Jean-Pascal Sutter

Virginie Béreau

Valentin Jubault

Kateryna Bretosh

Céline Pichon

Carine Duhayon

Magnetic Anisotropy of Transition Metal and Lanthanide Ions in Pentagonal Bipyramidal Geometry §

Magnetic Anisotropy of Transition Metal and Lanthanide Ions in Pentagonal Bipyramid Geometry

The magnetic anisotropy associated with a PBP coordination sphere is examined on the basis of experimental and theoretical investigations; its origin and characteristics are described, and the effects of crystal field, structural distortion, and the second coordination sphere are discussed. § Formalisms used in this paper: Spin Hamiltonian with ZFS terms describing the magnetic anisotropy: H 1 /3 µ , where D and E are the axial and rhombic ZFS parameters, S the spin, the last part corresponds to the Zeeman term, B stands for the magnetic field vector. The exchange interactions are given in accordance with Hamiltonians of type H = -JS1•S2 (example for a pair of spins)

Magnetic anisotropy is a key parameter of the behavior exhibited by magnetic materials. For instance, the hardness of a bulk magnet correlates with its magnetic anisotropy; the performance of a single molecule magnet (SMM) is highly dependent on large and strongly axial magnetic anisotropy, whereas for molecular Spin Qubits, small and in-plan magnetic anisotropy is preferable. The magnetic anisotropy emanates mainly from the metal centers constituting the compound; its characteristics (strength, axial or planar) depend on the metal ion, the electronic configuration, the coordination geometry, and the ligand field. It is therefore possible to impart magnetic anisotropy to a compound in a controlled way by chemical design.

Seven-coordinated metal complexes with pentagonal bipyramid-shaped coordination sphere (abbreviated to PBP hereafter) have emerged recently as an attractive option for achieving large magnetic anisotropy in a molecular unit. [START_REF] Bar | Magnetic anisotropy in two-to eight-coordinated transition-metal complexes: Recent developments in molecular magnetism[END_REF][START_REF] Gómez-Coca | Large magnetic anisotropy in mononuclear metal complexes[END_REF] This applies for transition metal and lanthanide ions with suitable electronic configurations. In several cases, mononuclear complexes have been found to exhibit SMM-type behaviors. More generally, this coordination geometry allows easy access to a wide range of axial or planar magnetic anisotropy that depends mainly on the metal ion involved.

Access to PBP shaped coordination sphere can be straightforward. Following a strategy documented in the 70s, [START_REF] Wester | Synthesis and characterization of novel pentagonal bipyramidal complexes of iron(II), cobalt(II), and zinc(II)[END_REF][START_REF] Drew | Seven-coordinate complexes of iron(II) with pentadentate macrocyclic ligands[END_REF][START_REF] Bishop | X-Ray crystal structure of a planar, high-spin iron(II) complex of a pentadentate unsaturated macrocycle formed by reaction of 2,9-di(1-methylhydrazino)1,10-phenanthroline monohydrochloride with 2,6-diacetylpyridine[END_REF] this geometry can be designed using a suitable pentadente ligand (Figure 1) to occupy five equatorial coordination sites of the metal center. [START_REF] Ivanovic-Burmazovic | Advances in Inorganic Chemistry[END_REF][START_REF] Popov | Metal complexes with polyfunctional ligands based of bis(hydrazones) of dicarbonyl compounds[END_REF][START_REF] Bhula | Complexes of tridentate and pentadentate macrocyclic ligands[END_REF] The pentadentate ligand also confers to the complex a good structural robustness making possible the substitution of the labile ligands (solvents, anions) in axial positions without compromising the coordination geometry, [START_REF] Gavey | Coordination complexes of 15-membered pentadentate aza, oxoaza and thiaaza Schiff base macrocycles "Old Complexes Offer New Attractions[END_REF] thus preserving the magnetic anisotropy. This allowed using these complexes as building blocks in the design of polynuclear systems such as SMM (Single Molecule Magnets) and SCM (Single Chain Magnets). The objective of this paper is to review the knowledge acquired on the magnetic anisotropy of transition metal and rare earth ions with PBP coordination sphere. A first section is devoted to the transition metal complexes, where the origin of the magnetic anisotropy in PBP geometry will be introduced and the main experimental conclusions summarized for the most relevant metal ions. The use of such PBP complexes as building units to incorporate controlled magnetic anisotropy in polynuclear species is also illustrated. The second section focuses on lanthanide ions.

I. Transition metal ions with pentagonal bipyramidal coordination polyhedron

The qualitative splitting pattern of the d orbitals in ideal pentagonal bipyramidal crystal field (D5h) is depicted in Figure 2a. It consists in two sets of two-degenerate orbitals, plus one orbital of higher energy. Such a situation is favorable for first-order spin-orbit coupling for electronic configurations leading to a filling of a degenerate level with 3 electrons. However, in real systems, the degeneracies are lifted due to distortion of the coordination sphere and unsymmetrical ligand field (Figure 2b-c). [START_REF] Ruamps | Origin of the Magnetic Anisotropy in Ni(II) and Co(II) Heptacoordinate Complexes[END_REF][START_REF] Sarkar | Role of Coordination Number and Geometry in Controlling the Magnetic Anisotropy in Fe II , Co II , and Ni II Single-Ion Magnets[END_REF] Therefore, spin-orbit coupling in the complexes results mainly from zero-field splitting (ZFS), and magnetic anisotropy is characterized by axial ZFS parameter D, and rhombic parameter E. It relies on coupling between ground electronic state and excited states, therefore electronic configuration and the energy of the electronic transitions dictate D. The value of D will be all the greater the smaller the energy gap between the ground state and the excited states. It follows that the strongest contribution to D will come from the coupling with the first excited states. For the electron transitions between orbitals with same magnetic quantum number, ml, [START_REF]The magnetic quantum numbers for the d orbitals is ml = 0 for dz, ml = 1 for dxz and dyz, and ml = 2 for dxy and dx2-y2[END_REF] the sign of the contribution to D is negative while transitions between orbitals of different ml yield positive values. These simple considerations make it possible to anticipate the sign of D for a given electronic configuration. For instance, the orbital filling for a d [START_REF] Ivanovic-Burmazovic | Advances in Inorganic Chemistry[END_REF] ion with high spin configuration (Figure 2b) leads to two electrons in the lowest energy orbital, , and one electron in each of the other four orbitals. The first excited quintet state results from the promotion of one electron from the orbital to the orbital, which are very close in energy, whereas second and third excited quintet (corresponding to the promotion of the electron to the and orbitals) are higher in energy. [START_REF] Bar | Pentagonal Bipyramid FeII Complexes: Robust Ising-Spin Units towards Heteropolynuclear Nanomagnets[END_REF] Consequently, the strongest contribution to the D parameter is expected from the first excited state, and since ml remains unchanged, this contribution is negative. An overall negative D value can therefore be anticipated for high-spin Fe II , and this is supported by experimental data (vide infra). For a high-spin d 7 configuration (Figure 2c) typical for Co II , the strongest contributions to the axial D parameter are expected from the excited quartet states resulting from the promotion of an electron from or orbitals to the orbital. [START_REF] Ruamps | Origin of the Magnetic Anisotropy in Ni(II) and Co(II) Heptacoordinate Complexes[END_REF] These contributions being positive, an overall positive D parameter can be expected for such a metal complex, which is indeed found experimentally. Of course, the actual magnitude of D will depend on all the contributions that are directly related to the effective energy diagram for the d orbitals. The latter relies on structural and chemical aspects. The magnetic anisotropy reported for various electronic configurations are reviewed below and the effects of structural and chemical features will be discussed.

I.1 d 1 ions (V IV )

Few PBP metal complexes of d 1 electronic configuration have been reported and the characterization of their magnetic features remained basic. The presence of a single electron in the dorbitals results in S = ½ spin state which excludes any ZFS, hence magnetic anisotropy. PBP V IV is found in oxo-bridged bimetallic [µ-O-{V(L2 NH2 )(MeOH)}2] 2+ complex and its magnetic behavior is consistent with two S = ½ spin centers. 14 I.2 d 2 ions (V III , Mo IV , W IV )

The presence of two electrons in the two low-lying orbitals (Figure 2) is anticipated to result in a ground spin state of S = 1 displaying magnetic anisotropy characterized by ZFS with a positive D parameter.

A very early example of heptacoordinated 3d 2 ion with an organic ligand set in PBP arrangement was K4[V(CN)7], 15 16 but no information about its magnetic anisotropy is available. A detailed investigation of the ZFS parameters for V III in PBP environment was performed for a series of complexes obtained with the pentadentate ligand H2L1 Ph in various states of deprotonation (Table 1). [START_REF] Bazhenova | The first pentagonal-bipyramidal vanadium (III) complexes with a Schiff-base N3O2 pentadentate ligand: synthesis, structure and magnetic properties[END_REF] Combined magnetic, high-field EPR, and theoretical studies concluded in the absence of first-order spin-orbit coupling due to degeneracy lifting of the two lower energy levels and converged to anisotropy parameters D in the range of 3.9-4.5 cm -1 , and negligibly small E. The magnetic behavior for two complexes, [V III (tepa)(µ-Sn2Q6)]n (tepa stands for tetraethylenepentamine, Q = S or Se), featuring an open N5-pentadentade ligand and either S or Se atoms in the apical positions have been reported but no information on the magnetic anisotropy was provided. [START_REF] Chen | One-Dimensional Vanadium(III) Chalcogenidostannates Incorporating [V(tepa)] 3+ Complexes as Bridging Groups[END_REF] Significantly larger ZFS effects have been found for second and third row metal ions. A 4d complex with Mo IV , [Mo(L1 Ph )Cl2], was found to undergo a rapid decrease of its magnetic moment below 50 K attributed to thermal depopulations of the excited MS = +/-1 levels resulting from ZFS of the S = 1 triplet state. [START_REF] Mironov | A new Mo(iv) complex with the pentadentate (N3O2) Schiff-base ligand: the first non-cyanide pentagonal-bipyramidal paramagnetic 4d complex[END_REF] The temperature dependence of the magnetic susceptibility (χM) was modeled considering a ZFS effect with D = 50 cm -1 , and it was noticed that a substantial temperature independent paramagnetism (TIP) contributed to the experimental behavior.

The effect of spin-orbit interaction is even more noticeable for 5d ions. The W IV complex, [W(CN)7] 3-, was found to exhibit a non-magnetic ground state at 2 K, and a χMT value increasing with T but reaching only 0.77 cm 3 mol -1 K at 300 K. This value, below the contribution expected for an S = 1 spin, suggests a partial thermal population of first excited levels (with MS = +/-1) even at 300 K, hence a large energy gap with ground level. The behavior was analyzed supposing ZFS of the S = 1 ground state and led to an axial parameter as large as D = 430 cm -1 . [START_REF] Birk | The Heptacyanotungstate(IV) Anion: A New 5 d Transition-Metal Member of the Rare Heptacyanometallate Family of Anions[END_REF] Ligand Field calculations supported the magnitude of the ZFS energy. [START_REF] Mironov | A new Mo(iv) complex with the pentadentate (N3O2) Schiff-base ligand: the first non-cyanide pentagonal-bipyramidal paramagnetic 4d complex[END_REF]

Complex

ZFS parameters (cm -1 ) Ref. Two situations can apply for a d 3 spin configuration in PBP geometry; either it is high spin and gives rise to a spin state S = 3/2, or it is low spin with S = ½.

