of magnetochemistry, a more important feature of these systems is that the presence of unquenched orbital angular momentum on 4d and 5d ions leads to highly anisotropic exchange interactions of these complexes with other spin centers (see Fig. 4). More specifically, the exchange interaction of these orbitally degenerate 4d and 5d complexes with attached high-spin 3d metal ions is described by anisotropic spin Hamiltonian H = −(J_xS^x₁S^x₂ + J_yS^y₁S^y₂ + J_zS^z₁S^z₂), in which the exchange parameters J_x, J_y, J_z can differ significantly from each other in both magnitude and sign. For instance, in trinuclear complex Mn^III₂Os^III composed of the central [Os^III(CN)₆]³⁻ hexacyanoosmate and two cyano-bridged Mn^III ions, the exchange coupling in the Os–CN–Mn linkages is described by an extremely anisotropic three-axis exchange tensor J with its main components of the opposite sign, J_x = −18, J_y = +35, and J_z = −33 cm⁻¹.⁹⁰

Even more unusual magnetic interactions are observed in PBP complexes [Mo^III(CN)₇]⁴⁻ and [Re^IV(CN)₇]⁴⁻, which produce anisotropic exchange interactions with a strict uniaxial symmetry of the spin Hamiltonian, −J_xy(S^x₁S^x₂ + S^y₁S^y₂) − J_zS^z₁S^z₂, irrespectively of the presence or absence of geometric symmetry of the exchange-coupled pair of magnetic ions.^40,42,91 The ratio between the exchange parameters J_z and J_xy is different for exchange-coupled pairs in the apical and equatorial positions of the [M(CN)₇] bipyramid. The apical pairs M–CN–Mn exhibit the Ising-type spin coupling (|J_z| > |J_xy|), such as J_z = −34, J_xy = −11 cm⁻¹ in the apical Mo^III–CN–Mn^II pairs in the Mo^IIIMn^II₂ trinuclear complex,⁹² while in the equatorial pairs spin coupling is close to the isotropic one with a small easy-axis (xy) anisotropic component (|J_z| < |J_xy|, |J_z − J_xy| ≪ |J_z|)⁴² (see Fig. 4 and 6 below).

Below we show in detail that these features make the PBP 4d³ and 5d³ complexes unique building blocks for tailoring high-performance SMMs. Of key importance is the fact that the ability of these complexes to automatically produce uniaxial Ising-type anisotropic spin coupling greatly facilitates molecular engineering of the axial magnetic anisotropy of a SMM cluster owing to the elimination of strict control of the coordination symmetry of the magnetic building units. This makes it easier to suppress under-barrier QTM processes and maximize the spin reversal barrier U_eff.

3. Engineering the spin-reversal barrier U_eff through uniaxial anisotropic spin coupling of PBP 4d/5d complexes: how it works

3.1. Comparison of strategies for high-performance SMMs

At the beginning of this section, it is instructive to compare different strategies for designing advanced SMMs. For the reasons outlined above in Section 2.1, below we no longer consider polynuclear 4f-SMMs due to the inherent weakness of exchange interactions of 4f-electrons; instead, we focus on transition-metal based SMMs. First, we consider general aspects concerning the origin of magnetic anisotropy in polynuclear SMMs based on transition-metal complexes. The spin Hamiltonian H_eff of the exchange-coupled spin cluster involving high-spin transition-metal centers (S_i) can be written as:

	(1)

where the first term represents isotropic spin coupling, the second term incorporates all single-ion ZFS interactions (S_iD_iS_i), and the last term refers to the anisotropic part of exchange interactions with G_ij being the tensor of anisotropic spin coupling between the spins S_i and S_j. Depending on the ratio between the relative strength of the isotropic exchange (J_ijS_iS_j), single-ion (S_iD_iS_i) and pair-ion (S_iG_ijS_j) anisotropic interactions, three principal strategies are applied to develop transition metal based SMMs (Fig. 3):

(i) Conventional strategy: J_ijS_iS_j > S_iD_iS_i ≫ S_iG_ijS_j. This situation frequently occurs in most polynuclear SMMs based on high-spin 3d ions (Mn³⁺, Fe³⁺, Ni²⁺) with dominant isotropic spin coupling J_ijS_iS_j, such as Mn₁₂Ac. In this regime, magnetic anisotropy of the spin cluster is mainly due to ZFS on magnetic ions; more specifically, it is quantified by a tensorial sum of the local ZFS anisotropies D_i of magnetically coupled 3d ions projected onto the ground-state spin multiplet 2S + 1.^12,13

(ii) Single-ion magnet strategy: S_iD_iS_i ≫ J_ijS_iS_j + S_iG_ijS_j. This case corresponds to the dominant single-ion magnetic anisotropy (first-order or second-order) of magnetically isolated orbitally-degenerate high-spin monometallic 3d-complexes featuring very weak exchange interactions. The single-ion magnet strategy has led to the record barriers among 3d-SMM (U_eff = 450 cm⁻¹) in linear two-coordinate Co²⁺ complexes (Fig. 2);^34,35 however, as mentioned above, further progress is hindered by the single-ion nature of 3d-SIMs (see above Section 2.2), (Fig. 2).

(iii) Alternative strategy based on anisotropic exchange interactions: S_iG_ijS_j ≫ J_ijS_iS_j + S_iD_iS_i. In this special regime, highly anisotropic exchange interactions S_iG_ijS_j dominate over isotropic exchange J_ijS_iS_j and single-ion ZFS energy S_iD_iS_i. Accordingly, magnetic anisotropy and spin-reversal barrier U_eff of a SMM are mainly due to pair-ion anisotropic spin coupling, not due to single-ion magnetic anisotropy. Highly anisotropic exchange interactions are produced by specially selected orbitally-degenerate 4d and 5d complexes (such as [Mo^III(CN)₇]⁴⁻ and [Re^IV(CN)₇]³⁻) in concert with exchange-coupled high-spin 3d metal ions (Fig. 3 and 4).

The last strategy is much less common than the conventional strategy (case (i)) and SIM strategy (case (ii)), which have been extensively developed over many years. Such a situation can largely be attributed to the fact that the current knowledge about anisotropic exchange interactions of transition-metal magnetic centers with unquenched orbital angular momentum is still rather limited. Below we overview the current state-of-the-art of this strategy and discuss its prospects for the development of high-performance SMMs.

The basic idea of this approach was originally suggested in 2003⁴⁰ and then further developed in ref. 41–43. It lies in the fact that highly anisotropic, Ising-type exchange interactions (such as −J_zS^z_iS^z_j − J_xy(S^x_iS^x_x + S^y_iS^y_j) with |J_z| ≫ |J_xy|) between the low-spin (S = 1/2) pentagonal-bipyramidal heptacyanide complex [Mo^III(CN)₇]⁴⁻ (or its 5d analogue [Re^IV(CN)₇]³⁻) with unquenched orbital momentum and high-spin 3d ions (Mn²⁺, Cr³⁺, V²⁺) can produce double-well potential and spin-reversal barrier U_eff in mixed 4d/5d–3d heterometallic clusters based on these complexes. Several years later, these theoretical findings were experimentally confirmed by syntheses of polynuclear SMMs based on [Mo^III(CN)₇]⁴⁻ and [Re^IV(CN)₇]³⁻ complexes, namely pentanuclear complex ReMn₄ (2008, U_eff = 33 cm⁻¹)⁹³ and several trinuclear complexes MoMn₂ (2013)⁹² and (2017)⁹⁴ (Fig. 4). In fact, SMM behavior of these complexes provides clear evidence that their magnetic anisotropy and spin-reversal barrier arise from anisotropic magnetic exchange since the low-spin Mo^III and Re^IV centers (S = 1/2) have no zero-field splitting and the ZFS parameter D of the Mn^II ions is known to be very small. Consequently, in these systems the barrier is controlled by the anisotropic exchange parameters J_z, J_xy (Fig. 4).

3.2. Origin of uniaxial anisotropic spin coupling of 4d³ and 5d³ PBP complexes

This section outlines the origin of the uniaxial anisotropic spin coupling of PBP 4d³ and 5d³ complexes with attached high-spin 3d ions.^40–42 The 4d³/5d³ complexes with an ideal (D_5h) PBP structure exhibit double orbital degeneracy of ground state, which is a low-spin orbital doublet ²Φ(M_L = ±1) with two components corresponding to the M_L = ±1 projection of the unquenched angular orbital momentum L on the polar z-axis of the bipyramid (Fig. 5) The orbital doublet can also be written in an equivalent form, in terms of two real wave functions ²Φ_xz = (yz)²(xz)¹ and ²Φ_yz = (xz)²(yz)¹ resulting from the two lowest d_xz and d_yz orbitals occupied by three electrons (Fig. 5). Spin–orbit coupling splits the orbital doublet ²Φ(M_L = ±1) into the ground φ(±1/2) and excited χ(±1/2) Kramers doublets (Fig. 5). The ground Kramers doublet φ(±1/2) features an anisotropic Ising-like g-tensor (such as g_z = 3.89 and g_x = g_y = 1.77 in [Mo^III(CN)₇]⁴⁻ complex) associated with unquenched orbital momentum (M_L = ±1).