The high-spin configuration has been found to apply in Cr III PBP derivatives (Table 2). In an ideal PBP geometry, two electrons would be in the low-lying and orbitals and the third would be shared by the and orbitals (Figure 2). Such a situation would lead to significant axial anisotropy (D < 0); however, real compounds exhibit coordination dissymmetry in the pentagonal plane due to Jahn-Teller effect (Figure 3) that lifts the / orbitals degeneracy aimed at reducing the total energy of the system. [START_REF] Bazhenova | A novel family of hepta-coordinated Cr(III) complexes with a planar pentadentate N3O2 Schiff base ligand: synthesis, structure and magnetism[END_REF][START_REF] Pichon | From Heptacoordinated CrIII Complexes with Cyanide or Isothiocyanate Apical Groups to 1D Heterometallic Assemblages with All-Pentagonal-Bipyramid Coordination Geometries[END_REF] As a result, magnetic anisotropy was evaluated to be very small with |D| in the order of 1-2 cm -1 . [START_REF] Pichon | From Heptacoordinated CrIII Complexes with Cyanide or Isothiocyanate Apical Groups to 1D Heterometallic Assemblages with All-Pentagonal-Bipyramid Coordination Geometries[END_REF] Theoretical calculations performed for [Cr(HL1 PhOMe )(Cl)2] and [Cr(L1 Ph )(CN)2] - moieties indicated a negative D close to -1 cm -1 . [START_REF] Bazhenova | A novel family of hepta-coordinated Cr(III) complexes with a planar pentadentate N3O2 Schiff base ligand: synthesis, structure and magnetism[END_REF][START_REF] Pichon | Cyano-Bridged Fe(II)-Cr(III) Single-Chain Magnet Based on Pentagonal Bipyramid Units: On the Added Value of Aligned Axial Anisotropy[END_REF][START_REF] Pichon | Trinuclear Cyanido-Bridged [Cr2Fe] Complexes: To Be or not to Be a Single-Molecule Magnet, a Matter of Straightness[END_REF] Such overall small magnetic anisotropy is rationalized by the energy difference of the and orbitals introduced by the Jahn-Teller distortion. The concomitant increase of the energy gap between the ground state and the first excited state, i.e. ( ) 1 ( ) 0 <-> ( ) 0 ( ) 1 reduces its negative contribution to D that becomes balanced by the positive contributions from the higher excited states. The known 4d 3 and 5d 3 ions with PBP coordination polyhedron have low spin configuration with an S = ½ ground spin state characterized by strongly anisotropic g parameters (Table 2). The isoelectronic cyanometallate complexes [Mo III (CN)7] 4-and [Re IV (CN)7] 3-are well investigated examples. Detailed magnetic studies down to 2 K have been reported for a structurally rigid complex, NEt4[Mo(L1 Ph )Cl2] and its behavior rationalized by ligand field calculations. [START_REF] Manakin | Et4N)[Mo III (DAPBH)Cl2], the first pentagonal-bipyramidal Mo(iii) complex with a N3O2-type Schiff-base ligand: manifestation of unquenched orbital momentum and Ising-type magnetic anisotropy[END_REF] Such compounds are not expected to exhibit magnetic anisotropy (ZFS takes place only for S > ½) but unquenched orbital momentum occurs. Due to the orbital degeneracy and strong spin-orbit coupling, the ground state of the PBP complex is split into two Kramers doublets (ϕ(±1/2) and χ(±1/2) in Figure 4). The ground-state Kramers doublet was found to exhibit strong magnetic anisotropy with spin and orbital momenta parallel to the apical direction of the complex. [START_REF] Manakin | Et4N)[Mo III (DAPBH)Cl2], the first pentagonal-bipyramidal Mo(iii) complex with a N3O2-type Schiff-base ligand: manifestation of unquenched orbital momentum and Ising-type magnetic anisotropy[END_REF] This results in a highly anisotropic g tensor; for instance g⊥ = 1.77 and g|| = , where Mo has PBP coordination sphere. [START_REF] Hursthouse | The X-ray crystal structure of NaK3[Mo(CN)7],2H2O and the structure of its anion in aqueous solution[END_REF] For the Re IV homologue, g⊥ = 1.759 and g|| = 3.66 have been found. [START_REF] Bennet | New cyanometalate building units: Synthesis and characterization of[END_REF]28 Somewhat less anisotropic g was observed for a PBP W III derivative with mixed carbonyl/cyanide ligand set, cis-[W(CN)5(CO)2] 2-, but EPR was recorded in solution. [START_REF] Karunadasa | Synthesis and Redox-Induced Structural Isomerization of the Pentagonal Bipyramidal Complexes [W(CN)5(CO)2] 3and [W(CN)5(CO)2] 2[END_REF] Ab initio calculations performed for [Mo(L1 Ph )Cl2] -reveal large anisotropy for the magnetic susceptibility with a susceptibility along the Cl-Mo-Cl direction, χz, about two order of magnitude larger than the χx and χy components. Such a situation was found to favor highly anisotropic exchange interaction with 3d ions which can be source for magnetic anisotropy in polynuclear compounds. [START_REF] Mironov | New Approaches to the Problem of High-Temperature Single-Molecule Magnets[END_REF][START_REF] Mironov | Origin of Dissimilar Single-Molecule Magnet Behavior of Three Mn II 2Mo III Complexes Based on [Mo III (CN)7] 4-Heptacyanomolybdate: Interplay of Mo III -CN-Mn II Anisotropic Exchange Interactions[END_REF][START_REF] Mironov | Mechanism of a Strongly Anisotropic Mo III -CN-Mn II Spin-Spin Coupling in Molecular Magnets Based on the [Mo(CN)7] 4-Heptacyanometalate: A New Strategy for Single-Molecule Magnets with High Blocking Temperatures[END_REF] PBP d 3 units in polynuclear compounds. These PBP complexes have been used in the preparation of polynuclear compounds because of the exchange interactions they can establish with the paramagnetic ions to which they are bound. For instance, 1-D compounds have been formed with [Cr(L1 R )(CN)2] -and Mn II , [START_REF] Pichon | From Heptacoordinated CrIII Complexes with Cyanide or Isothiocyanate Apical Groups to 1D Heterometallic Assemblages with All-Pentagonal-Bipyramid Coordination Geometries[END_REF] Fe II , [START_REF] Pichon | Cyano-Bridged Fe(II)-Cr(III) Single-Chain Magnet Based on Pentagonal Bipyramid Units: On the Added Value of Aligned Axial Anisotropy[END_REF] or Ni II , [START_REF] Bretosh | A ferromagnetic Ni(II)-Cr(III) single-chain magnet based on pentagonal bipyramidal building units[END_REF] the last two are ferromagnetic SCMs. Trinuclear [Cr2Fe] complexes involving same Cr metallo-ligand and PBP Fe II were found to behave as SMMs. [START_REF] Pichon | Trinuclear Cyanido-Bridged [Cr2Fe] Complexes: To Be or not to Be a Single-Molecule Magnet, a Matter of Straightness[END_REF] The combination of PBP [Mo(CN)7] 4-and Mn II units, which do not exhibit any magnetic anisotropy due to ZFS, can lead to compounds with a behavior characterized by magnetic anisotropy. For instance, [Mo(CN)7] 4-has been involved in several 3-D magnets, some with ferrimagnetic order for temperatures above 100 K. [START_REF] Milon | Nanoporous magnets of chiral and racemic [{Mn(HL)}2Mn{Mo(CN)7}2] with switchable ordering temperatures (TC = 85 K ↔ 106 K) driven by H2O sorption (L = N,N-dimethylalaninol)[END_REF][START_REF] Tanase | Substantial increase of the ordering temperature for [Mn(II)/Mo(CN)7]-based magnets as a function of the 3d ion site geometry: Example of two supramolecular materials with Tc = 75 and 106 K[END_REF][START_REF] Tomono | Vanadium(II) Heptacyanomolybdate(III)-Based Magnet Exhibiting a High Curie Temperature of 110 K[END_REF] A rather unexpected feature of these magnets containing S = ½ units and high-spin Mn II is the large magnetic hysteresis loops they can exhibit. This correlates with the actual geometry of the [Mo(CN)7] 4-moieties in the framework, [START_REF] Chibotaru | Magnetic Anisotropy of [Mo(CN)7] 4-Anions and Fragments of Cyano-Bridged Magnetic Networks[END_REF] with the largest magnetic anisotropy (i.e. large magnetic hysteresis) observed when Mo units exhibit a PBP shape. [START_REF] Magott | Correlating magnetic anisotropy with [Mo(CN)7] 4geometry of Mn II -Mo III magnetic frameworks[END_REF] Similarly, discrete or 1-D derivatives involving PBP [Mo(CN)7] 4-and Mn II were found to behave as SMM or SCM but this is the case only when the Mn is connected to the CN-ligands in the apical positions of the Mo III . [START_REF] Wang | A Docosanuclear {Mo8Mn14} Cluster Based on [Mo(CN)7] 4[END_REF][START_REF] Qian | A Single-Molecule Magnet Based on Heptacyanomolybdate with the Highest Energy Barrier for a Cyanide Compound[END_REF][START_REF] Wu | Reversible On-Off Switching of a Single-Molecule Magnet via a Crystal-to-Crystal Chemical Transformation[END_REF][START_REF] Shi | Enhanced Single-Chain Magnet Behavior via Anisotropic Exchange in a Cyano-Bridged Mo III -Mn II Chain[END_REF] The actual origin of the magnetic anisotropy exhibited by these polynuclear species results from anisotropic Mo-Mn exchange interactions. [START_REF] Mironov | Origin of Dissimilar Single-Molecule Magnet Behavior of Three Mn II 2Mo III Complexes Based on [Mo III (CN)7] 4-Heptacyanomolybdate: Interplay of Mo III -CN-Mn II Anisotropic Exchange Interactions[END_REF] Same applies for 5d derivative [Re(CN)7] 3-in PBP geometry. Several pentanuclear [M II 4Re] complexes involving PBP [Re(CN)7] 3-and = Mn II , Ni II , and Cu II were reported to exhibit magnetic anisotropy. [START_REF] Freedman | A Redox-Switchable Single-Molecule Magnet Incorporating [Re(CN)7] 3[END_REF][START_REF] Zadrozny | Slow Magnetic Relaxation and Charge-Transfer in Cyano-Bridged Coordination Clusters Incorporating [Re(CN)7] 3-/4[END_REF] Complexes Spin state ZFS parameters D(E) (cm -1 ) Ref.