In distorted PBP complexes, the ground orbital doublet ²Φ(M_L = ±1) splits into two orbital singlet states ²Φ_xz and ²Φ_yz separated by an energy δ (Fig. 5). This splitting tends to quench the orbital momentum and reduce magnetic anisotropy. In this case, magnetic anisotropy depends on the ratio between the SOC constant ζ_4d/5d and the orbital splitting energy δ. The overall picture changes insignificantly when the splitting energy is smaller than the SOC, δ < ζ_4d/5d; in fact, this regime typically occurs in moderately distorted PBP complexes due to the strong SOC of 4d and especially 5d transition metal ions.⁷⁵

Magnetic coupling of the ground Kramers doublet φ(±1/2) with high-spin 3d ions (such as Mn^II) is described by an anisotropic spin Hamiltonian H_eff. Herein we give insight into the origin of H_eff following the computational scheme developed for the Mo^III–CN–Mn^II exchange-coupled pairs in a trinuclear Mo^IIIMn^II₂ cluster composed of the PBP [Mo^III(CN)₇]⁴⁻ complex and two Mn^II ions.⁴²

With the SOC on Mo^III switched off (ζ_4d = 0), spin coupling in Mo–CN–Mn pairs is described by an isotropic orbitally dependent spin Hamiltonian:

Horb = A + RSMoSMn,	(2)

where A and R are spin-independent and spin-dependent orbital operators (acting on the orbital variables only), respectively; S_Mo and S_Mn are spin operators of Mo^III and Mn^II ions. In the space of the ²Φ(M_L = ±1) × |S,M_S〉 wave functions (× stands for the antisymmetrized product and |S,M_S〉 are spin wave functions of the ⁶A₁ ground state of Mn^II), the A and R orbital operators are represented by 2 × 2 matrices:

	(3)

where J₁ and J₂ are orbital exchange parameters corresponding to the real wave functions ²Φ_xz and ²Φ_yz (see Fig. 3). With the SOC on Mo^III switched on, the isotropic orbitally dependent spin Hamiltonian Ĥ_orb(2) converts into an effective anisotropic spin Hamiltonian Ĥ_eff describing spin coupling between the ground Kramers doublet φ(±1/2) (regarded as a fictitious spin 1/2) and the true S = 5/2 spin of Mn^II. The operator Ĥ_eff is obtained by projection of H_orb (eqn (3)) onto the restricted space of wave functions |m, M_S〉 = φ(m) × |S_Mn, M_S〉, where m = ±1/2 is a projection of the fictitious spin S_Mo(eff) = 1/2 on the polar z-axis of the bipyramid, and |S_Mn, M_S〉 is the ground-state wave function of high-spin ion Mn^II (S = 5/2) with the spin projection M_S. Ĥ_eff is calculated by equating the matrix elements of H_eff and A + RS_MoS_Mn in the space of wave functions |m, M_S〉, i.e. 〈m, M_S|Ĥ_eff|m′, M′_S〉 = 〈m, M_S|A + RS_MoS_Mn|m′, M′_S〉. The resulting anisotropic spin Hamiltonian Ĥ_eff takes the form:

Ĥeff = C − JzSzMoSzMn − Jxy(SxMoSxMn + SyMoSyMn),	(4)

where J_z = (J₁ + J₂)/2, J_xy = (J₁ − J₂)/2, and |J₁| ≥ |J₂|; here C = (A₁₁ + A₂₂)/2 is a constant which can be ignored in further calculations (see ref. 42 for more details). The relationship between anisotropic exchange parameters J_z and J_xy differs significantly for apical and equatorial Mo–CN–Mn pairs. In the apical pairs, there are two antiferromagnetic (AF) orbital exchange parameters J₁, J₂ < 0; therefore, according to the relation between J₁, J₂, J_z and J_xy in eqn (4), this results in the Ising-type anisotropic spin coupling with |J_z| > |J_xy| (Fig. 6a). In the special case of the linear apical pair Mo–CN–Mn with J₁ = J₂ and J_xy = (J₁ − J₂)/2 = 0, the anisotropic spin coupling acquires a pure AF Ising character −J_zS^z_MoS^z_Mn with J_z < 0.^40,42 By contrast, in the equatorial pairs Mo–CN–Mn, the orbital parameters obey the relations J₁ < 0 (AF), J₂ > 0 (F) and |J₁| ≫ |J₂| (see ref. 42 for details) resulting in the nearly isotropic spin Hamiltonian H_eff(3) with a small easy-plane (xy) anisotropic component, (|J_z| < |J_xy| and |J_z − J_xy| ≪ |J_z|) (Fig. 6b).⁴² Superexchange calculations reveal that in both the apical and equatorial pairs, the anisotropic exchange parameters J_z, J_xy increase considerably upon bending of the Mo–CN–Mn groups due to opening of new superexchange pathways (Fig. 6).⁴² It is also important to note that the low-symmetry spin terms, the rhombic term J_rh(S^x_MoS^x_Mn − S^y_MoS^y_Mn) and the antisymmetric Dzyaloshinskii–Moriya exchange G[S_Mo × S_Mn], are always absent in H_eff(3), even though they may be allowed by symmetry for strongly bent Mo–CN–Mn groups.

Thus, these results reveal a remarkable property of 4d³ and 5d³ PBP complexes to provide anisotropic exchange interactions of uniaxial symmetry, regardless of the particular geometric configuration of the exchange-coupled magnetic spin centers (Fig. 4 and 6).⁴² The underlying reason behind strict uniaxial symmetry of the spin Hamiltonian H_eff lies in the fact that the SOC operator ζ_4d/5dLS of 4d or 5d ions does not mix the ²Φ(M_L = +1) and ²Φ(M_L = −1) wave functions due to the selection rules ΔM_L = 0,±1 for the non-zero matrix elements of the orbital operator L. This implies that the SOC operator ζ_4d/5dLS is diagonal in the active space of wave functions, i.e., it transforms into the z-component ζ_4d/5dL_zS^z of the SOC operator. Consequently, within the space of wave functions ²Φ(M_L = ±1) × |S,M_S〉, the total Hamiltonian A + RS_MoS_Mn + ζ_4dLS_Mo of the exchange-coupled pair is equivalent to A + RS_MoS_Mn + ζ_4dL_zS^z_Mo. Of key importance is the fact that the latter Hamiltonian commutes with the operator S^z_Mo + S^z_Mn of the total spin projection on the pentagonal z-axis of the bipyramid. Therefore, the projection of the total spin M_S = M_S(Mo) + M_S(Mn) of the Mo^III–CN–Mn^II pair on the pentagonal z axis is a good quantum number, whereas the total spin of the system S = S_Mo + S_Mn is not such. Accordingly, all spin states of the pair are classified by projection M_S of the total spin; this dictates the uniaxial nature of the anisotropic exchange spin Hamiltonian H_eff(4). The guaranteed absence of low-symmetry spin coupling terms (J_rh(S^x_MoS^x_Mn − S^y_MoS^y_Mn) and G[S_Mo × S_Mn]) in the exchange spin Hamiltonian H_eff(4) is very helpful in suppressing of the unwanted transverse magnetic anisotropy in a SMM cluster (see below).

3.3. Origin of the double-well potential and SMM behavior of the apical MoMn₂ complex

The basic idea of employing highly anisotropic spin coupling of PBP complexes of heavy transition metals (such as [Mo^III(CN)₇]⁴⁻ and [Re^IV(CN)₇]³⁻) for designing high-performance SMMs was first theoretically proposed in ref. 40 and then further developed in ref. 41–43. Later on, these theoretical results were corroborated experimentally for a pentanuclear cross-like complex ReMn₄ [(PY5Me₂)₄Mn₄Re(CN)₇]⁴⁺, PY5Me₂ = 2,6-bis[1,1-bis(2-pyridil)ethyl]-pyridine; (U_eff = 33 cm⁻¹; 2008⁹³) and two linear trinuclear complexes MoMn₂, [Mn(LN₅Me)(H₂O)]₂[Mo(CN)₇]·6H₂O (U_eff = 40.5 cm⁻¹, T_B = 3.2 K; 2013⁹²) and [Mn(L)(H₂O)]₂[Mo(CN)₇]·2H₂O (U_eff = 44.9 cm⁻¹, T_B = 2.5 K; 2017⁹⁴) (see Fig. 4). Remarkably, despite small nuclearity and rather low ground-state spin (M_S = ±9/2), linear trinuclear complexes MoMn₂^92,94 exhibit the highest energy barriers (U_eff = 40.5 and 44.9 cm⁻¹) among cyano-bridged SMMs. Considering zero (Mo^III, Re^IV) or very small (Mn^II, |D| < 0.1 cm⁻¹)⁹² single-ion ZFS anisotropy on the magnetic ions, such marked SMM behavior of these complexes clearly indicates that the magnetic anisotropy and barrier U_eff are solely based on anisotropic spin coupling. Theoretical analysis⁴² of magnetic properties of these complexes reveals an Ising-type anisotropic spin coupling in the apical M(4d/5d)–CN–Mn pairs (|J_z| > |J_xy|, such as J_z = −34, J_xy = 11 cm⁻¹ in MoMn₂⁹²) and easy-plane spin coupling (|J_z| < |J_xy|) in the equatorial pairs. Anisotropic exchange parameters J_z, J_xy and SMM characteristics U_eff and T_B of ReMn₄⁹³ and MoMn₂ complexes^92,94 are summarized in Fig. 4.