Experimental

Theory (g) [Cr(HL1 NH2 )(H2O)2] 2+

I.4 d 4 ions (Mn III )

Examples of high-spin d 4 complexes with PBP coordination sphere are scarce. The magnetic anisotropy for two Mn III derivatives, [Mn(L3)X2]PF6 (X = Cl -, Br -) have been reported. These complexes have been obtained by oxidation of pre-existing PBP Mn II complex [Mn(L3)Cl(MeOH)]PF6 with either NOPF6 or Br2. [START_REF] Dabrowiak | Accessibility of Manganese oxidation states. Control by pentaaza macrocyclic ligands[END_REF] Their Curie constants of 2.95-3.0 cm 3 mol -1 K are in agreement with S = 2 spin state. Axial ZFS parameter of D = -2.11 cm -1 and -2.59 cm -1 , respectively for X = Cl and Br with g|| = 1.95, g⊥ = 1.98, were estimated from low temperature magnetic susceptibility behaviors. [START_REF] Cofield | Low-temperature magnetic susceptibility and zero-field splitting in some high-spin manganese(III) compounds[END_REF] The very few reports on PBP Mn III complexes could be ascribed to the limited stability of this higher oxidation state in pentagonal bipyramidal coordination sphere. For example, oxidation of the Mn II complex formed with ligand L3 allowed isolation of the Mn III derivative, whereas with homologous ligands but with ring sizes of [16] or [17] atoms spontaneous reduction was observed in the absence of oxidant. Similar observations were made for complexes based on the ligand H2L1 R . Oxidation of the Mn II complexes with Br2 led to green solutions indicating oxidation to Mn III but this color faded after a short time to orange color characteristic of the divalent complexes. 50 I.5 d 5 ions (Mn II , Fe III ) With half field d-shell, a high-spin 3d [START_REF] Bishop | X-Ray crystal structure of a planar, high-spin iron(II) complex of a pentadentate unsaturated macrocycle formed by reaction of 2,9-di(1-methylhydrazino)1,10-phenanthroline monohydrochloride with 2,6-diacetylpyridine[END_REF] ion is expected to display weak magnetic anisotropy. EPR studies performed on Mn II complexes have consistently yielded very small D parameters, typically below 0.1 cm -1 (Table 3). A typical example is [Mn(L3)(H2O)2]•2Cl for which extensive X and Q band EPR studies performed in the solid state for a diluted sample at 300 K and 77 K, led to an axial crystal-field parameter D = 0.07 cm -1 . [START_REF] Jiménez-Sandoval | Magnetostructural behavior of the complex [MnL(H2O)2]Cl2, 4H2O at variable temperature studied bu electron spin resonance (L = 2,13-dimethyl-3[END_REF] For [Mn(L5 R )] 2+ (R = 2-benzimidazolylmethyl), [START_REF] Drahoš | Structural, magnetic, redox and theoretical characterization of seven-coordinate first-row transition metal complexes with a macrocyclic ligand containing two benzimidazolyl N-pendant arms[END_REF] a combined analysis of low temperature magnetic behavior and theoretical calculations resulted in negative D values (-0.30 and -0.12 cm -1 , respectively). Moreover, D was found rather insensitive to the nature of the ligands in the apical positions for the series of complexes [Mn(L5 H )X2] with X = Cl -, Br -, I -, N3 -, or NCS -. [START_REF] Drahoš | Structural, Magnetic, and Redox Diversity of First-Row Transition Metal Complexes of a Pyridine-Based Macrocycle: Well-Marked Trends Supported by Theoretical DFT Calculations[END_REF][START_REF] Drahos | Structural and magnetic properties of heptacoordinated MnII complexes containing a 15-membered pyridine-based macrocycle and halido/pseudohalido axial coligands[END_REF] Fe III complexes with PBP coordination sphere are readily stabilized by a pentadentate ligand and have high-spin electronic configuration. [START_REF] Fleischer | The structure of two seven-coordinate complexes of iron(III)[END_REF][START_REF] Nelson | Seven-Coordination in Some Mononuclear and Binuclear Iron(III) Complexes Containing a Pentadentate Macrocyclic Ring[END_REF][START_REF] Darmanović | Combined Experimental and Theoretical Investigation of the Origin of Magnetic Anisotropy in Pentagonal Bipyramidal Isothiocyanato Co(II), Ni(II), and Fe(III) Complexes with Quaternary-Ammonium-Functionalized 2,6-Diacetylpyridine Bisacylhydrazone[END_REF][START_REF] Constable | Iron complexes of derivatised pentadentate macrocyclic ligands; the crystal and molecular structure of dichloro(6,13-(bis-2-hydroxyethyl)-6H, 13H-tripyrido[cd,fg,lm] [1,2,4,7,9,10,13] heptaazapent adecine)iron (III) chloride[END_REF][START_REF] Craig | Synthesis of a novel heptacoordinated Fe(III) dinuclear complex: experimental and theoretical study of the magnetic properties[END_REF] Earlier Mössbauer results for a series of [Fe(L3)X2] + derivatives suggested an effect of the apical ligands on the sign of D, with a change from positive (X = Cl -, Br -, I -) to negative (X = NCS -, N3 -). [START_REF] Cotton | EPR spectra of seven coordinate iron(III) complexes[END_REF][START_REF] Deeney | Relaxation effects in the mössbauer spectra of some sevencoordinate iron(III) complexes[END_REF] EPR studies for derivatives with X = Cl -and NCS -pointed to small |D| values in the order of 1 cm -1 while magnetic susceptibility investigations for X = I -and NCS -derivatives resulted in |D| = 10.3 and 7.98 cm -1 , respectively. [START_REF] Scoville | A low temperature magnetic suceptibility study of the zero field splitting in seven coordinate high-spin iron(III) complexes based on a pentadentate macrocyclic nitrogen ligand[END_REF] A detailed investigation for [Fe(L1 NMe3 )(NCS)2] + lead to values of |D| = 1.67 and 1.57 cm -1 (from EPR and susceptibility data), whereas theoretical calculations confirmed a negative sign for this parameter. [START_REF] Darmanović | Combined Experimental and Theoretical Investigation of the Origin of Magnetic Anisotropy in Pentagonal Bipyramidal Isothiocyanato Co(II), Ni(II), and Fe(III) Complexes with Quaternary-Ammonium-Functionalized 2,6-Diacetylpyridine Bisacylhydrazone[END_REF] The Mössbauer spectra at 4.2 K for [Fe(L1 NMe3 )(NCS)2] + and [Fe(L3)(NCS)2] + display marked differences, the first consists in a broad singlet whereas the second shows a six-line pattern. This latter is attributed to longer spin-spin relaxation times. [START_REF] Deeney | Relaxation effects in the mössbauer spectra of some sevencoordinate iron(III) complexes[END_REF] Regardless of any interest in magnetic anisotropy, PBP Mn II complexes have been widely used as building blocks for polynuclear structures. [START_REF] Gavey | Coordination complexes of 15-membered pentadentate aza, oxoaza and thiaaza Schiff base macrocycles "Old Complexes Offer New Attractions[END_REF] The related Fe III PBP derivatives seem to have attracted much less interest. [START_REF] Venkatakrishnan | Self-assembly of a Fe III (L) complex with octacyano metallate [MIV(CN)8] 4-(L = pentadentate macrocyclic ligand, M = Mo, W) : Crystal structure and magnetic properties[END_REF]

Complexes

Spin state ZFS parameters (cm -1 ) Ref.

Mn(II)

[Mn(H2L1 NH2 )(NCS

I.6 d 6 ions (Fe II )

In PBP coordination sphere Fe II has high-spin configuration with S = 2 (Figure 2) and was found to exhibit a magnetic anisotropy characterized by a negative D parameter (Table 4). This easy-axis anisotropy is perpendicular to the pentagonal plane of the PBP geometry, aligned along the X-Fe-X direction (X are the atoms in apical positions) as depicted in Figure 5 by the blue arrow. [Fe(H2L1 Ph )Cl2] with its magnetic axes; easy-axis is depicted in blue, x and y are green and red, respectively (Reproduced from reference [START_REF] Bar | Pentagonal Bipyramid FeII Complexes: Robust Ising-Spin Units towards Heteropolynuclear Nanomagnets[END_REF] with permission from Wiley-VCH, copyright 2022), and sketch showing the first three excited states which coupling with ground state give strongest contributions to D for PBP Fe II complexes.

The first quantitative information on the axial ZFS parameter of Fe II in this geometry was provided for [Fe(L3)(H2O)2]•2Cl with a D value of -17 cm -1 deduced from magnetization and high-field EPR experiments. [START_REF] Venkatakrishnan | Enhanced Ion Anisotropy by Nonconventional Coordination Geometry: Single-Chain Magnet Behavior for a [{Fe II L}2{Nb IV (CN)8}] Helical Chain Compound Designed with Heptacoordinate Fe II[END_REF] Subsequent examples revealed that the magnetic anisotropy exhibited by Fe II can vary significantly with the coordination environment of the metal center, D values ranging between -25 cm - 1 and +7.9 cm -1 have been reported (Table 4). For instance, in a series of complexes with pentadentate ligand H2L1 Ph in equatorial positions, the presence of either Cl or H2O in the axial coordination sites of Fe II resulted in a decrease of its magnetic anisotropy from D = -13.3 to -4.0 cm -1 , respectively. [START_REF] Bar | Pentagonal Bipyramid FeII Complexes: Robust Ising-Spin Units towards Heteropolynuclear Nanomagnets[END_REF] Theoretical calculations showed that the main contribution to the negative D parameter is brought by a single excited state corresponding to the promotion of an electron from the to the orbital (Figure 5). Since ZFS is inversely proportional to the energy difference between the ground state and the excited states, D for a PBP Fe II complex mainly depends on the energy gap between the two lowest quintet states (i.e. the ground and the first excited state). This energy difference can be related directly to the energy difference between the and the orbitals. Calculations performed for [Fe(H2L1 Ph )Cl2] revealed close lying orbitals with an energy difference of ca 170 cm -1 while for [Fe(L1 Ph )(MeOH)H2O](BF4)2 this gap reaches ca 410 cm -1 . This situation has been rationalized by the πinteractions occurring between the Fe II and the ligands in apical positions (Figure 6). For Cl -, the lone pairs have two identical π-interactions with the metal ion in the x and y directions whereas for the Oligands (H2O or ROH) only a single π-interaction takes place, which differentiates the from the orbital. For this reason, the contribution from the first excited state to the overall D for [Fe(H2L1 Ph )Cl2] is stronger than for [Fe(H2L1 Ph )(MeOH)H2O]•2BF4 with respectively -28.30 and -18.95 cm -1 ; in agreement with the more negative D value found experimentally for the former complex. The same argument of symmetrical metal-ligands π-interactions was shown to hold for N-bonded cyanide ligands in [Fe(H2L1 Ph ){Ni(CN)4}], which D is similar to that of [Fe(H2L1 Ph )Cl2]. It may be noticed that the largest magnetic anisotropies have been reported for Fe complexes with N-coordinated nitrile groups in apical positions. [START_REF] Deng | Synthesis and magnetic studies of pentagonal bipyramidal metal complexes of Fe, Co and Ni[END_REF][START_REF] Mondal | Effect of Axial Ligands on Easy-Axis Anisotropy and Field-Induced Slow Magnetic Relaxation in Heptacoordinated FeII Complexes[END_REF] It is interesting to note that the quadrupole splitting (∆) observed by Mössbauer spectroscopy for a series of [Fe(HL1 Ph )X2] complexes has been found to vary significantly depending on the ligands in apical positions. [START_REF] Bar | Pentagonal Bipyramid FeII Complexes: Robust Ising-Spin Units towards Heteropolynuclear Nanomagnets[END_REF][START_REF] Bar | Single-ion magnet behaviour of heptacoordinated Fe(II) complexes: on the importance of supramolecular organization[END_REF] Thus, a quadrupole splitting of ∆ = 3.07 mm s -1 was observed when X = ROH while smallest splitting with ∆ = 1.67 mm s -1 was found for X = Cl; for X = {Ni(CN)4} an intermediate value of ∆ = 2.29 mm s -1 was obtained. This effect of the apical ligands can be paralleled by the variations of D of these complexes which range from -4.0 cm -1 for X = ROH to -13.3 cm -1 for X = Cl, whereas an intermediate anisotropy with D = -10.7 cm -1 characterizes the complex with X = {Ni(CN)4}.