With the theoretical background developed in ref. 40 and 42, the origin of the SMM behavior of trinuclear MoMn₂ complexes with two apical Mo–CN–Mn linkages^92,94 can be rationalized in a natural way in terms of the uniaxial anisotropic spin coupling of the central PBP [Mo(CN)₇]⁴⁻ complex. The energy spectrum of spin states of these complexes is described by the anisotropic spin Hamiltonian

	(5)

where i runs over two Mn^II ions in MoMn₂. Simulation of the static magnetic properties of MoMn₂⁹² with eqn (5) has resulted in anisotropic exchange parameters J_z = −34, J_xy = −11 cm⁻¹ corresponding to an AF Ising-type spin coupling. Spin energy levels of MoMn₂ calculated with these exchange parameters are shown in Fig. 7. Importantly, the projection M_S of the total spin of the MoMn₂ cluster on the pentagonal z-axis of the PBP [Mo(CN)₇]⁴⁻ complex, M_S = S^z_Mn(1) + S^z_Mo + S^z_Mn(2), is a good quantum number due to the uniaxial symmetry of the anisotropic spin coupling −J_xy(S^x_MnS^x_Mo + S^y_MnS^y_Mo) − S^z_MnS^z_Mo in two Mo–CN–Mn linkages. Therefore, similarly to the case of 3d-based SMMs, the energy spectrum pattern of spin states of MoMn₂ can be visualized by a E vs. M_S plot because each spin state has a definite value of M_S. The butterfly shaped spin energy diagram of MoMn₂ features a clear double-well character for low-lying spin states, which is an essential attribute of a SMM system (Fig. 7); at the same time, it differs considerably from the DS²_z parabolic energy profile typical of 3d-SMMs. The doubly degenerate ground state of MoMn₂ is a well-isolated Kramers doublet M_S = ±9/2 with pure Ising-type magnetic anisotropy (Fig. 7). Moreover, what is especially important for high-performance SMMs, pure Ising-type magnetic anisotropy (characterized by the g-tensor components g_z > 0, g_x, g_y = 0) appears in all low-lying spin states with M_S ranging from ±9/2 to ±3/2. As a result, the QTM processes are strongly suppressed both in the ground and excited spin states, so the barrier U_eff rises up to the top of the double-well potential curve with the M_S = ±1/2 state (which is the lowest in energy to lose axiality), whose energy of 47 cm⁻¹ is reasonably consistent with the experimental barrier of U_eff = 40.5 cm⁻¹ (Fig. 7).⁹² Remarkably, this situation repeats exactly the scenario of the axial limit of magnetic anisotropy in the linear record-breaking lanthanide complexes,^30–32 in which the ground and excited CF energy levels are represented by pure M_J states with precise Ising-type anisotropy. However, in contrast to lanthanide SIMs, where the perfect magnetic axiality is achieved solely by adjusting the strict axial symmetry of the crystal field (which is extremely sensitive to even subtle distortions in the coordination environment of the lanthanide ion), in the apical MoMn₂ SMMs^92,94 the axial limit of magnetic anisotropy is attained automatically, simply due to the fact that the axial symmetry of the anisotropic spin coupling (eqn (4)) does not depend on the geometric symmetry (Fig. 6).⁴² Obviously, the barrier U_eff of MoMn₂ is controlled by the anisotropic exchange parameters J_z and J_xy rather than by the ZFS anisotropy of Mn^II ions (D = −0.07 cm⁻¹, E ≈ 0⁹²), which is too small to match the value of U_eff = 40.5 cm⁻¹. Detailed analysis of the spin energy spectrum of MoMn₂ reveals that the barrier is close to U_eff ≈ 2|J_z − J_xy| = 2|J₂| (see Fig. 12 from ref. 42); in other words, the barrier U_eff is approximately equal to the double absolute value of the smaller orbital exchange parameter J₂ involved in the orbitally-dependent spin Hamiltonian (3).⁴² Interestingly, J₂ and U_eff ≈ 2|J₂| are rather insensitive to bending of the C–N–Mn groups (see Fig. 6a in ref. 42).

On the other hand, analysis of magnetic data of the two SMM-silent equatorial isomers of MoMn₂ (i.e., cis- (2) and trans- (3) isomers of MoMn₂ reported in ref. 92) (Fig. 7) in terms of the spin Hamiltonian (eqn (5)) revealed an easy-plane nature of the exchange anisotropy (with |J_z| < |J_xy|) in the equatorial Mo–CN–Mn pairs, such as J_z = −7.5, J_xy = −9 for 2 and J_z = 0, J_xy = −4 for 3, just as predicted by the theory for the equatorial pairs.⁴² This leads to a single-well pattern of the E versus M_S plot for 2 and 3 with a M_S = ±1/2 ground Kramers doublet resulting in the absence of magnetic bistability and SMM behavior (Fig. 8). Indeed, the equatorial isomers of MoMn₂ were found to be simple paramagnets down to 1.8 K.⁹²

3.4. Regularities in the variation of the barrier U_eff in heterometallic Mo_kMn_m clusters: interplay of anisotropic exchange interactions in the apical and equatorial Mo^III–CN–Mn^II linkages

The above results indicate that anisotropic Ising-type exchange interactions (eqn (4)) of 4d³ and 5d³ PBP complexes greatly facilitate the reaching of the axial limit of magnetic anisotropy (similar to that in the record-breaking linear single-ion 4f-SMMs),^30–32 even in the absence of high axial symmetry of the SMM molecule, as is the case of the linear trinuclear complexes MoMn₂ having no geometric symmetry (Fig. 4).^92,94 Another important feature is that the barrier is proportional to the anisotropic exchange parameters, U_eff ∝ |J_z − J_xy| = |J₂|.⁴² This lays the foundation for a very efficient strategy for the development of high-T_B SMMs, which is based on new principles for creating exceptionally high molecular magnetic anisotropy. The specific principles and ways for the development of this strategy are discussed below.

For a primary insight into this strategy, it is relevant to overview some regularities in the variation of the barrier U_eff in hypothetical small heterometallic complexes Mo_kMn_m composed of the PBP units [Mo^III(CN)₇]⁴⁻ and high-spin Mn^II ions (Fig. 8–11); particularly, it allows to clarify the function of the apical and equatorial Mo–CN–Mn linkages in engineering the barrier. To this end, we calculate the spin energy spectra of Mo_kMn_m clusters with the spin Hamiltonian

	(6)

where the sum 〈ij〉 runs over all neighboring cyano-bridged pairs Mo(i)–CN–Mn(j) in the cluster. Then we compare the E vs. M_S spin energy diagrams of several Mo_kMn_m complexes with parallel alignment of the pentagonal z-axes of the [Mo^III(CN)₇]⁴⁻ complexes. Calculations are performed with the J_z = −34, J_xy = −11 cm⁻¹ exchange parameters for the apical Mo–CN–Mn linkages (obtained for the apical MoMn₂ SMM complex)⁴² and J_z = J_xy = −10 cm⁻¹ for the equatorial ones (in which the minor easy-plane xy-component is omitted for simplicity, Fig. 6b). As in the case of the apical MoMn₂ clusters, the projection of the total spin M_S of the cluster onto the pentagonal z-axis is a good quantum number, thereby each spin state of Mo_kMn_m cluster is characterized by a definite M_S value. Again, in these E vs. M_S diagrams, the barrier is formally determined by the energy position of the lowest spin state to lose axiality (M_S = 0 or 1/2).

First, comparative calculations for two MoMn₂ isomers with one and two apical groups Mo–CN–Mn shows that the barrier U_eff drops from 47 to 15 cm⁻¹ when one apical pair is replaced by an equatorial one; the MoMn₂ complexes with two equatorial groups loose SMM behavior owing to the absence of a double-well potential (Fig. 8b and c). On the other hand, in the series of MoMn_m complexes (m = 2–4) with two apical Mo–CN–Mn groups, an increase in the number of the equatorial groups has little effect on the barrier, but only increases the ground state spin M_S (Fig. 9). This is consistent with the fact that equatorial pairs with an almost isotropic exchange interaction (Fig. 6b) do not contribute to the molecular magnetic anisotropy.

Calculations for other Mo_kMn_m clusters with two apical pairs (n = 2) result in barriers comparable to those in MoMn_m clusters (Fig. 10). Again, the U_eff is close to 2|J_z − J_xy| = 46 cm⁻¹, just as established in ref. 42. Somewhat lower barrier for the Mo₂Mn₃ zig-zag chain (Fig. 10c) as compared to the Mo₂Mn₂ square (Fig. 10a) is likely due to less favorable topology of the apical and equatorial exchange interactions. However, at larger equatorial exchange parameters (J > 30 cm⁻¹) the barrier always reaches the maximum value of U_eff ≈ 46–48 cm⁻¹ being close to 2|J_z − J_xy| = 46 cm⁻¹.

Comparative calculations of the spin energy diagrams for Mo_kMn_m clusters with four apical Mo^III–CN–Mn^II linkages (n = 4) indicate that the barrier is about two times larger (74–83 cm⁻¹) than in the apical MoMn₂ clusters (47 cm⁻¹) with n = 2 (Fig. 11). More extended comparative calculations for Mo_kMn_m clusters with variable parameters J_z, J_xy show that in these systems the maximum achievable barrier U_eff is proportional to the number of apical pairs n; more quantitatively, it is approximately determined by U_eff ≈ |J_z − J_xy|n.⁴²

It is also crucial to evaluate the influence of the strength of approximately isotropic exchange interactions of the equatorial Mo–CN–Mn pairs on the barrier U_eff in polynuclear Mo_kMn_m complexes. To this end, we compare the spin energy diagrams of the ladder cluster Mo₃Mn₃ (n = 4) with fixed anisotropic exchange parameters for the apical pairs (J_z = −34, J_xy = −11 cm⁻¹) and variable isotropic exchange parameters (J = J_z = J_xy, ranging from −1 to −30 cm⁻¹) for the equatorial pairs (Fig. 12).

These results show that moderately strong exchange interactions of the equatorial Mo–CN–Mn pairs (J ≈ −10 cm⁻¹, comparable in magnitude with J_z, J_xy in the apical pairs) are important to improve the SMM performance, as they remove low-lying spin levels (Fig. 12a and b) that can promote undesirable under-barrier magnetic relaxation. Note that at weak equatorial exchange interactions (J < 3 cm⁻¹, Fig. 12a and b), the barriers _eff are close to the calculated barrier of 47 cm⁻¹ in the isolated trinuclear apical complex MoMn₂ (Fig. 7 and 9a). This implies that in this case the Mo₃Mn₃ cluster operates in the regime of weakly coupled independent MoMn₂ units, similarly to the case of weakly coupled lanthanide ions in polynuclear Ln-based complexes (see above Section 2.1) In a wider context, the equatorial exchange interactions carry out an important function of integrating the local pair-ion magnetic anisotropies produced by the apical Mo^III–CN–Mn^II linkages into the overall magnetic anisotropy. The same function is served by isotropic exchange interactions in ordinary polynuclear 3d-SMMs, which combine the single-ion ZFS anisotropy of individual 3d ions to produce magnetic anisotropy of an SMM cluster.^12–14

3.5. Experimental evidences

The above theoretical results have been corroborated experimentally in a series of publication on low-dimensional molecular assemblies, 0D (clusters, SMMs)^92–94 and 1D chain compounds (single-chain magnets, SCMs)^95,96 based on [Mo^III(CN)₇]⁴⁻ complexes and Mn^II ions. Chronologically, the first experimental confirmation of the theoretical prediction of high-T_B SMMs based on anisotropic spin coupling of 4d/5d PBP complexes^40,41 was reported in 2008 for the pentanuclear cross-like ReMn₄ complex involving the central PBP [Re^IV(CN)₇]³⁻ anion (Fig. 4).⁹³ Although the theoretical analysis of its magnetic properties is still absent, the SMM performance of ReMn₄ (U_eff = 33 cm⁻¹) can easily be rationalized in terms of the butterfly-shaped E vs. M_S diagram calculated above for the MoMn₄ isoelectronic complex with U_eff = 42 cm⁻¹ (Fig. 9c). Several similar ReM₄ complexes (M = Ni^II and Cu^II) were subsequently reported to exhibit slow magnetic relaxation.⁹⁷ However, the most complete and unambiguous experimental evidence was obtained in 2013 by the synthesis of three isomers of the trinuclear Mo^IIIMn^II₂ complex based on the PBP [Mo^III(CN)₇]⁴⁻ anion, of which the apical complex exhibited high SMM characteristics (U_eff = 40.5 cm⁻¹, T_B = 3.2 K, τ₀ = 2.0 × 10⁻⁸ s),⁹² which are comparable to those of the Mn₁₂Ac SMM. A detailed theoretical analysis of the origin of the SMM behavior of MoMn₂ was done in ref. 42 (see above Section 3.3). In 2017, the same research group reported one more apical MoMn₂ complex with very close SMM performance (U_eff = 44.9 cm⁻¹, T_B = 2.5 K, τ₀ = 1.6 × 10⁻⁸ s) (Fig. 4).⁹⁴ Pronounced magnetic anisotropy and magnetic hysteresis were also found to occur in extended polynuclear complexes involving PBP [Mo^III(CN)₇]⁴⁻ moieties and high-spin 3d ions, Mo₈Mn₁₄⁹⁸ and Mo₆Ni₁₂.⁹⁹

Apart from SMM clusters, several 1D Mo^III–Mn^II chain compounds featuring SCM behavior have been prepared and magnetically characterized.^95,96 As in the case of MoMn₂ SMMs,^92,94 magnetic anisotropy and slow magnetic relaxation in these chain systems arise from anisotropic exchange interactions of apical Mo–CN–Mn linkages. In this regard, of particular interest is a single-chain magnet [Mn(bida)(H₂O)]₂[Mo(CN)₇]·6H₂O (bida = 1,4-bis(4-imidazolyl)-2,3-diaza-1,3-butadiene), in which PBP [Mo^III(CN)₇]⁴⁻ anion and the Mn^II ions form a double zigzag 2,4-ribbon structure, (Fig. 13).⁹⁵ This chain can be described as a 1D assembly {MoMn₂}_n of the apical Mn–Mo–Mn units connected by the equatorial cyanide groups, whose structure is similar to the structure of two apical MoMn₂ SMMs reported in ref. 92 and 94 (Fig. 4). Thus, in terms of magnetism, this double chain {MoMn₂}_n can be considered as a 1D array of magnetically coupled MoMn₂ SMMs. This chain compound exhibits the record performance among cyano-bridged SCMs (Δ_τ1 = 178 K and T_B = 5.2 K) (Fig. 13 and 14).⁹⁵ Noteworthy, in the {MoMn₂}_n SCM, the calculated intrinsic anisotropic barrier Δ_A ≈ 64–66 K is fairly close to the energy barriers U_eff reported for the two trinuclear apical MoMn₂ SMMs (58.5 K⁹² and 64.6 K⁹⁴). It can also be noted that at low temperatures the barrier Δ_τ2 = 126 K of {MoMn₂}_n (Fig. 14) is fairly close to the barrier U_eff = 112 K predicted in ref. 42 for the double cluster Mo₂Mn₄ (Fig. 11a), whose structure is similar to that of the Mo₂Mn₄ unit in the {MoMn₂}_n SCM (see Fig. 13, the central structure). This provides evidence that the anisotropic Ising-type exchange interactions of apical Mo–CN–Mn linkages in the {MoMn₂}_n chain play the same important role in producing of the spin-reversal barrier as in discrete trinuclear MoMn₂ SMMs (Fig. 4).^92,94 Moreover, the much higher value of the total spin–flip energy barrier Δ_τ1 = 178 K in the {MoMn₂}_n chain compared to the barriers in the individual apical MoMn₂ SMMs (58.5 K and 64.6 K) points to the integrating role of equatorial exchange interactions (nearly isotropic) in enhancing the barrier, as discussed above for the model Mo₃Mn₃ clusters (see Fig. 12).

Rather interesting interplay of anisotropic and isotropic exchange interactions in the apical and equatorial Mo–CN–Mn linkages happens in three 1D chain complexes {[Mn(dpop)][Mn(dpop)(H₂O)][Mo(CN)₇]·7.5H₂O}_n (1), {[Mn(dpop)][Mn(dpop)(H₂O)][Mo(CN)₇]·9H₂O}_n (2) and {[Mn(dpop)][Mn(dpop)(H₂O)][Mo¹(CN)₇][Mn(dpop)][Mn(dpop)(H₂O)][Mo²(CN)₇]·23H₂O}_n (3) reported in ref. 96. The structure of these compounds involves decorated zig-zag chains, in which PBP [Mo^III(CN)₇]⁴⁻ units are connected with three Mn^II ions through bridging CN groups. Compounds 1 and 3 are SCMs with an energy barrier of Δ/k_B = 69.5 K and 68.8 K, respectively, whereas complex 2 is a simple paramagnet. Similarly to the case of the three isomeric MoMn₂ complexes (Fig. 8),⁹² the difference in the SCM behavior is due to the number of apical Mo–CN–Mn groups in the Mo^III centers. In 1, Mo^III is connected with two Mn^II ions in the equatorial positions and with one Mn^II in the axial position. By contrast, in 2 all three Mo–CN–Mn linkages of Mo^III are in the equatorial position, which do not provide magnetic anisotropy owing to nearly isotropic spin coupling.⁴² Complex 3 exhibits a SCM behavior similar to that of complex 1 because half of the chains in 3 are the same as that in complex 1. On the other hand, significantly lower SCM performance of 1 compared to the double chain compound {MoMn₂}_n⁹⁵ (Δ/k_B = 69.5 K in 1vs. 178 K in {MoMn₂}_x) correlates well with the smaller number of apical Mo–CN–Mn linkages in 1, which are a source of magnetic anisotropy. In other words, to obtain SCMs with a high energy barrier, it is required not only to ensure a PBP coordination of Mo^III, but also to maximize the number of Mo–CN–Mn apical linkages.

Therefore, the experimental results on low-dimensional Mo^III–Mn^II molecular magnets convincingly evidence the correctness and consistency of the theoretical foundations of the alternative concept of high-performance SMMs based on anisotropic exchange interactions of 4d/5d PBP complexes, which was presented in theoretical works.^40–42

3.6. Engineering high barriers U_eff with enhanced exchange parameters: Mo^III–V^II clusters

As shown above for Mo_kMn_m clusters (Fig. 8–11), the barrier U_eff is proportional to the anisotropic exchange parameters J_z, J_xy for apical pairs and also to the number n of apical pairs, U_eff ≈ |J_z − J_xy|n. Therefore, apart from increasing the nuclearity of a SMM cluster with keeping parallel alignment of the pentagonal axes of PBP complexes, another efficient way to increase the barrier is to enhance anisotropic exchange interactions. In this respect, it is of interest to estimate the value of the barrier U_eff achievable with the largest known exchange parameters in the Mo^III–CN–M(3d) cyano-bridged exchange-coupled pairs involving high-spin 3d ions M(3d). For this purpose, the ions of divalent vanadium V^II are especially interesting since they are prone to exhibit extremely strong exchange interactions due to the more diffuse 3d orbitals inherent to early transition metal ions.¹⁰⁰ The experimental information on the exchange parameters in [Mo^III(CN)₇]⁴⁻–V^II molecular magnets is scarce or absent.¹⁰¹ However, there are well documented data on the Mo^III–CN–V^II exchange parameters in Mo^IIIV^II₄ (J = −122 cm⁻¹)¹⁰² and Mo^III₂V^II₃ (J = −228 cm⁻¹)¹⁰³ cyano-bridged complexes involving octahedral high-spin (S = 3/2) hexacyano complex [Mo^III(CN)₆]³⁻ and high-spin (S = 3/2) V^II ions. Based on these data, the anisotropic exchange parameters in the [Mo(CN)₇]⁴⁻–V^II system were estimated to be J_z = −300, J_xy = −50 cm⁻¹ for the apical Mo^III–CN–V^II pairs and J_z = J_xy = −150 cm⁻¹ for the equatorial pairs.⁴³ With these exchange parameters, comparative calculations of the spin energy diagrams of various Mo_kV_m clusters were performed⁴³ in terms of a spin Hamiltonian similar to that in eqn (6).

	(7)

where i and j indexes numerate, respectively, Mo and V centers; the 〈ij〉 sum runs over all Mo(i)–CN–V(j) pairs in the Mo_kV_m cluster (here, the Mo–Mo and V–V interactions are neglected). Below are presented the results of calculations of spin energy diagrams for Mo_kV_m clusters with two, four, and six Mo^III–CN–V^II apical pairs and with different numbers of equatorial pairs.