An overall more negative D can be also achieved if the positive contributions to D arising for higher excited states are reduced. This possibility was illustrated with the complexes [Fe(H2L1 NHPh )X2], where X = NCS -, NCSe -, or N(CN)2 -are ligands leading to weak π-interactions with the metal orbitals. Theoretical calculations revealed an energy difference of about 4000 cm -1 between the low lying / orbitals and the / orbital set; 69 a gap significantly larger than the ca 2600 cm -1 found for [Fe(H2L1 Ph )Cl2]. [START_REF] Bar | Pentagonal Bipyramid FeII Complexes: Robust Ising-Spin Units towards Heteropolynuclear Nanomagnets[END_REF] For this series of complexes, D spanning from -14.3 to -25.9 cm -1 have been deduced from magnetic behaviors (Table 4). A strong modulation on D was evidenced for PBP complexes based on ligand L5 R where R groups are two moieties coordinated in the apical positions of Fe II . For R = carboxylate the magnetic anisotropy was characterized by D = -9.6 cm -1 whereas a positive value of 7.9 cm -1 was obtained with R = benzimidazole. [START_REF] Drahoš | Structural, magnetic, redox and theoretical characterization of seven-coordinate first-row transition metal complexes with a macrocyclic ligand containing two benzimidazolyl N-pendant arms[END_REF][START_REF] Antal | Structure and Magnetism of Seven-Coordinate FeIII, FeII, CoII and NiII Complexes Containing a Heptadentate 15-Membered Pyridine-Based Macrocyclic Ligand[END_REF] For the latter, the positive value for D was attributed to a distortion of the coordination polyhedron with respect to PBP geometry. This example well illustrates that the energy difference between the and the orbitals is also related to structural considerations. Thus it will be all the smaller when the ligand set in the equatorial positions form a regular pentagonal polyhedron and when this ligand field is more symmetrical. Consequently, magnetic anisotropy will increase the more the coordination polyhedron becomes closer to PBP geometry. Moreover, approaching degeneracy of the and the orbitals should also favor the emergence of first order spin-orbit coupling that might be the best way to reach substantial magnetic anisotropy in PBP Fe II complexes.

Complexes ZFS parameters (cm

[Fe(H2L1 R )Cl2] R = Ph R = NH2 -13.3 -13.0 - 3 2.30 2.16
SMMs: Several Fe complexes showed SMM-like behavior (Table 4), which is associated with their axial anisotropy. However, slow relaxation is usually observed only when a static magnetic field is applied. Since Fe II has integer spin, rhombic anisotropy (E) leads to fast resonant quantum tunneling of magnetization (QTM) through degenerate energy levels. This fast relaxation of the magnetization can be efficiently reduced upon application of a magnetic field that lifts the degeneracy of the ±mS levels. However, this may not be sufficient to observed SMM behavior even if complexes have similar D (see Table 4). Spin-dipolar interactions between neighboring centers in the lattice are also responsible for the relaxation. Such spin-lattice interactions are suppressed when the spin in the lattice have their easy axes all aligned along the same direction. This may be obtained by serendipity as a result of the crystal packing but can also be controlled by crystal engineering. For instance, the diamagnetic cyanometallate [Ni(CN)4] 2-has been used to organize PBP Fe II complexes in 1D [Fe(L1 R ){Ni(CN)4}] arrays (Figure 7) and thus align the directions of the easy axis of all Fe centers in the same direction. [START_REF] Bar | Single-ion magnet behaviour of heptacoordinated Fe(II) complexes: on the importance of supramolecular organization[END_REF][START_REF] Mondal | Alignment of Axial Anisotropy in a 1D Coordination Polymer shows Improved Field Induced Single Molecule Magnet Behavior over a Mononuclear Seven Coordinated Fe II Complex[END_REF] SMM behavior characterized by Ueff/kB= 49 K was obtained for [Fe(L1 Ph ){Ni(CN)4}] whereas only fast relaxation was observed for [Fe(L1 Ph )Cl2] that exhibits a very similar magnetic anisotropy but a crystal packing of tilted molecules. 70 From Table 4 it can be noticed that Ueff/kB may vary substantially even for complexes exhibiting similar magnetic anisotropy. In addition to the fact that different relaxation processes may possibly be involved, the way the temperature dependence of the relaxation time was analyzed may contribute. This is well illustrated by a report on [Fe(L4)(MeCN)2](BPh4)2 for which modeling the linear variation of lnτ = f(T -1 ) in the high-temperature part by the Arrhenius law gave Ueff/kB = 50 K whereas analysis over the whole T-domain by a multi-process expression comprising the Arrhenius component yielded Ueff/kB = 89 K. [START_REF] Deng | Synthesis and magnetic studies of pentagonal bipyramidal metal complexes of Fe, Co and Ni[END_REF] It must be mentioned that PBP Fe II complexes involving pentadentate ligands L3 or L4 with either NCS - or CN -ligands in the apical positions have been found to undergo a spin change from S = 2 to a diamagnetic state when lowering the temperature. This spin change was found to be related to a structural change from hepta-to hexa-coordination due to a rupture of linkage between Fe and one site of the pentadente ligand. [START_REF] Wang | Towards synergy between spin-crossover and metal-ligand bond break in molecular crystals: structural investigations of eight seven-coordinated Fe(ii) macrocyclic complexes[END_REF] These derivatives are not concerned by magnetic anisotropy and therefore are not considered herein, a review on the topic can be found in the following reference. [START_REF] Gavey | Coordination complexes of 15-membered pentadentate aza, oxoaza and thiaaza Schiff base macrocycles "Old Complexes Offer New Attractions[END_REF] However, it was found that the PBP geometry and high spin state of [Fe(L3)(CN)2] can be photoregenerated at low temperature, [START_REF] Ababei | Rational Design of a Photomagnetic Chain: Bridging Single-Molecule Magnets with a Spin-Crossover Complex[END_REF] which should restore the magnetic anisotropy of Fe.

PBP Fe II as building unit:

These Ising-type anisotropy Fe II complexes have been involved in the design of polynuclear nanomagnets (Table 5). A cyanide-bridged bimetallic complex, [Fe(tpa){ReCl4(CN)2}], characterized by a ferromagnetic Fe-Re interaction of 6 cm -1 and a molecular ZFS D = -2.3 cm -1 , was shown to give rise to slow magnetic relaxation albeit with a small relaxation barrier. [START_REF] Harris | A cyano-bridged Fe II Re IV (CN)2 cluster incorporating two high-magnetic anisotropy building units[END_REF] Trimetallic [Fe II Cr III ] complexes with different metal ion ratio have been reported. Compound [{Fe(L4)(H2O)}2{Cr(CN)6}] comprises two PBP Fe II centers in ferromagnetic interaction with a central Cr III (J = 7.4 cm -1 ). [START_REF] Zhang | First Fe(ii)-based cyano-bridged single molecule magnet [CrIIIFeII2] with a large anisotropy[END_REF] This compound exhibits SMM-type behavior with Ueff/kB = 44.3 K. Several [FeCr2] compounds with a single PBP Fe as source of magnetic anisotropy were shown to behave as SMM but with noticeable differences in Ueff/kB despite very similar chemical features (Table 5). [START_REF] Pichon | Cyano-Bridged Fe(II)-Cr(III) Single-Chain Magnet Based on Pentagonal Bipyramid Units: On the Added Value of Aligned Axial Anisotropy[END_REF][START_REF] Pichon | Trinuclear Cyanido-Bridged [Cr2Fe] Complexes: To Be or not to Be a Single-Molecule Magnet, a Matter of Straightness[END_REF] Theoretical insights revealed that the decrease of the energy barrier for demagnetization results from the bending of the Fe-NC linkages with respect to the normal of the pentagonal plane. Such bending was shown to affect both the magnetic anisotropy of the Fe center and the ferromagnetic Fe-Cr interactions. [START_REF] Pichon | Trinuclear Cyanido-Bridged [Cr2Fe] Complexes: To Be or not to Be a Single-Molecule Magnet, a Matter of Straightness[END_REF] Pentanuclear [Fe3W2] complexes obtained by association of [Fe(H2L1 R )(H2O]2] 2+ and [W(CN)8] 3-were found to exhibit rather strong ferromagnetic Fe-W interaction (J = 30 cm -1 ). [START_REF] Bar | Pentagonal Bipyramid FeII Complexes: Robust Ising-Spin Units towards Heteropolynuclear Nanomagnets[END_REF] In these complexes the terminal PBP Fe centers have one of their apical positions occupied by a H2O ligand that drastically reduces the magnetic anisotropy of these centers. Only central Fe site provides strong magnetic anisotropy which may account for the modest SMM-type behavior with Ueff/kB of just 35 K in DC field. PBP Fe II centers are found in several SCMs. A seminal example is the ferrimagnetic chain [{Fe(L3)}2{Nb(CN)8}] characterized by Ueff/kB = 74 K and the opening of a magnetic hysteresis below 2 K. [START_REF] Venkatakrishnan | Enhanced Ion Anisotropy by Nonconventional Coordination Geometry: Single-Chain Magnet Behavior for a [{Fe II L}2{Nb IV (CN)8}] Helical Chain Compound Designed with Heptacoordinate Fe II[END_REF] The ferromagnetic [Fe(H2L1 NH2 ){Cr(L1 Ph )(CN)2}]•PF6 SCM was designed to ensure parallel orientation of the axial anisotropy of the PBP Fe units (Figure 8a). This nanomagnet is characterized by an energy barrier for demagnetization of Ueff/kB = 113 K and the opening of a magnetic hysteresis loop below 5 K. [START_REF] Pichon | Cyano-Bridged Fe(II)-Cr(III) Single-Chain Magnet Based on Pentagonal Bipyramid Units: On the Added Value of Aligned Axial Anisotropy[END_REF] , Copyright 2022 American Chemical Society), (bottom) 1D-azido-bridged [Fe(L5 H )(N3)]•ClO4 , the red arrows represents the easy axis of magnetization of a Fe II center positioned along Nazido-Fe-Nazido axis, thus highlighting the tilt angle at the origin of weak ferromagnetism and SCM behavior (Adapted with permission from Ref. [START_REF] Drahoš | Single-Chain Magnet Based on 1D Polymeric Azido-Bridged Seven-Coordinate Fe(II) Complex with a Pyridine-Based Macrocyclic Ligand[END_REF] , copyright 2021 American Chemical Society). Homonuclear chains consisting solely of PBP Fe II centers in antiferromagnetic interactions can exhibit SCM behavior. This occurs when the easy anisotropy axes of the Fe centers along the 1D coordination polymer are not collinear (Figure 8), leading to spin-canting in the ground state and to the emergence of a magnetization despite antiferromagnetic Fe-Fe interactions. Such a behavior is reminiscent of weak ferromagnetism. For instance, in cyanide-bridged 1D-[Fe(L3)CN]•BF4 chain, the directions of the apical axes are tilted by 7° and the exchange interaction is of JFeFe = -4.3 cm -1 . This SCM is characterized by Ueff/kB = 35.9 K. [START_REF] Shao | Spin canting, metamagnetism, and single-chain magnetic behaviour in a cyano-bridged homospin iron(II) compound[END_REF] The closely related chain [Fe(L4)CN] + associated to 4-aminobenzene-4'-sulfonic anion (ABSA -) is a SCM with Ueff/kB = 26.1 K. [START_REF] Shao | Structural and magnetic tuning from a field-induced single-ion magnet to a single-chain magnet by anions[END_REF] In µ1,3-azido-bridged [Fe(L5 H )N3]•ClO4 zig-zag chain, antiferromagnetic interactions of JFeFe = -2.1 cm -1 take place and the angle between the axial directions is 18.5° (Figure 8, bottom). This compound is an SCM with Ueff/kB = 87.5 K and exhibits a magnetic hysteresis loop below 3 K. 76

Compounds

I.7 d 7 ions (Co II )