These calculations show that, as in the case of Mo_kMn_m clusters, the barrier is proportional both to the value of the anisotropic exchange parameters J_z, J_xy for apical Mo^III–CN–V^II linkages and to their total number n in the cluster (Fig. 15 and 16). However, due to the smaller spin of V^II ion (S = 3/2 vs. S = 5/2 for Mn^II), in Mo_kV_m clusters the barrier is approximately described by U_eff ≈ 0.5|J_z − J_xy|n (Fig. 15 and 16). Again, at a fixed n, the number of equatorial Mo–CN–V linkages has little effect on the barrier U_eff, but increases considerably the ground state spin ±M_S (Fig. 15). Due to significantly larger exchange parameters of V^II ions, the calculated barriers for Mo^III–V^II clusters are much higher than for Mo^III–Mn^II clusters. For example, the calculated barrier U_eff may reach 741 cm⁻¹ for the ladder cluster Mo₄V₄ (Fig. 16).⁴³ Estimates for larger clusters show that the barrier can exceed 1000 cm⁻¹ (Fig. 17),⁴³ which roughly corresponds to U_eff ≈ 0.5|J_z − J_xy|n.

Thus, an increase in the anisotropic exchange parameters of PBP 4d/5d complexes opens up a direct and efficient way to scale up the SMM characteristics – U_eff and T_B. Some specific approaches to achieve this goal are discussed below.

4. Further development of the strategy: new building blocks, structures and approaches

4.1. Search for new 4d/5d complexes with forced PBP coordination imposed by planar pentadentate macrocyclic ligands: theoretical calculations

Despite the notable progress that has been made in preparation of SMMs based on [Mo^III(CN)₇]⁴⁻ and [Re^IV(CN)₇]³⁻ complexes,^44,45 further advances in this field of research may be hindered by significant weaknesses of these complexes as building blocks, which are inherent in the coordinated cyanometallates:

• [Mo^III(CN)₇]⁴⁻ and [Re^IV(CN)₇]³⁻ complexes have an excessive number of external coordination positions by cyanide ligands tending to form extended 2D and 3D coordination frameworks rather than low-dimensional structures (clusters and chains);

• The PBP [Mo^III(CN)₇]⁴⁻ complex is structurally labile and often subject to a strong distortion, which significantly reduces magnetic anisotropy;¹⁰⁴

• The [Re^IV(CN)₇]³⁻ complex has an unfavorable redox potential incompatible with a number of high-spin 3d ions (Mn^II, V^II, Fe^II) due to the tendency to reduce to the diamagnetic trivalent form;⁹³

• In polynuclear cyano-bridged clusters based on polycyanide complexes, exchange interactions with attached high-spin 3d ions invariably occur through cyanide bridging groups, which are not efficient enough as mediators of spin exchange interactions. This limits the value of the achievable exchange parameters J_z, J_xy and, hence, the contributions to the magnetic anisotropy and the barrier, U_eff ∝ |J_z − J_xy|n.

Therefore, for the further development of the strategy, new PBP 4d and 5d complexes with unquenched orbital angular momentum, free of such issues, are needed. Particularly attractive for this purpose are PBP [M(4d/5d)(L5)X₂] complexes with pentadentate macrocyclic ligands L5, which ensure a pentagonal coordination of the transition metal atom M(4d/5d) in the equatorial plane (with a planar chelate ring of the N₅, N₃O₂, N₂O₃, or O₅ type) and block its equatorial coordination positions, leaving two apical positions free (yielding anisotropic Ising-type spin coupling, Fig. 6), which can be occupied by diverse ligands X (such as CN⁻, OH⁻, O²⁻, N³⁻) capable of bearing the bridging function with attached high-spin 3d ions. However, despite the fact that numerous PBP complexes of this type are widely known for 3d transition metals,⁷³ information on the 4d and 5d congeners is extremely scarce; in fact, it is limited to two complexes reported in 90's^105,106 and two recently synthesized PBP molybdenum complexes [Mo^IVCl₂(DAPBH)]⁷⁶ and [Mo^IIICl₂(DAPBH)]⁻.⁸⁷ Such a situation is rather surprising, especially given that closely related phthalocyanine and porphyrin 4d and 5d complexes are quite common.^107,108 In order to fill this gap, we have started a targeted theoretical search for new PBP 4d and 5d complexes with unquenched angular orbital momentum and study of their structure, magnetic properties and electronic structure using quantum chemical calculations.¹⁰⁹ These studies have shown that there are many ways to prepare PBP M(4d/5d)(L5)X₂ complexes with planar-pentagonal coordination of 4d and 5d ions ensured by various planar macrocyclic pentadentate ligands L5 in the equatorial plane, as well as to control their structural parameters and charge state by combining diverse precursors and substituent groups.

The molecular structures resulted from density functional theory (DFT) calculations of various PBP 4d and 5d complexes with L5 macrocyclic ligands of various types, based on 2,6-diacetylpyridine and pyridine-2,6-dicarbaldehyde, cyclic polypyridines, polypyrroles, etc., have been obtained (Fig. 18). Of these, of particular interest are PBP complexes providing small energy splitting δ of the ground orbital doublet ²Φ(M_L = ±1) (Fig. 5). In this respect it is important to note that, although the L5 ligands depicted in Fig. 18 do not provide perfect pentagonal symmetry (D_5h) of the N₅ or N₃O₂ chelate node necessary for the strict degeneracy of the orbital doublet ²Φ_xz,yz, the splitting energy δ of ²Φ_xz,yz generally tends to be small (often less than the SOC energy ζ_4d/5d, Fig. 5) due to the fact that the xz and yz orbitals in a PBP coordination can only participate in relatively weak π-type interactions with the ligands, so the ground orbital doublet e³(d_xz,d_yz) = ²Φ_xz,yz (Fig. 5) is less susceptible to the asymmetry of the donor atom set and structural distortions of the PBP coordination polyhedron. A number of PBP 4d and 5d complexes M(4d/5d)(L5)X₂ complexes have been found to exhibit a low splitting energy δ of the two lower degenerate magnetic orbitals e(xz, yz) (structures 1–3, 5–7, 9–10 in Fig. 18), which preserves the unquenched orbital momentum and results in high magnetic anisotropy. These calculations indicate that employing various pentadentate macrocyclic ligands L5 and apical ligands X would allow to control the PBP coordination of the required quality (close to the ideal D_5h symmetry), vary the charge state of the complex, and also stabilize the desired valence state of the central 4d/5d metal atom. This avenue of research is presently underway, both theoretically and experimentally.

4.2. Synthesis of 4d and 5d PBP complexes with pentadentate equatorial ligands: chemical challenges

In this section, we discuss progress in the synthesis of new PBP 4d complexes with organic planar pentadentate ligands and consider some potential obstacles to be overcome within preparation of the PBP complexes of 4d/5d metals with the Schiff-base ligands. As mentioned above, this field of research has been barely explored, with only few known examples of PBP 4d/5d complexes.^{76,87,105,106} Although quantum chemical calculations predict numerous L5 pentadentate ligands capable of providing a PBP coordination (Fig. 18), derivatives – both macrocyclic and acyclic – of 2,6-diacetylpyridine are among the most popular and easily accessible.^73,110,111

These ligands force metal ions to adopt PBP geometry and protect the equatorial sites from the unwanted interactions, while apical ligands can be varied. Moreover, toolbox of organic chemistry can be used for the adjustment of molecular properties (solubility, electric charge, spatial arrangement of molecules in crystal lattice) via ligand modifications.

Recently we isolated PBP complex of molybdenum – (Et₄N)[Mo^IIICl₂(DAPBH)] with the metal ion in the low-spin d³ configuration (Fig. 19).⁸⁷ This compound is a true electronic counterpart of PBP [Mo^III(CN)₇]⁴⁻ complex with orbitally degenerate e³(d_xz,d_yz) ground state featuring small splitting energy, δ = 140 cm⁻¹ ≪ ζ_Mo = 700 cm⁻¹. Considerable divergence between M(H) magnetization curve and Brillouin function for S = ½ (Fig. 19c) corroborates the presence of unquenched orbital momentum. These results demonstrate that pentadentate Schiff-base ligands can be a better alternative to cyanide ligands because they form complexes with similar electronic structure and, in addition, provide robust molecular structure with blocked equatorial coordination sites along with diverse options for the apical ligand modification. This fully justifies our approach.

The most straightforward way to the preparation of the orbitally degenerate PBP complexes is the direct reaction between metal-containing precursors with the metal center in the required oxidation state and the ligand along with the proton acceptor (if needed). However, this direct approach comprises many challenges due to properties of the specific ligands and the intricate chemical reactivity of 4d/5d transition metals. Following the periodic trends, 4d/5d metals have preference for higher oxidation states and tendency towards a more covalent bonding (including metal–metal bonding), as compared to 3d metals. Here we consider some implications of that reactivity (Scheme 1).

In case of macrocyclic ligands L5, the direct synthesis does not seem to work well and is likely to lead to the complexes with cis-configuration of the apical ligands, while acyclic ligands render the desired trans-configuration. Nb^IVCl₄(THF)₂ was shown to react with closely related tetradentate Schiff-base ligands – acyclic H₂acen and macrocyclic H₂L^tetra-aza (H₂acen = N,N′-ethylene bis(acetylacetonylideneimine), H₂L^tetra-aza = 7,16-dihydro-6,8,15,17-tetramethydibenzo-[b,i][1,4,8,11]tetra-azacyclotetradecine) with the formation of trans-[Nb(acen)Cl₂] and cis-[NbCl₂(L^tetra-aza)], correspondingly (see Fig. 20).¹¹²

Another important point to keep in mind when dealing with Schiff-base ligands is their probable redox activity. It has long been known that salen-like ligands can accommodate, upon reduction by alkaline metals, up to two electrons via formation of C–C bonds with the requisite assistance of transition metal ions.^113–118 Interestingly, reduction of niobium(V) salophen complex (salophen²⁻ = N,N′-o-phenylene bis(salicylideneaminato)) dianion does not stop at the formation of the C–C bonds but proceeds further due to the creation of a double metal–metal (NbNb) bond, while reduction of similar molybdenum(IV) salophen complex leaves the imine CN bonds intact and leads only to metal–metal bonding.¹¹⁹ Recently, a paper by K. J. Lamb et al. has been published that demonstrated oxidative properties of H₂salophen ligands.¹²⁰ Widely used synthetic protocol for the preparation of Cr(III)–salen complexes from the ligand and Cr^IICl₂ proved to be a rather complicated reaction that includes formation of tetrahydroquinoxalines as a side product resulting from the ligand reduction:

Our works on PBP complexes of vanadium(III) and chromium(III) also suggest the presence of similar reactions in the case of H₂DAPBH ligand.^121,122

In 2017 we examined (NH₄)₂[Mo^IIICl₅(H₂O)] as a Mo^III precursor for synthesis of trans-[Mo^IIICl₂(DAPBH)]⁻ in the reaction with H₂DAPBH ligand and Et₃N, which resulted in some unidentified redox reaction and subsequent crystallization of neutral trans-[Mo^IVCl₂(DAPBH)].⁸⁷ Though no attempts to isolate any co-products were successful, we believe that this outcome can stem from a disproportionation reaction or the ligand-assisted oxidation of the metal center. Later we made use of oxidizing properties of the free H₂DAPBH ligand towards Mo(CO)₆ in synthesis of trans-[Mo^II(DAPBH)(CO)(MeCN)], which, after the comproportionation reaction with trans-[Mo^IVCl₂(DAPBH)], finally led to the desired trans-[Mo^IIICl₂(DAPBH)]⁻ (see Scheme 2).⁸⁷

Although this comproportionation synthesis of Mo(III) PBP complex seems characteristic of molybdenum chemistry and scarcely transferable even to the closest molybdenum congener – tungsten, this reaction demonstrates that fine balancing of the interplay between redox properties of the ligand and the metal ion can lead to orbitally degenerate PBP complexes of 4d/5d metals with Schiff-base ligands.

Bis-hydrazide derivatives of 2,6-diacetylpyridine have two active protons and usually undergo double deprotonation leading to the ligand charge of −2. For the metal ions in higher oxidation states (Mo(V), W(V)), it is reasonable to have ligands able to adopt higher net charge upon deprotonation. Palomero and Jones have reported a new family of trianionic acyclic amido-bis(amidate) ligands that promote pentagonal bipyramidal coordination with early 3d/4d/5d transition metals in highest oxidation states (+4 and +5) with the non-magnetic d⁰ configuration:¹²³

This ligand family needs further examination with respect to the preparation of high-valence paramagnetic complexes of middle transition metals. Mo^IV(NMe₂)₄¹²⁴ seems a good entry to begin with.

These and other synthetic approaches highlight a more sophisticated chemistry of PBP 4d and 5d complexes with Schiff-base ligands compared to their 3d congeners.⁷³ So far, this field of research remains largely underdeveloped; the interest in new 4d/5d complexes with unquenched orbital angular momentum could fuel further progress.

4.3. Enhancing anisotropic spin coupling of PBP 4d/5d complexes through monoatomic apical bridging ligands

As mentioned before, the inevitable mediation of CN bridging groups in the magnetic spin coupling in polynuclear SMMs based on the heptacyanide complexes imposes restrictions on the maximum exchange parameters in cyano-bridged systems; their upper limit is probably reached in the Mo^III–CN–V^II exchange-coupled pairs, J_z ≈ 200–300 cm⁻¹.⁴³ Therefore, in order to further enhance exchange interactions, it will be necessary to move from cyanide bridging groups to other groups supplying a more efficient spin coupling. In this regard, PBP complexes [M(4d/5d)(L5)X₂] with macrocyclic pentadentate ligands L5 (Fig. 18) offer much greater flexibility in the option of the apical ligands X, some of which can provide significantly higher anisotropic exchange parameters compared to cyanide ligands. In particular, especially strong exchange interactions can be obtained with monoatomic apical bridges (X = O, N, C), as it happens in oxo-bridged, nitrido-bridged and carbido-bridged ligands.^125–129 Thus, very strong antiferromagnetic spin coupling has been reported for binuclear μ-oxo bridged complexes of high-spin 3d ions with linear M(3d)–O–M(3d) units (M(3d) = Cr^III, Fe^III, Fe^IV) and short M(3d)–O distances (1.75–1.80 Å), Table 1. Even shorter metal-μ(X) distances (∼1.65–1.70 Å) occur in nitrido-bridged and carbido-bridged complexes, which can cause exceedingly strong AF exchange interactions, such as −J > 600 cm⁻¹ in some [Fe^IV–(μ-N)–Fe^IV]⁵⁺ complexes.¹²⁹ However, these ligands tend to stabilize high valence states of the transition metal atoms and to form the cation-radical form of macrocyclic porphyrin and phthalocyanine ligands.¹³⁰

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The notable difference between the capacity of the diatomic μ-CN and monoatomic μ-O bridging ligands as mediators of the spin coupling can most clearly be seen from a comparison of structurally related linear binuclear Cr^III complexes [(NH₃)₅Cr^IIICNCr^III(NH₃)₅]⁵⁺ (J = −32 cm⁻¹)¹³¹ and [(NH₃)₅Cr^IIIOCr^III(NH₃)₅]⁴⁺ (J = −450 cm⁻¹).¹²⁵ On the other hand, a comparison between the isoelectronic binuclear cyano-bridged Cr^III and Mo^III complexes [(NH₃)₅Cr^IIICNCr^III(NH₃)₅]⁵⁺ (J = −32 cm⁻¹)¹³¹ and [(CN)₅Mo^III–CN–Mo^III(CN)₅]⁵⁻(J = −226 cm⁻¹)¹³² shows how strongly the exchange interaction increases upon moving from 3d magnetic orbitals to more diffuse 4d and 5d orbitals of heavy transition metals. Therefore, following the basic trend of increasing exchange interactions in the series 3d ≪ 4d < 5d,⁷⁵ one would expect even stronger exchange interactions for M(4d)–O–M(3d) and M(5d)–O–M(3d) μ-oxo bridged exchange-coupled pairs compared to those of M(3d)–O–M(3d) pairs presented in Table 1.

Some number of μ-oxo bridged heterometallic 4d/5d–3d complexes have been reported in the literature, including dimers and trimers (Fig. 20),^133–136 their magnetic properties were also examined.^134,135 However, reliable systematic data on the actual exchange parameters are largely absent because of the problems in adequate interpretation of the complicated magnetic properties, which are often difficult to analyze in terms of conventional magnetochemical models due to the strong SOC in 4d and 5d ions. For example, the reported low Fe-the actual exchange parameters are largely absent because of the problems in adequate interpretation of the complicated magnetic properties, which are often difficult to analyze in terms of conventional magnetochemical models due to the strong SOC in 4d and 5d ions. For example, the reported low Fe–Ru exchange parameters (few tens of wavenumbers) for a Fe^III–O–Ru^IV–O–Fe^III trinuclear complex, [(salmah)Fe–O–Ru(TPP)–O–Fe(salmah)] (salmah = N,N′-(4-methyl-4-azaheptane-1,7-diyl)bis(salicylaldimine); TPP = 5,10,15,20-tetraphenylporphyrin) (Fig. 20c),¹³⁵ were obtained within a simple isotropic exchange model (i.e., −JS₂(S₁ + S₃) − J₁₃S₁S₃), which does not take into account complex electronic structure of Ru^IV ion in the ligand field of the N₄O₂ coordination (D_4h symmetry), where strong SOC results in a non-magnetic ground state arising from ZFS of the S = 1 spin of Ru^IV with a large positive D parameter (many tens of cm⁻¹). In this case, magnetic calculations result in much larger exchange parameters, such as J_Fe–Ru = −240 cm⁻¹ and D = +50 cm⁻¹.

Apart from the larger radial extension of 4d and 5d orbitals, there is one more reason to expect larger exchange parameters for low-spin 4d and 5d PBP complexes [M(4d/5d)(L5)X₂] (Fig. 18) with monoatomic apical ligands μ-X = O, N, C. It lies in the fact that the above high exchange parameters J in the spin Hamiltonian H = −JS₁S₂ refer to dimers of high-spin 3d ions with S₁ = S₂ = 3/2, 2 and 5/2 (Table 1). However, upon passing from the homometallic linear group M(3d)–μ(X)–M(3d) to heterometallic M(4d/5d)–μ(X)–M(3d) groups involving a low-spin PBP 4d/5d complex (S₁ = 1/2) with the same bridging ligand μ(X) = O, N, C (Fig. 21), the exchange parameter J in −JS₁S₂ increases by a factor of ≈1.5 due to the difference in the value of spin S₁ and in the number of active superexchange pathways (see ref. 43 for more details). Therefore, considering large J values collected in Table 1, in heterometallic dimers M(4d/5d)–μ(X)–M(3d) involving PBP [M(4d/5d)(L5)X₂] complexes and high-spin 3d ions the exchange parameters can reach values of at least |J| ≈ 600–800 cm⁻¹. A further increase in the exchange parameters due to more diffuse 4d and 5d orbitals suggests much higher achievable values of exchange parameters in heterometallic oxo-bridged M(3d)–O–M(4d/5d) dimers, presumably |J| > 1000–1500 cm⁻¹ (Fig. 21).