A substantial number of heptacoordinated Co II complexes with PBP coordination sphere are known and their magnetic anisotropy has been studied in detail (Table 6). Besides the derivatives using a pentadentate equatorial ligand to stabilize a PBP coordination polyhedron, a series of complexes comprising a heterocyclic amine (pyridine, bipy, etc…) and κ 2 -NO3 -anions in their coordination spheres have been investigated. All these complexes are characterized by large positive D parameters, typically between 25 and 40 cm -1 . The observed modulation of D does not seem to be directly related to the degree of distortion of the coordination geometry. [START_REF] Wang | Magnetic anisotropy and slow magnetic relaxation of seven-coordinate cobalt(II)-nitrate complexes[END_REF] The seminal theoretical calculations performed for [Co(H2L1 Ph )(H2O)NO3]•NO3 indicated that the large positive value of D for this complex (31 cm -1 ) results mainly from the contributions of three excited states, all positive (Figure 9). [START_REF] Ruamps | Origin of the Magnetic Anisotropy in Ni(II) and Co(II) Heptacoordinate Complexes[END_REF] These theoretical insights lead to the conclusion that the magnetic anisotropy of the Co ion could be modulated by tuning the coupling of the ground state and the excited states through the characteristics of the ligand set. For example, weak σ-donor ligands in apical positions would shift the orbital downwards, reducing the energy difference with the other orbitals, thereby strengthening their coupling and resulting in a larger D value. Similarly, a more symmetric pentadentate ligand coordinated in equatorial positions would reduce the energy difference between the and orbitals, and enhance the positive contribution to D from the 1 st excited doublet. These considerations have been used to account for variations in the D values found experimentally. For instance, replacement of oxygen-ligands at apical positions of [Co(H2L1 Ph )(H2O)NO3] + by NCS -led to a decrease of D from 32 cm -1 to 15.9 cm -1 that was attributed to the more σ donor nature of thiocyanate ligands. [START_REF] Dey | Modulation of the coordination environment: a convenient approach to tailor magnetic anisotropy in seven coordinate Co(ii) complexes[END_REF] A related effect has been found for a series of [Co(L7 Me )Y2] n+ (Y = SPh -, H2O, NCS - , pyridine, CN -) complexes by altering Y ligands from weak-field SPh -to strong σ-donor CN -ligands leading to a gradual decrease of D from 34.5 cm -1 to 17.3 cm -1 . [START_REF] Shao | Syntheses, structures, and magnetic properties of three new chain compounds based on a pentagonal bipyramidal Co(ii) building block[END_REF][START_REF] Shao | Probing the Effect of Axial Ligands on Easy-Plane Anisotropy of Pentagonal-Bipyramidal Cobalt(II) Single-Ion Magnets[END_REF] Still with the idea of modulating the ligand field strength in the axial positions, the effect of the halogen ligands in [Co(L5 H )X2] was found to induce lesser changes on D with values of 38, 41, and 35 cm -1 , respectively for X = Cl -, Br -, and I -. [START_REF] Drahoš | Impact of Halogenido Coligands on Magnetic Anisotropy in Seven-Coordinate Co(II) Complexes[END_REF] However, the increase of D does not simply follow the order of the ligand field reduction given by spectrochemical series (Cl > Br > I) but rather the trend suggested by the Mayer bond order [START_REF] Bridgeman | The Mayer bond order as a tool in inorganic chemistry Dalton Trans[END_REF] (Co-I > Co-Cl > Co-Br).

Such trends can only be deduced for a series of compounds whose alterations are strictly limited to the substitution of apical positions. The [Co(L5 R )] n+ complexes based on the heptadentate ligand L5 R , where R consists of two arms allowing the coordination of specific groups in the apical positions of Co(II), are a good illustration. [START_REF] Drahoš | Structural, magnetic, redox and theoretical characterization of seven-coordinate first-row transition metal complexes with a macrocyclic ligand containing two benzimidazolyl N-pendant arms[END_REF] Changing the apical ligands from pyridine to benzimidazole induced an increase of D from 34 to 40 cm -1 , in apparent contradiction with the decrease anticipated for stronger σ donor groups. The origin of this effect has been found in structural distortions that alter the axial and equatorial ligand fields. An ab initio modeling revealed that axial or equatorial bond length variations can have a significant influence on the overall D value. Obviously in these complexes, the effect on D of the bond characteristics of the apical benzimidazole ligands is largely offset by the contribution due to a modification of the equatorial field.

Chemical alterations of the equatorial ligand may also have substantial effects on D. This is especially understandable for pentadentate H2L1 R that can be neutral, mono-, or di-anionic (see Appendix 1). For instance, [Co(H2L1 Ph )(H2O)X]X complexes (X = NO3 -, Br -, I -) involving the neutral ligand are characterized by D values in the range of 30-32 cm -1 whereas a significantly reduced magnetic anisotropy with D = 13.1 cm -1 was reported for the related complex [Co(L1 Ph )(H2O)2] with deprotonated ligand. This decrease was attributed to a shift to higher energies of the excited doublet state as a result of the shrinking of the equatorial metal-ligand bond distances due to the di-anionic ligand. [START_REF] Dey | Modulation of the coordination environment: a convenient approach to tailor magnetic anisotropy in seven coordinate Co(ii) complexes[END_REF] Seven coordinated Co II complexes have also been obtained when bidentate nitrate ions and aromatic heterocyclic amines (pyridine, bipy, phen, terpy, …) coordinate the metal center. Deviation from PBP geometry is often larger than for the complexes with pentadentate equatorial ligands [START_REF] Wang | Magnetic anisotropy and slow magnetic relaxation of seven-coordinate cobalt(II)-nitrate complexes[END_REF] but ZFS parameters are similar (Table 6). For [CoL3(NO3)2] (with L = 3-tert-butylpyridine or isoquinoline), and [CoL(NO3)2MeCN)] (with L = bipy or phen), the D values are in the narrow range of 31-36 cm -1 . [START_REF] Wang | Magnetic anisotropy and slow magnetic relaxation of seven-coordinate cobalt(II)-nitrate complexes[END_REF][START_REF] Chen | Slow magnetic relaxation in mononuclear seven-coordinate cobalt(ii) complexes with easy plane anisotropy[END_REF] Related complexes of formula [CoL(NO3)2] with L = 2,6-dipyrazolyl-pyrazine or 2,6-dipyrazolyl-pyridine, exhibit magnetic bistability in the temperature range 230 -240 K. [START_REF] Juhasz | Bistability of magnetization without spin-transition in a high-spin cobalt(II) complex due to angular momentum quenching[END_REF][START_REF] Su | Assembling an alkyl rotor to access abrupt and reversible crystalline deformation of a cobalt(II) complex[END_REF] A structural phase transition distorts the environment of the cobalt and alters the angular contribution to the magnetic moment of the complexes. For example, the derivative with pyrazine ligand has a distorted PBP coordination sphere (with a Shape parameter of 4.06) [START_REF] Casanova | Shape and symmetry of heptacoordinated transition-metal complexes: structural trends[END_REF] at low T that rearranges to capped trigonal prim above the critical temperature. Unfortunately, the ZFS parameter D of these different phases does not seem to have been determined.

Field-induced SMMs:

Planar magnetic anisotropy (i.e., D > 0) should not lead to blockage of magnetization since there is no energy barrier between the lowest energy ± Ms states. However, many of these PBP complexes were found to exhibit a slow relaxation of magnetization in a magnetic field.

The origin of such field-induced SMM behavior in compounds with easy plane anisotropy (positive D) has been attributed to the van Vleck cancellation mechanism that hinders direct phonon-induced transitions between states of the ground state. [START_REF] Gómez-Coca | Origin of slow magnetic relaxation in Kramers ions with non-uniaxial anisotropy[END_REF] This situation results from the effect of a magnetic field on the electronuclear spin entanglement occurring in Co II . Therefore, temperature dependence of the relaxation time is best modelled by a Raman model and possible contribution from a direct process. Nevertheless, the figure of merit for these field-induced Co SMMs has long been a pseudobarrier for demagnetization (Ueff) obtained by analyzing the temperature dependence of the relaxation time (τ) by an Arrhenius low. Therefore, this pseudo energy barrier is also mentioned in Table 6.

PBP Co as building unit:

Several examples of heteronuclear derivatives involving Co II PBP units as a source of strong magnetic anisotropy have been described. A very elegant approach has been to functionalize a H2L1 R ligand so that it can connect to several metal ions. A series of bimetallic Co II Ln III complexes (Figure 10a) have been achieved by designing the R moieties of the ligand to contain an additional hexadentate [N2O4] pocket suitable for coordination to a Ln III ion. [START_REF] Shen | Heterometallic MIILnIII (M = Co/Zn; Ln = Dy/Y) Complexes with Pentagonal Bipyramidal 3d Centers: Syntheses, Structures, and Magnetic Properties[END_REF] In [Co(L1 CMeN2HCONH2 )Ln(NO3)2]NO3, the metal ions are bridged by the oxygen atoms common to both cavities. Ferromagnetic Co II -Dy III interactions have been observed, and the Co-Y derivate was found to behave as a field-induced SMM (Table 6).

Following the more classical building-block strategy, PBP Co II complexes have been assembled with cyanometallate derivatives. A chiral magnet, [{Co(L4)}2{Cr(CN)6}]•ClO4, was obtained by assembling [Co(L4)(H2O)2] 2+ and [Cr(CN)6] 3-units. [START_REF] Zhang | A cyano-bridges Cr III Co II ferromagnet with a chiral nanotubular structure constituted of interlocked single and double helices[END_REF] This 3-D tubular network of cyano-bridged Co and Cr centers exhibited ferromagnetic ordering below Tc = 12 K and a magnetic hysteresis with a coercive field of 165 Oe at 1.8 K. The 2-D ferromagnet [{Co(L3)}3{Cr(CN)6}2] was reported to have similar characteristics with Tc = 15 K but small coercive field. [START_REF] Zhang | Synthesis, crystal structure and magnetic properties of a new cyanide-bridged two-dimensional CrIII2CoII3 ferromagnet[END_REF] A 2-D metamagnet with honeycomb network was obtained with [Co(TODA)] 2+ (TODA stands for 1,4,10-Trioxa-7,13-diazacyclopentadecane) and [Cr(CN)6] 3-. This compound showed antiferromagnetic ordering below 12 K but a butterfly-shaped hysteresis loop with coercive field of 720 Oe. [START_REF] Shao | Two-dimensional frameworks formed by pentagonal bipyramidal cobalt(II) ions and hexacyanometallates: antiferromagnetic ordering, metamagnetism and slow magnetic relaxation[END_REF] Assemblage with diamagnetic [Co(CN)6] 3-gave same structure topology. The absence of exchange interactions allowed confirming the magnetic anisotropy for the Co centers (D = 29.9 cm -1 ) and resulted in field-induced SMM behavior. The preservation of the strong magnetic anisotropy of the PBP Co site (D = 32.9 cm -1 ) with axial positions occupied by two cyanometallatenitrogen atoms, was also confirmed in the 1D polymer [{Co(H2L1 Ph )}{Ni(CN)4}] formed with diamagnetic [Ni(CN)4] 2-. [START_REF] Bar | Pentagonal Bipyramid FeII Complexes: Robust Ising-Spin Units towards Heteropolynuclear Nanomagnets[END_REF] 2-D and 1-D hollows networks have been achieved with [Co(L4)(H2O)2] 2+ and [Fe(CN)6] 3- metallo-ligand. [START_REF] Pan | A heterometallic nanosized tube {Fe[(CN)6]2Co(L N3O2 )]3}n and two of its lamellar polymorphous isomers[END_REF] Ferromagnetic Co-Fe interactions were found to take place but no SCM behavior was evidenced for the 1-D derivative. A chiral ligand derived from lactic acid hydrazide was used to impart chirality to 1-D K[{Co(H2L1 lact )}{Fe(CN)6}] (lact stands for lactic acid derived hydrazide group). This compound has ferroelectric properties and can be processed in an aqueous medium. [START_REF] Choudhury | Accessing water processable cyanido bridged chiral heterobimetallic Co(II)-Fe(III) one dimensional network[END_REF] Discrete heterometallic complexes in which Co II is exchange coupled with another metal ion have also been reported. These comprise the pentanuclear complexes [{Co(H2L1 Ph )}3{M(CN)6}2] (M = Cr III or Fe III ), [START_REF] Batchelor | Pentanuclear Cyanide-Bridged Complexes Based on Highly Anisotropic Co II Seven-Coordinate Building Blocks: Synthesis, Structure, and Magnetic Behavior[END_REF] and [{Co(H2L1 R )}3{W(CN)8}2] with R = Ph, BiPh (Figure 10b). [START_REF] Bar | Pentagonal Bipyramid FeII Complexes: Robust Ising-Spin Units towards Heteropolynuclear Nanomagnets[END_REF] Ferromagnetic Co-M interactions have been observed in each case with JCoCr = 5.4 cm -1 and JCoW = 19 cm -1 , leading to large ground spin states but for none of these compounds slow relaxation of the magnetization was observed. Complexes ZFS parameters (cm -1 ) and g SMM relaxation characteristics

Ref. experimental

Theory (c) Orbach (f) Raman (g) Direct (h) HDC 95 (c) in Zn 24 (c) 1.4×10 -3 127 8.17 Table 6. Magnetic anisotropy in high-spin PBP Co II complexes, and their SMM characteristics.

D (a) |E| g D E Ueff/kB (K) A (K -n s -1 ) n B (K -1 s -1 Oe -2 ) (kOe) [Co(H2L1 Ph )(H2O)X]X X = NO3 - X = Br - X = I -

I.8 d 8 ions (Ni II )

Heptacoordinate Ni II complexes are much less common than other 3d ions. 107 This can be related to the Jahn-Teller effect which tends to strongly distort or even reshape the coordination polyhedron to favor geometries more favorable to a lifting of the degeneracy of partially occupied orbitals. This difficulty can be overcome when a pentadentate ligand is used to fix the equatorial positions and impose a PBP coordination sphere to the Ni II ion. [108][109][110] This approach allowed obtaining PBP Ni II complexes with the various ligands depicted in Figure 1. However, for the pentadentate ligands comprising oxygen as connecting atoms, Ni-O distances close or higher than 2.5 Å are usually observed which lead to an important distortion of the PBP geometry. [START_REF] Drahoš | Structural, Magnetic, and Redox Diversity of First-Row Transition Metal Complexes of a Pyridine-Based Macrocycle: Well-Marked Trends Supported by Theoretical DFT Calculations[END_REF][START_REF] Deng | Synthesis and magnetic studies of pentagonal bipyramidal metal complexes of Fe, Co and Ni[END_REF]106,110 In PBP coordination sphere Ni II has high-spin configuration with S = 1 (Figure 11) and exhibits a magnetic anisotropy characterized by a negative D parameter. Experimental D values span from -6 to -28 cm -1 (Table 7). Positive D values have been reported but these resulted from an analysis of the temperature dependence of χMT only, which does not allow discriminating the sign of D for powder samples. Ab initio calculations showed that the main contributions to D come from the spin-orbit coupling of the ground state with first three triplet excited states (Figure 11). [START_REF] Ruamps | Origin of the Magnetic Anisotropy in Ni(II) and Co(II) Heptacoordinate Complexes[END_REF] The overall negative D value results from a large and negative contribution arising from the coupling between the ground state and the first excited triplet state, while the contributions from the other excited states are positive and much smaller. The observed D will therefore depend on the relative strengths of these opposite contributions that are governed by the differences of the energy levels of the involved orbitals. Based on this theoretical insights, it has been suggested that the negative contribution arising from the first excited triplet state could be increased by achieving a more symmetrical ligand field in the equatorial plane of Ni II , thus reducing the energy difference between the and the orbitals.

Additionally, the observed negative D value could be strengthened by reducing the positive contributions to D. This would be obtained using apical ligands with large σ-donor and less effective πdonor characteristic that increase the energy differences with the 2 nd and 3 rd excited triplet states. [START_REF] Ruamps | Origin of the Magnetic Anisotropy in Ni(II) and Co(II) Heptacoordinate Complexes[END_REF] Complexes ZFS parameters (cm -1 ) and g PBP distortion (a) experimental Theory (d) Ref. These guidelines motivated experimental work to gather quantitative data on achievable D values. For instance, in the series of complexes based on ligands H2L1 R or L5 R , the more negative D values (respectively -28.1 cm -1 and -17.2 cm -1 ) have been obtained when apical positions are occupied by imidazole units, which are good σ-donor ligands. Closely related values were found with N-bound cyanides in the apical positions. However, the structural distortion appears to have an effect too. This is suggested by the large difference in D found for [Ni(H2L1 NH2 )(imidazole)2] 2+ and [Ni(L5 CH2bzIm )] 2+ , both of which displaying imidazoles in their apical positions but the coordination sphere for the latter shows a larger deviation from reference geometry (shape parameters respectively of 0.34 and 1.2, Table 7). The effect of structural distortions is even better illustrated by the series of crystal phases obtained with [Ni(H2L1 NH2 )(NCS)2] for which D changes from -15.5 cm -1 to -11.5 cm -1 as distortion increases (shape parameter of 0.45 and 0.90, respectively). The same trend is found for the [Ni(H2L1 R )(H2O)2] 2+ derivatives, confirming the decrease of |D| for these Ni complexes by structural distortions. Table 8 gathers the calculated contributions to D arising from the coupling with the three first triplet excited states for a series of complexes. For the H2L1 R ligand-based complexes, substantial differences can be noticed in the contribution of the first triplet excited state, reflecting the effect of the coordination sphere distortion. These calculated contributions help to understand the differences in D values found experimentally for these complexes. A theoretical investigation pointed also to a strong effect of the equatorial ligand field, the magnetic anisotropy becoming more negative as the ligand field is weaker. [START_REF] Drahoš | Structural, magnetic, redox and theoretical characterization of seven-coordinate first-row transition metal complexes with a macrocyclic ligand containing two benzimidazolyl N-pendant arms[END_REF] For none of these complexes a SMM-type behavior was ever evidenced. 12a). [START_REF] Bretosh | A ferromagnetic Ni(II)-Cr(III) single-chain magnet based on pentagonal bipyramidal building units[END_REF] Here too ferromagnetic Ni-Cr interactions take place, of the order of JNiCr = 10 cm -1 in a trinulear [NiCr2] complex. Chain compounds made up with diamagnetic [Ni(CN)4] 2-and [Ni(H2L1 Ph )(H2O)2] 2+ or [Ni(L7 Me )(H2O)2] 2+ showed that PBP Ni units with N-bound cyanide ligands in the apical positions retain large magnetic anisotropy (respectively -17.7 and -14.4 cm -1 , Table 7). [START_REF] Bar | Pentagonal Bipyramid FeII Complexes: Robust Ising-Spin Units towards Heteropolynuclear Nanomagnets[END_REF][START_REF] Bretosh | A ferromagnetic Ni(II)-Cr(III) single-chain magnet based on pentagonal bipyramidal building units[END_REF] A related anisotropy, -15.4 cm -1 , was found in a trimetallic complex [{Ni(H2L1 NH2 )(H2O)}2{W(CN)8}] involving a diamagnetic W IV unit. 112

D (b) |E| g D E
A linear trinuclear Ni complex featuring a central ion with PBP geometry was obtained using a tricompartmental ligand N,N'-bis(3-methoxysalicyl)-2,6-pyridine dicarbohydrazide (Figure 12b). 117 The magnetic behavior described for this compound is quite intriguing. It would correspond to the contribution of three S = 1 spins while two of the Ni ions are in a square-planar environment and, therefore, should be diamagnetic. The limited number of heterometallic compounds constructed with preformed PBP Ni II complexes is likely related to the Jahn-Teller effect which leads to significant distortion of the coordination sphere of Ni II . It may even favor a structural reorganization to an octahedral coordination polyhedron when the chemical integrity of the PBP coordination sphere gets disturbed. For instance, a slightly basic medium (ex. in DMF or in the presence of some cyanometallates) induces an instantaneous rearrangement of [Ni(H2L1 Ph )(H2O)2]•2NO3 to a bimetallic complex in which the Ni is 6-coordinated (Figure 13). [START_REF] Bretosh | A ferromagnetic Ni(II)-Cr(III) single-chain magnet based on pentagonal bipyramidal building units[END_REF]118 However, this structural fragility seems to be reduced with a more rigid ligand to stabilize the equatorial coordination sphere. 33

I.9. d 9 (Cu II )
Several examples of Cu II complexes with PBP coordination polyhedron are known. As for the other transition metal ions, this geometry can be induced by a ligand constraining a pentagonal equatorial coordination arrangement (Table 9). A general feature of all these Cu II complexes is their axially compressed PBP coordination sphere. As a consequence, the orbital is highest in energy and accommodates the unpaired electron. The ground spin state S = ½ for PBP Cu II excludes any contribution from ZFS. However, EPR revealed substantial g-anisotropy (Table 9 This overview of the magnetic anisotropies of transition metal ions shows that this property is directly related to the electronic configuration d n . For this reason, it can be rationally imparted to a coordination complex. By adjusting the deformation of the PBP coordination sphere and possibly the ligand field in the axial and equatorial positions of the complex, values of the axial ZFS parameter D between -30 and +40 cm -1 are readily available by chemical design. This possibility is particularly interesting for the design of materials where the magnetic anisotropy has an important part in the magnetic behavior of the system, whether it is a nanomagnet (SMM or SCM) or a classical magnet.

II. Lanthanide ions with pentagonal bipyramidal coordination sphere

Trivalent lanthanide ions are very attractive magnetic centers to achieve SMMs with high energy barrier for magnetization reversal, Ueff/kB, and a significant blocking temperature, TB. The 4f ions (except La III , Gd III and Lu III ) exhibit an inherent magnetic anisotropy due to a strong spin orbit coupling resulting from the unquenched orbital angular momentum. 131,132 In contrast to transition metal ions, in lanthanide complexes the spin-orbit coupling energy is larger than the crystal field splitting by an order of magnitude of 10 to 100. Although crystal field effects (i.e. the electrostatic interaction between the ligand-and the f-electrons) are small, they are large enough to lift the degeneracy of the mJ states of the J multiplets and to be the real origin of the magnetic anisotropy in the f elements. Therefore SMM characteristics of a 4f compound are directly linked to crystal field considerations. The dynamic of the demagnetization is related to the ± mJ of lowest energy and to the energy difference between the ground and the first excited mJ microstate. Ideally, to ensure high blocking temperatures, ground mJ should have largest J value (i.e. mJ = ± 6 for Tb III , ± 15/2 for Dy III , etc…) and the energy gap with next mJ state must be as large as possible.

The role of the crystal field in optimizing the anisotropy for each Ln III was discussed by Rinehart and Long. 133 For an Ln ion, each mJ state is characterized by a specific aspheric spatial distribution of its 4f electron density (Figure 14, bottom). The valence electron density distribution for the ± mJ state with largest J for each trivalent Ln is depicted in Figure 14. 134,135 Their spatial shape is either axially compressed (i.e. oblate, for Ce III , Pr III , Nd III , Tb III , Dy III , and Ho III ) or axially elongated (i.e prolate, for Pm III , Sm III , Er III , Tm III , and Yb III ), except that of Eu III , Gd III and Lu III which is spherical. Since the electronic repulsion between the electron densities of the Ln center and the ligands results in a spatial distribution of the 4f n -electron cloud that minimizes these electrostatic interactions, it is possible to adjust the crystal field distribution to stabilize the ground mJ state with largest J. For instance, for an Ln III with oblate density distribution of its ground mJ, electron density is larger in the x,y-plane directions than along the z-direction (Figure 14), therefore electrostatic interactions with its coordination sphere is minimal when ligand field is weak in the equatorial positions and strong along the z axis. Conversely, to stabilize an mJ state with a prolate electronic distribution, a stronger ligand field in the plane and weaker along the apical directions is required to minimize electrostatic interactions between the 4f electron cloud and its coordination sphere. When these conditions are met, the magnetic anisotropy is maximal and the reversal of magnetization via excited ±mJ states requires more energy, i.e. referring to an Arrhenius behavior, the energy barrier U/kB is large.