4.4. Some heterometallic magnetic structures toward highest SMM performance

Based on the above results, it is now time to discuss some specific heterometallic structures toward high-performance SMMs based on 4d and 5d PBP complexes. Probably, the initial step could be an attempt to assemble high-T_B SMMs from already known magnetic building blocks ensuring strong spin coupling and high magnetic anisotropy, such as PBP [Mo^III(CN)₇]⁴⁻ complex and [(PY5Me₂)V^IIL]²⁺ complex, in which V^II ion is encapsulated in the PY5Me₂ pentadentate ligand to prevent formation of extended polymer structures (Fig. 22). It is important to note that mononuclear complex (PY5Me₂)V^II has already been successfully used as a building block in the synthesis of a pentanuclear cross-like cluster Mo^IIIV^II₄, [(PY5Me₂)₄V^II₄Mo^III(CN)₆]⁵⁺, composed of the central high-spin (S = 3/2) octahedral [Mo^III(CN)₆]³⁻ complex and four [(PY5Me₂)V^II]²⁺ units connected through CN groups, (Fig. 22a).¹⁰² The Mo^III–CN–V^II exchange interactions are found to be strong, J = −122 cm⁻¹;¹⁰² even larger exchange parameter of J = −228 cm⁻¹ has been reported for a trigonal–bipyramidal Mo^III₂V^II₃ cluster with two [Mo^III(CN)₆]³⁻ complexes in the apical positions.¹⁰³ For the [Mo(CN)₇]⁴⁻–V^II systems, these data were used to estimate anisotropic exchange parameters J_z = −300, J_xy = −50 cm⁻¹ for the apical Mo^III–CN–V^II pairs and J_z = J_xy = −150 cm⁻¹ for equatorial pairs.⁴³ Therefore, combination of [Mo^III(CN)₇]⁴⁻ and [(PY5Me₂)V^II]²⁺ building blocks is expected to yield a five-nuclear cross-like Mo^IIIV^II₄ complex (Fig. 22b), similar to the known Re^IVMn^II₄ SMM complex (U_eff = 33 cm⁻¹) assembled from rhenium PBP [Re^IV(CN)₇]³⁻ complex and [(PY5Me₂)Mn^IIL]²⁺ complexes (Fig. 4).⁹³ The calculated spin energy diagram predicts the energy barrier around 300 cm⁻¹ (Fig. 22); the blocking temperature is also expected to be high.

Significantly higher SMM characteristics can be obtained in clusters with oxo-bridged groups featuring short M–O distances and strong exchange interactions (see Section 4.3). The existing trinuclear clusters shown in Fig. 22 can be used as a base for the synthesis of such SMMs. In these structures, one should try to replace the central planar tetradentate porphyrin or phthalocyanine macrocycle (Fig. 23a) with a planar pentadentate pentagonal macrocycle L5 (such as depicted in Fig. 18) centered by a suitable 4d³ or 5d³ metal ion with unquenched orbital angular momentum, M(4d/5d) = Mo^III, Ru^V, W^III, Re^IV, Os^V (Fig. 23b). Synthetically, this task may be rather feasible, especially considering that the electronic structure of planar π-conjugated pentadentate macrocycles (Fig. 18) has much in common with the electronic structure of aromatic cycles of porphyrins and phthalocyanines. Calculations similar to those performed above for Mo^III–Mn^II clusters show that, even with a fairly conservative estimate of the anisotropic exchange parameters of J_z = −1000, J_xy = −200 cm⁻¹, the barrier in the trinuclear linear cluster M(3d)–O–M(4d/5d)–O–M(3d) can exceed 1500 cm⁻¹ (Fig. 23b), the current record value for Ln-based SIMs.^30–32

Even higher barriers are expected for extended structures of this type, shaped as fragments of linear heterometallic chains, such as linear pentanuclear oxo-bridged cluster shown in Fig. 24. In this case, following the established correlation U_eff ∝ |J_z − J_xy|n, the barrier can exceed 2000 cm⁻¹ due to larger number n of M(3d)–O–M(4d/5d) apical pairs in the SMM cluster; specific calculations result in U_eff = 2373 cm⁻¹ (Fig. 24).

These calculations reveal a huge potential of these systems toward new record SMM performance; indeed, even small trinuclear clusters (Fig. 23b) can potentially exhibit barriers comparable to or greater than the maximum barriers in lanthanide SMMs, around 1500 cm⁻¹.^30–32 However, practical realization of this strategy is currently greatly hampered by the extremely poorly developed chemistry of PBP 4d and 5d complexes with macrocyclic pentadentate ligands (Fig. 18).

4.5. General principles of molecular engineering high-T_B SMMs based on 4d/5d PBP complexes

Summarizing the above results, we can formulate some general principles of the molecular engineering high barriers in SMMs based on the use of uniaxial anisotropic exchange interactions of PBP 4d³ and 5d³ complexes. In heterometallic 4d/5d–M(3d) clusters, the apical M(4d/5d)–(X)–M(3d) groups are the key factor governing magnetic anisotropy, which produce uniaxial anisotropic exchange interactions of the Ising type, −J_zS^z_iS^z_j − J_xy(S^x_iS^x_x + S^y_iS^y_j) with |J_z| > |J_xy|. The contribution from a single apical group to the overall molecular magnetic anisotropy is proportional to the amplitude of the exchange parameters J_z, J_xy, namely |J_z − J_xy|.⁴² More specifically, the contribution is quantified by |J_z − J_xy|α, where the factor α takes into account the value of the spin S of the high-spin 3d ion; approximately, it is given by α ≈ 0.4S. In particular, α ≈ 1 for spin S = 5/2 of Mn^II ions.⁴² Thus, as established from the above considerations, in SMM clusters with several apical groups (n), the maximum value of the barrier is determined by the ratio U_eff ∝ |J_z − J_xy|n. This allows the barrier to scale both by enhancing the exchange parameters J_z, J_xy, and by increasing the number n of apical groups in the polynuclear cluster. Of these two factors, the first is particularly important, as can be seen from calculations in Section 4.3. Therefore, a special care has to be taken to increase magnetic coupling of PBP 4d/5d complexes with connected high-spin 3d ions. In particular, this can be achieved by using monoatomic bridging ligands with a short metal–ligand distance, as discussed in Section 4.3. The use of organic bridging radicals in the apical positions of PBP 4d/5d complexes to enhance the anisotropic exchange parameters may also be promising.

In clusters with a single PBP complex, magnetic axiality is obtained automatically, as is the case in the MoMn₂ and ReMn₄ SMM clusters (Fig. 4) and in the hypothetical trinuclear cluster shown in Fig. 23b. However, in extended clusters with several PBP complexes it is necessary to provide parallel orientation of the pentagonal axes of the PBP complexes in order to keep strict axiality of the magnetic anisotropy. Unwanted transverse magnetic anisotropy can arise due to non-parallel orientation of the easy axes of the local Ising-type spin couplings. In this regard, the use of high-spin 3d ions with large ZFS energy (Mn^III, Co^II) is undesirable because of possible decrease in magnetic axiality caused by non-parallel orientation of pentagonal axes of PBP complexes and principal ZFS axes of 3d ions. In extended polynuclear clusters, it is also important to provide sufficient magnitude of exchange interactions in the equatorial plane in order to incorporate the local Ising-type anisotropies into the global molecular anisotropy, as has been illustrated for the Mo₃Mn₃ clusters (Fig. 12). In particular, these conditions can be met in layered structures consisting of alternating layers of PBP 4d/5d complexes and high-spin 3d ions, as shown in Fig. 25. Alternatively, exchange interactions in the equatorial plane can be enhanced indirectly, through ferro- or ferrimagnetic two-dimensional layers of exchange-coupled 3d ions, with parallelly oriented PBP complexes between them (Fig. 26). This structure is preferable for PBP complexes of the [M(4d/5d)(L5)X₂] type (Fig. 18), in which coordination positions of the 4d or 5d metal ion in the equatorial plane are blocked by planar pentadentate macrocyclic ligands L5. Importantly, the lamellar structures shown in Fig. 25 and 26 can be expanded both in the apical and equatorial directions thereby providing opportunity to scale the barrier, in accordance with U_eff ∝ |J_z − J_xy|n. Square grid structures (Fig. 17) may also be promising to this end.

The structures shown in Fig. 21–26 give some idea of the general line of research aimed at practical realization of record-breaking SMM performance. Undoubtedly, synthetic route to these structures is highly challenging, especially given that very little is known about 4d/5d PBP complexes with pentadentate ligands L5 and their chemical behavior (Fig. 18).

5. Summary and outlook

The strategy presented here realizes, in a specific form, the general idea of creating high-performance SMMs by combining strong magnetic anisotropy of metal ions with unquenched orbital angular momentum through exchange interactions. In this regard, it is important to emphasize the difference between the strategies for developing polymetallic SMMs based on 4f and 4d/5d elements:

• In Ln-SMMs, it is easy to have a large unquenched orbital angular momentum (3 ≤ L ≤ 6, which is inherent in all Ln³⁺ ions except Gd³⁺), but it is difficult to arrange strong exchange interactions between Ln³⁺ ions. On the contrary, in 4d/5d transition metal complexes it is more difficult to obtain an unquenched orbital angular momentum (L = 1, M_L = ±1, the smallest among L ≠ 0), but much easier to have strong exchange interactions.

• Multi-spin Ln-SMMs are tried to be assembled from magnetically coupled mononuclear lanthanide complexes with high axial magnetic anisotropy, which are themselves high-performance SIMs.^19,57,58 In an alternative strategy outlined in the paper, neither the PBP 4d/5d complexes nor the high-spin 3d ions possess single-ion magnetic anisotropy, and they are certainly not SIMs. They produce magnetic anisotropy only cooperatively, through anisotropic exchange interactions.

• In Ln-SMMs, axiality of magnetic anisotropy is achieved by tuning the highly anisotropic crystal field environment, through adjustment of the geometric axiality of the ligand surrounding. By contrast, in SMMs based on PBP 4d/5d complexes, the axiality of magnetic anisotropy is reached through uniaxial anisotropic exchange interactions whose symmetry does not depend on the geometric symmetry.

In essence, both strategies follow the general idea of converting unquenched orbital angular momentum into high SMM performance, but they do it in very different ways. However, outside of the f-block elements, only a few transition metal complexes are capable of simultaneously providing the unquenched orbital angular momentum and strong exchange interactions. Of these, only PBP 4d/5d complexes are adequate as building blocks for high-performance SMMs due to their inherent ability to generate uniaxial exchange interactions.

On the other hand, the strategy under review differs significantly from the conventional strategy for multi-spin 3d SMMs (Fig. 3). Indeed, while in polynuclear 3d SMMs the isotropic exchange interaction does not contribute to the molecular magnetic anisotropy and serves only as an adhesive between the spins of magnetically anisotropic metal ions, in the present strategy anisotropic exchange interactions themselves are an efficient and sole source of molecular magnetic anisotropy. The latter is evidenced by the fact that low-spin PBP 4d/5d complexes and high-spin 3d ions exhibit no or very small single-ion ZFS anisotropy.