The control of the coordination geometry around the 4f-ion is therefore of crucial importance, and with respect to the aforementioned model, low-coordinate lanthanide complexes with high order of symmetry are attractive, but challenging candidates to synthesize. [136][137][138][139][140] To circumvent those synthetic difficulties, Ln complexes belonging to an axial symmetry group such as trigonal and pentagonal bipyramids (D3h and D5h) are viable alternatives, 141, 142 the D5h geometry being the point of interest of this review.

Focusing on complexes showing SMM-type magnetic behaviors, two families of rare earth complexes in PBP symmetry can be identified. The first family concerns complexes formed with monodentate ligands, the second family involves polydentate ligands. Dy III derivatives have been most investigated and have been shown to exhibit largest axial anisotropy when strong-field ligands (alkoxide, siloxide, phosphine oxide, phosphonic diamide, phosphonic triamide, etc…) are located in the axial positions of the rare earth whereas equatorial positions are occupied by weak-field ligands (such as H2O, THF, pyridine, polydentate ligands). Promising behaviors have also been obtained with other Ln ions. The most striking results are reviewed in the following.

Figure 14. Shape of the 4f electron cloud for the ±mJ state with the largest J for the trivalent 4f [START_REF] Bar | Magnetic anisotropy in two-to eight-coordinated transition-metal complexes: Recent developments in molecular magnetism[END_REF][START_REF] Gómez-Coca | Large magnetic anisotropy in mononuclear metal complexes[END_REF][START_REF] Wester | Synthesis and characterization of novel pentagonal bipyramidal complexes of iron(II), cobalt(II), and zinc(II)[END_REF][START_REF] Drew | Seven-coordinate complexes of iron(II) with pentadentate macrocyclic ligands[END_REF][START_REF] Bishop | X-Ray crystal structure of a planar, high-spin iron(II) complex of a pentadentate unsaturated macrocycle formed by reaction of 2,9-di(1-methylhydrazino)1,10-phenanthroline monohydrochloride with 2,6-diacetylpyridine[END_REF][START_REF] Ivanovic-Burmazovic | Advances in Inorganic Chemistry[END_REF][START_REF] Popov | Metal complexes with polyfunctional ligands based of bis(hydrazones) of dicarbonyl compounds[END_REF][START_REF] Bhula | Complexes of tridentate and pentadentate macrocyclic ligands[END_REF][START_REF] Gavey | Coordination complexes of 15-membered pentadentate aza, oxoaza and thiaaza Schiff base macrocycles "Old Complexes Offer New Attractions[END_REF][START_REF] Ruamps | Origin of the Magnetic Anisotropy in Ni(II) and Co(II) Heptacoordinate Complexes[END_REF][START_REF] Sarkar | Role of Coordination Number and Geometry in Controlling the Magnetic Anisotropy in Fe II , Co II , and Ni II Single-Ion Magnets[END_REF][START_REF]The magnetic quantum numbers for the d orbitals is ml = 0 for dz, ml = 1 for dxz and dyz, and ml = 2 for dxy and dx2-y2[END_REF][START_REF] Bar | Pentagonal Bipyramid FeII Complexes: Robust Ising-Spin Units towards Heteropolynuclear Nanomagnets[END_REF][START_REF] Shongwe | Unprecedented [V2O]6+ Core of a Centrosymmetric Thiosemicarbazonato Dimer: Spontaneous Deoxygenation of Oxovanadium(IV)[END_REF] Ln ions, and (bottom) for each mJ state of Dy III , showing the evolution from a prolate electrondensity cloud for m15/2 to an oblate spatial distribution for m1/2 (reprinted from ref. 135 with permission from Royal Society of Chemistry).

II.1 PBP complexes with monodentate ligands

The reported examples of Ln III complexes with PBP coordination polyhedron formed by only monodentate ligands and behaving as SMMs are listed in Table 10 with their characteristic magnetic and geometrical information. For this family of compounds, the dominating influence of the axial ligands is seen through the almost linear Lax-Ln-Lax arrangement (varying from 173.5°, entry 15, to 179.2°, entry 6) and through the Lax-Ln bond distances shorter than the Leq-Ln bond distances. This is perfectly illustrated by [Dy(CH3CH(C6F5)O)2(THF)5][BPh4] 143 (Table 10, entry 34) which has one of the highest energy barrier (2114 K) and blocking temperature (22 K) reported for PBP complexes. For this derivative, the two axial ligands are fluorinated alkoxides with a Lax-Dy-Lax angle of 177.5°, and Lax-Dy bond lengths of 2.102 Å, significantly shorter than the Leq-Dy bond lengths (2.434 Å, Figure 15). The distortion of the Dy coordination polyhedron from the ideal D5h geometry is small as supported by shape parameter of 0.461. Several important points are noted for this family of compounds. The nature of the negatively charged ligand coordinated in axial positions to the rare earth seems to be a predominant criterion for the optimization of the magnetic properties of these systems. This is clearly illustrated by the Dy III complexes [DyX 1 X 2 (THF)5]•BPh4 (with X 1 = Cl, OPh, OCMe3 and OSiMe3; X 2 = Cl, Br, OPh, OCMe3 and OSiMe3; Table 10, entries 17, 18, 21-22, 27-28), [144][145][146][147] and [DyX 2 (THF)5]•BPh4 (X 2 = CH3(C6F5)CHO -, pyrazolate, PhO -, Me3CO -, Me3SiO -, Table 10, entries 19-20, 24, 26, 29-30, 34). [143][144][145][146] When one and then the two axial Cl -ligands of [DyCl2(THF)5] + are replaced by phenolate ligands to give [DyCl(PhO)(THF)5] + and [Dy(PhO)2(THF)5] + , respectively, the effective energy barrier for magnetization reversal, Ueff/kB, increases from 83 K to 1329 K with a blocking temperature shift from 7 K to 12 K. 145 This trend is corroborated by the remarkable results obtained for [Dy(CH3CH(C6F5)O)2(THF)5]•BPh4 (entry 34), where the Dy-alkoxyl bond distance are shorter.

The nature of the second coordination sphere of the rare earth center is also a point of importance. For the series of complexes [Dy((Me2N)3PO)2(H2O)5]n•3nX (X = Cl, n = 1; X = Br, n = 2, and X = I, n = 1; Table 10 entries 7-9), 148,149 [Dy(cy3PO)2(H2O)5]•3X (X = Cl, Br, CF3SO3, entries 14-16), 150,151 and [Ho(pyr3PO)2(H2O)5]X3 (X = Cl, Br, entries 12-13), 152 where various phosphonic triamide and phosphine oxide act as strong axial ligands and water molecules occupy the equatorial coordination sites of the Ln ions, the value of Ueff/kB was found to significantly change with the nature of the anions associated to the complex. Theoretical calculations of the energy barrier (Ucal) for model molecules derived from the two complexes [Dy((Me2N)3PO)2(H2O)5]Cl3•((Me2N)3PO)•H2O and [Dy((Me2N)3PO)2(H2O)5]I3•2((Me2N)3PO), 148,149 showed that moving the second coordination sphere away from the magnetic center (i.e. reducing or even suppressing the H-bond interactions with the metal-bonded H2O), reduces the negative-charge density of the O atom of the coordinated H2O. This lessens the equatorial crystal field strength and, consequently, amplifies the axial field effect. An illustration is given by the two Ho complexes [Ho(pyr3PO)2(H2O)5]Cl3 and [Ho(pyr3PO)2(H2O)5]Br3. 152 The replacement of Cl -by Br -leads to a greater separation between the five equatorially coordinated water molecules and the counter ions (the Oeq water••• X -distances range from 3.014 to 3.119 with X = Cl -and from 3.182 to 3.262 Å for X = Br -), which implies a weakening of the H-bond interactions. Concomitantly, the axial Ho-O bond distances are reduced and the axial O-Ho-O angle becomes more linear (entries 12 and 13 in Table 10). The stronger and more linear axial crystal field acting on Ho III as a result of the reduced effect of the second coordination sphere leads to an increase in Ueff/kB from 350 K (X = Cl -) to 418 K (X = Br -). 150 Furthermore, these complexes provide an illustration that the second coordination spheres can also modify the coordination polyhedron of the Ln III center. For the complex with Cl -as a counter ion (Figure 16), the second coordination sphere consists in an asymmetrical 11-membered H-bonded ring formed by the five coordinated water molecules, four Cl -, one free tricyclohexylphosphine oxide whereas with Br -as counter ion, a symmetrical 10-membered ring (a five-pointed star) is formed between the five water molecules, the three Br -ions and two free phosphine oxide molecules. In [Dy(cy3PO)2(H2O)5]Br3, the PBP polyhedron around the Dy center is slightly more compressed than that in [Dy(cy3PO)2(H2O)5]Cl3 (see entries 14 and 15 in Table 10) which results in a coordination geometry closer to the ideal D5h symmetry. The combined effects resulting from the modulation of the second coordination sphere lead to an increase of the blocking temperature from 11 K to 20 K for [Dy(cy3PO)2(H2O)5]Br3. The alteration of the counter ions associated to a PBP Ln complex is the usual approach followed to modulate the influence of the second coordination sphere on the SMM behaviors (Table 10 and11). The crystallization medium is another possibility that can be used because solvent molecules are often part of the crystal lattice and even involved in the composition of the second coordination sphere. This leads to emphasize the attention that must be paid to the aging of the samples; the loss of lattice solvent molecules can affect the second coordination sphere and significantly change the magnetic behavior of a compound even if the structure of the complex is apparently not modified.

SMM relaxation characteristics

II.2 PBP complexes with polydentate ligands

The rare earth complexes in PBP symmetry obtained with polydentate ligands providing 2 to 6 donors atoms for metal coordination and exhibiting SMM behavior are gathered in Table 11. In most of these complexes, the multidentate ligand occupies the equatorial positions of the PBP coordination sphere around the rare earth ion, without necessarily involving full denticity. The axial positions are then occupied by anionic and/or neutral ligands (entries 1 to 12 and 30 to 47). These complexes can give rise to large energy barrier for magnetization reversal.

As mentioned before, pentadentate ligands are well suited to direct the formation of PBP coordination spheres, this also applies for Ln III ions provided that the ligands in the apical positions are strictly monodentate. 163 For instance, Dy complex [Dy(L N5 )(Ph3SiO)2]•BPh4 164 (Table 11, entry 31) is based on a cyclic pentadentate ligand (L N5 is an homologue of L3 (Figure 1) with propylene instead of ethylene units between the imine and amine N-atoms), with triphenylsilanolate in the apical positions, it was found to behave as an SMM with Ueff/kB = 1108 K and a blocking temperature TB = 5 K. In [DyCu5(quinha)5(sal)2(py)2]•CF3SO3, 165 a more unusual metallacrown, [15-MCCu-5] made of Cu II ions and quinaldichydroxamic acid (H2quinha), was involved as macrocyclic ligand to occupy the equatorial positions of the Dy III ion whereas phenoxyl groups are in the apical positions. For this complex, an SMM behavior with energy barrier Ueff/kB = 900 K (Table 11, entry 37) was evidenced.

Complexes with the axial positions occupied by moieties belonging to the multidentate ligand have been obtained with hexadentate ligands derived from ethylenediamine (entries 13 to 27), [166][167][168][169][170] propylenediamine (entry 27), 166 and tris(2-aminoethyl)amine (entries 28, 29). 171,172 The five equatorial positions are occupied by remaining coordinating units of the multidentate ligands and additional ligands such as halide or solvent molecules. The complex series, [Dy(bbpen-R)X] 168-170 (Table 11, entry 14-26) is worth mentioning as several derivatives exhibit among the highest Ueff/kB values for PBP complexes with values as large as 1162 K and blocking temperatures up to 21 K.