Thus, the strategy employs an alternative approach to create magnetic anisotropy, i.e., through pair-ion magnetic anisotropy rather than through single-center magnetic anisotropy (Fig. 3 and 4). However, it is important to emphasize that in most cases anisotropic exchange interactions are of no use for tailoring advanced SMMs, either because of small exchange parameters (few tens of cm⁻¹) or low (non-axial) symmetry of anisotropic exchange interactions, and often for both reasons together. In particular, this is typically the case for 3d ions and complexes with unquenched orbital angular momentum, such as Co^2+137–139 and [Fe^III(CN)₆]³⁻.¹⁴⁰ Comparative analysis of magnetic properties of various mononuclear 4f, 3d, 4d and 5d complexes as molecular building blocks with unquenched orbital angular momentum showed that the only favorable exception are orbitally degenerate PBP 4d³ and 5d³ complexes, such as [Mo^III(CN)₇]⁴⁻ and [Re^IV(CN)₇]³⁻. First, they reveal a unique property to cause highly anisotropic spin coupling of a perfect uniaxial symmetry, −J_zS^z_iS^z_j − J_xy(S^x_iS^x_j + S^y_iS^y_j), regardless of the presence or absence of the local geometric symmetry. This greatly facilitates attaining the axial limit of magnetic anisotropy of a SMM cluster as there is no longer a need to control the coordination symmetry of the magnetic building units. This is in great contrast to the situation for mono-ionic 4f and 3d SIMs, where even slight departures from the rigorous axial symmetry of the SMM molecule lead to a significant decrease in the barrier. Due to high magnetic axiality in heterometallic 4d/5d–3d clusters, the under-barrier QTM processes are suppressed and the barrier rises to the top of the double-well potential, as is the case in Mo^IIMn^II₂ SMM complexes (Fig. 7).

Secondly, in SMM clusters based on 4d/5d PBP complexes and high-spin 3d ions, the barrier U_eff is controlled by anisotropic exchange parameters J_z and J_xy and the number n of the apical linkages with attached 3d ions, U_eff ∝ |J_z − J_xy|n. This is a great advantage of the strategy, because the exchange parameters are considerably simpler to increase than the single-ion ZFS energy D, which rarely exceeds 100 cm⁻¹. One more advantage is that the straightforward correlation between the barrier U_eff and the number of apical groups n enables the barrier to be scaled by increasing the nuclearity of the SMM cluster. Note that scaling the barrier is impossible for the record mononuclear 4f and 3d SIMs, whose magnetic anisotropy is already close to the natural limit of magnetic anisotropy per one metal ion.

The goal of this paper is to provide the most detailed overview of the strategy based on 4d³ and 5d³ PBP complexes, its current state and prospects for further development. Much attention is paid to the theoretical foundations of the strategy. To this end, the origin of uniaxial anisotropic exchange interactions −J_zS^z_iS^z_j − J_xy(S^x_iS^x_j + S^y_iS^y_j) between the PBP complex [Mo^III(CN)₇]⁴⁻ and Mn^II ions attached at the apical and equatorial positions of the bipyramid is elucidated in detail. A comparative analysis of the spin energy diagrams of various Mo_kMn_m polynuclear complexes revealed that the maximum value U_eff ∝ |J_z − J_xy|n of the barrier is only reached in the presence of sufficiently strong exchange interactions in the equatorial plane; these interactions aggregate the |J_z − J_xy| contributions from the apical exchange-coupled pairs into the total magnetic anisotropy.

Central to the article is the problem of further development of the strategy and an assessment of its prospects. So far, the achieved SMM performance of Mo^IIIMn^II₂ complexes is rather low, U_eff ≈ 40–45 cm⁻¹ and T_B ≈ 3 K^92,94 (although it is record-breaking among cyanide SMMs) due to a limited magnitude of exchange interactions afforded by the cyanide bridging groups. However, the significance of these results (both experimental^92–94 and theoretical⁴²) lies not in the high U_eff and T_B values, but in the fact that they convincingly proved the consistency and practical feasibility of the new principle of designing advanced SMMs based on the anisotropic exchange interactions of PBP 4d and 5d complexes. The major problem is that so far [Mo^III(CN)₇]⁴⁻ and [Re^IV(CN)₇]³⁻ are the only available PBP 4d and 5d building blocks with unquenched orbital angular momentum. Although these systems helped to fully prove the feasibility of the new approach, they have not yet made a breakthrough in the SMM performance due to low exchange parameters (several tens of cm⁻¹, see Fig. 4) that hindered to reach higher SMM characteristics.

Since the barrier U_eff is controlled by the value of the anisotropic exchange parameters, U_eff ∝ |J_z − J_xy|n, it is necessary to find ways to significantly enhance the exchange parameters of PBP 4d/5d complexes. It is especially important to overcome the limitations imposed by the bridging μ-CN group in heptacyanide complexes. To this end, we have announced the search and study of new PBP 4d and 5d complexes, which are free from problems inherent to [Mo^III(CN)₇]⁴⁻ and [Re^IV(CN)₇]³⁻ heptacyanide complexes. Specifically, we consider PBP complexes [M(4d/5d)(L5)X₂] with pentadentate macrocyclic L5 ligands, which provide pentagonal coordination of the transition metal ion M(4d/5d) in the equatorial plane and allow various ligands X to occupy two apical positions, some of which (X = O, N, C) can provide much stronger interactions than cyanide bridging groups. Recently, our research group reported the synthesis and magnetic properties of the PBP molybdenum(III) complex [Mo^IIICl₂(DAPBH)]⁻ with Schiff base ligand that has 4d³ low-spin configuration and unquenched first-order orbital angular momentum.⁸⁷ Unfortunately, information on other similar complexes is not available in the literature. However, our theoretical calculations predicted numerous molecular structures of 4d³ and 5d³ PBP complexes [M(4d/5d)(L5)X₂] with various pentadentate ligands L5 and apical ligands X. We have shown that monoatomic μ-oxo bridging ligands with short M–O distances (≈1.8 Å) can potentially provide exceedingly strong anisotropic Ising-type exchange interactions in apical M(4d/5d)–μO–M(3d) linkages, on the order of J_z ≈ 1000 cm⁻¹ or higher. Our calculations demonstrate that with such strong exchange interactions, even in small M(3d)–O–M(4d/5d)–O–M(3d) trinuclear clusters the barrier can reach a value of about 1500 cm⁻¹, which corresponds to the current record barrier in mononuclear dysprosium-based SMMs. Even higher barrier can be obtained in extended structures of this type. We also discussed some specific ways to synthesize such complexes based on known similar μ-oxo bridged heterometallic trinuclear structures involving porphyrin and phthalocyanine 4d and 5d complexes.

These results provide some ideas for developing polynuclear SMMs with exceptionally high performance, potentially surpassing the record performance of mononuclear Dy SMMs. The general principles of the design of advanced SMMs based on PBB 4d and 5d complexes are also set. However, we are fully aware of the current state-of-the-art in this field and the long distance that separates the basic idea from its practical realization. Nevertheless, there are two reasons to be optimistic. First, the basic idea of using anisotropic exchange interactions of 4d/5d PBP complexes to create high-performance SMMs has been reliably proven, both experimentally and theoretically. In particular, the power of anisotropic exchange interactions as a source of magnetic anisotropy is vividly demonstrated by the fact that small trinuclear MoMn₂ clusters exhibit the same SMM performance (U_eff = 40.5 cm⁻¹, T_B = 3.2 K, τ₀ = 2.0 × 10⁻⁸ s)⁹² as a large Mn₁₂Ac cluster (U_eff = 45 cm⁻¹, T_B = 3 K, τ₀ = 2.8 × 10⁻⁸ s).¹⁴¹ The main difficulty in further progress lies in rather weak exchange interactions via cyano-linkages, which so far does not allow these systems to compete with the lanthanide SMMs. Secondly, 4d/5d complexes with macrocyclic pentadentate ligands L5 based on pyridinic and pyrrolic units (Fig. 18) are very similar in electronic structure to π-conjugated aromatic porphyrin and phthalocyanine complexes involved in heterometallic μ-oxo bridged 4d–3d clusters reported in ref. 133–136. This significantly increases the chances of obtaining polynuclear heterometallic oxo-bridged clusters involving PBB (4d/5d)(L5) complexes (whose prototypes are shown in Fig. 21b, 23b and 24) by using the synthetic approaches employed in preparation of structurally related polynuclear oxo-bridged clusters based of 4d/5d porphyrin and phthalocyanine complexes (Fig. 20).

It is also very likely that the new approaches toward high-T_B SMMs may be overshadowed by the current high-profile success of lanthanide SMMs. However, times may change: for instance, we can look at the situation in the field of SMM before 2003, the age of the dominance of Mn-based SMMs, which was then disappeared in a flurry of work on lanthanide SMMs. Regardless of how the field develops over the next few years however, one thing is certain: uniaxial anisotropic exchange interactions −J_zS^z_iS^z_j − J_xy(S^x_iS^x_j + S^y_iS^y_j) of PBP 4d³ and 5d³ complexes are a powerful source of magnetic anisotropy, which is quantitatively defined by the anisotropic exchange parameters, |J_z − J_xy|; significant growth of the exchange parameters can cause dramatic changes in the field of SMMs. Consequently, the concept of high-performance SMMs based on 4d/5d PBP complexes with unquenched orbital angular momentum could be an attractive alternative to the currently dominant lanthanide-based SMM strategy.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the Russian Science Foundation (project no. 18-13-00264-P). Yu. V. M. and T. A. B. acknowledge support by the Ministry of Education and Science of the Russian Federation, State task AAAA-A19-119071190045-0 in part of the development and implementation of strategies for the synthesis of 4d and 5d PBP complexes. V. S. M. acknowledges support by the Ministry of Science and Higher Education within the State assignment FSRC ‘Crystallography and Photonics’ RAS in part of the development of computational approaches for analysis of extreme magnetic anisotropy in transition-metal complexes.

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