For these complexes involving polydentate ligands, the axial versus equatorial ligand-field strengths can be modulated too. The electrostatic potential in the equatorial plane can be modified by adapting the Ln-Leq bonds to have, for instance, a smaller crystal field contribution when coordinated to a Ln ion with oblate-shaped 4f-electron cloud for its largest mJ state (ex. Dy III ). This is nicely illustrated with the three series of compounds [Dy(bbpen)X] (Table 11 entries 14-15, Figure 17) 168 and [Dy(bbpen-CH3)X] (entries 19-20), 169 and [Dy(bbpen-OMe)X] (entries 21-26) 170 where the modification of the equatorial halogen ligand from Cl -to weaker crystal field ligand Br -leads to a large increase of Ueff/kB and, to a lesser extent, of TB. Same effect was observed for [Zn2Dy(TTT Cl )2L]•X (X = NO3 -, CF3SO3 -, BPh4 -, entry 29) 172 when equatorial ligand L was changed from methanol to weaker field ligands acetone, DMF, and finally N-methylpyrrolidone. A change of the ligand field can be obtained also by a modification of the donor atoms or functions of the polydentate ligand itself. For instance, changing imine to amine ligand can lower the crystal field contribution. This is illustrated by a series of Schiff-base Dy complexes and their amine-ligand homologues, [Dy(Bpen)Cl3] 173 (

II.3 PBP Ln complexes as building units

The use of Ln complexes as building units to achieve polynuclear nanomagnets taking advantage of the large axial magnetic anisotropy of the PBP Ln centers starts to be explored. For instance, trinuclear compounds [{Dy(bbpen)}2{M(CN)6}] -(M = Fe III , Co III ) 167 (Figure 18) were formed by assembling of [Dy(bbpen)] + and either [Fe(CN)6] 3-or [Co(CN)6] 3-, and the linkage takes place in the equatorial plane of the PBP coordination sphere of Dy. These complexes behave as SMMs characterized, for the Co derivative, by energy barriers for magnetization reversal as high as 955 K and a blocking temperature of 15 K (Table 11, entries 16 and 17). These values well compare with that of the mononuclear [Dy(bbpen)X] complexes (Table 11, entries 14 and 15), whereas for Fe III derivative, the presence of exchange interactions was found to induce a faster relaxation of the magnetization. metallacrowns by an hydroxyl group (Figure 19, Table 11 entry 38). 165 Each Dy III is located in the cavity of a metallocrown of five Cu II centers and exhibits a PBP coordination sphere where the bridging hydroxyl group occupies an apical position. This double-decker arrangement leads the anisotropy axes of the two Dy centers to be almost collinear, and to a ferromagnetic Dy-Dy interaction. This 3d-4f SMM is characterized by a Ueff/kB = 837 K, and a magnetic hysteresis up to 6 K.

III. Final comments and outlook

This overview of the magnetic anisotropies associated to a pentagonal bipyramidal coordination sphere for transition metal and lanthanide ions permits to highlight some general trends that can guide the chemist for the design of a compound with determined properties.

For the transition metal ions, the magnetic anisotropy arising from zero-field splitting is directly related to the d n electronic configuration. For this reason, it can be rationally imparted to a coordination complex. Complexes characterized by a D of a few cm -1 are accessible with V III (D > 0) or Cr III (D < 0) while larger anisotropies result from the use of Co II (D > 0), Fe or Ni (D <0). The ZFS parameters D and E are directly related to the effective energy diagram for the d orbitals of the considered metal ion, therefore adjusting the symmetry of PBP coordination sphere and possibly the ligand field in the axial and equatorial positions of the complex permits achieving larger anisotropies. For 3d ions, values up to -30 cm -1 (for Ni II ) and +40 cm -1 (for Co II ) of the axial ZFS parameter D are readily available by chemical design. The move to 4d and 5d metal ions leads to even larger anisotropies. Little information is currently available on these heavier ions, but they are very promising and could bridge the gap between the magnetic anisotropy exhibited by 3d ions and that of Ln ions in PBP geometry, thus opening new perspectives for efficient transition metal-based nanomagnets.

For rare-earth ions, the pentagonal bipyramidal geometry is especially interesting because its axial symmetry allows control of both the axial and equatorial components of the ligand field. The balance between axial and equatorial ligand field plays a key role in the anisotropy, and thus in the SMM characteristics of the complexes. To achieve largest magnetic anisotropy, it must be adapted to the spatial distribution of the 4f electron density of the ground mJ state of the considered Ln ion. This is well illustrated by the PBP Dy III complexes for which optimization of the strong axial field ligands and weak field equatorial ligands has already yielded among the best SMMs after the Dy-metallocene derivatives. 185,186 A large choice of ligands, monodentate or polydentate, enables to constrain a coordination polyhedron close to the ideal pentagonal bipyramidal geometry and allows fine control of the ligand field in the axial and equatorial positions.

The influence of the second coordination sphere, the H-bonds networks, etc. should not be neglected when optimizing the SMM behavior of Ln derivatives and this may apply too for transition metal complexes. Rigorous work combining a close correlation between the structures of the complexes, their magnetic properties and theoretical calculations has clearly demonstrated the significant effects of the second coordination sphere on the ligand field acting on the metal ion, and consequently on the SMM behavior. These effects should not be seen as necessarily negative, the second coordination sphere may be an additional way of engineering the ligand field acting on the Ln ion.

In addition to the flexibility of their chemical design, it is quite remarkable that complexes with PBP coordination geometry are generally stable and structurally robust. This allows involving these complexes as building units with controlled magnetic anisotropy in the assembly of polynuclear materials. This is particularly interesting for the design of materials where magnetic anisotropy plays an important role in the intended magnetic behavior. There is no doubt that the involvement of PBP complexes in the construction of polynuclear magnetic systems represents an axis of development for these complexes in the near future. Appendix 1: A geometrical parameter to ascertain the degree of protonation of the hydrazide units in (H2-XL1 R ) x-ligand (x = 0, 1 or 2)

The 2,6-diacetylpyridine-bis(R-acylhydrazone) ligand can be involved in coordination to a metal ion in its neutral form, H2L1 R , or as mono-, (HL1 R ) -, or doubly-deprotonated, (L1 R ) 2-species. Due to the possible ambiguity in determining with certainty the degree of protonation of the ligand in coordination complexes by a structural study by X-ray diffraction, we have conducted a statistical study on the geometrical characteristics (distances and angles) of the ligand for the structures available in the CCDC data base. It appeared that the most selective geometrical criterion was the value of the Na-Nb-Cb angle (Figure 20) because it seems to depend little on the multiple factors that are the nature of the metal, the temperature of the measurement, the quality of the refinement. Thus, for transition metal complexes about 98% of the 136 structures with a hydrogen on each of the hydrazide groups (x = 0 ) present Na-Nb-Cb angles higher than 110°, with an average of about 114.5°. If we take into account only the structures with an angle >110°, the lower quartile is 113.8, the upper quartile is 115.2°, for a maximum value of 119.9°. Of the 52 structures assumed to have a fully deprotonated ligand (x = 2), 89% have a Na-Nb-Cb angle < 110°, with an average value of 109.1°. For the remaining 11% values range up to 117°. Finally, of the 9 structures deposited with a partially deprotonated ligand (x = 1), eight show Na-Nb-Cb angles greater than 110° for the H-bearing hydrazide and values less than 110° for the deprotonated moiety. For instance, in [Cr(HL1 Ph )(NCS)2] (Figure 20) these angles are respectively 113.0(1)° and 108.2(1)°. [START_REF] Pichon | From Heptacoordinated CrIII Complexes with Cyanide or Isothiocyanate Apical Groups to 1D Heterometallic Assemblages with All-Pentagonal-Bipyramid Coordination Geometries[END_REF] From this statistical study, it appears that the threshold of 110° for the value of the Na-Nb-Cb angle seems to be relevant to determine the protonated (> 110°) or deprotonated (< 110°) form of the hydrazide moieties of this ligand. A very similar situation applies for the Ln III complexes. Examination of 102 structures spanning over the whole 4f series lead to an average Na-Nb-Cb angle of about 115.5° when each of the hydrazide groups carries a hydrogen (x = 0 ) and of 109.1° when the hydrazide is deprotonated (x = 1 or 2). No obvious differences were found along the Ln series, indicating no effect due to the size of the metal ion. The threshold, 111°, relevant to determine the protonated (> 111°) or deprotonated (< 111°) form of the ligand is hardly different to that found for the transition metal derivatives.

Figure 1 .

 1 Figure 1. Selection of typical pentadentate ligands used in pentagonal bipyramidal complexes (for H2L1 R see also Appendix 1).

Figure 2 .

 2 Figure 2. Orbital energy diagrams for (a) ideal pentagonal bipyramidal geometry (D5h), and (b-c) in real systems after lifting of the degeneracy (qualitative sketches), with electron filling for Fe II and Co II , respectively.

17 [ 19 (

 1719 experimental theory [V(H2L1 Ph )Cl2]Cl -D = 3.9; E = 0.035 17 [V(HL1 Ph )(NCS)2] -D = 4.0; E = 0.09 17 [V(L1 Ph )(MeOH)2]Cl D = 4.5; E = 0 (a) D = 4.6; E = 0 (b) D = 3.98; E = 0.06 Mo(L1 Ph )Cl2] D = 50; E = 0.025 (b) D = 49.8; E = 0.025 NBu4)3[W(CN)7] D = 330; E = 100 (b) D = 430; E = 38 (c) D = 279; E = 0.14 19, 20 (a) from HF-EPR data; (b) from magnetic susceptibility data; (c) from M versus H data

Figure 3 .

 3 Figure 3. Comparison of the Cr III -ligand bond length (Å) in the equatorial plane in (a) [Cr(HL1 PhOMe )Cl2] and (b) [Cr(L1 PhOMe )(MeO)(MeOH)]. (Reprinted from ref. 21 with permission from Elsevier, copyright 2021)

Figure 4 .

 4 Figure 4 . Ligand field calculations for [Mo III (L1 Ph )Cl2] -: (a) 4d orbital energies of the complex. (b)Energy spectrum of the 4d 3 LF states (Excited quartet spin states (S = 3/2) are marked with blue lines). (c) Electronic structure of the ground state of the complex. The ground state is the orbital doublet 2 Φ(ML = ±1) with unquenched orbital momentum ML = ±1 resulting from the e 3 (xz,yz) doubly degenerate electronic configuration (where d±1 = (dxz ± idyz)/2 1/2 are complex d-orbitals with the definite projection of the orbital momentum ml = ±1). The 2 Φ(ML = ±1) doublet is split (by δ = 140 cm -1 ) into two real components 2 Φxz = (yz) 2 (xz) 1 and 2 Φyz = (yz) 1 (xz) 2 , which are further split by the spin-orbit coupling ζMoLS into the ground ϕ(±1/2) and excited χ(±1/2) Kramers doublets. The ground Kramers doublet ϕ(±1/2) exhibits Ising-type magnetic anisotropy; the orbital composition of its wave functions is indicated. (Reproduced from Ref.[START_REF] Manakin | Et4N)[Mo III (DAPBH)Cl2], the first pentagonal-bipyramidal Mo(iii) complex with a N3O2-type Schiff-base ligand: manifestation of unquenched orbital momentum and Ising-type magnetic anisotropy[END_REF] with permission from The Royal Society of Chemistry.)

[ 58 [ 60 [ 58 [ 61 [

 58605861 Fe(L3)Cl2]ClO4 |D| = 0.3, E/D = 0.03 (b) Fe(L3)X2]ClO4 X = Br, I, NCS 59, Fe(L3)(NCS)2]ClO4 |D| = 0.5, E/D = 0.13 (b) Fe(L1 NMe3 )(NCS)2]NCS 5/2 |D| = 1.67, |E| = 0.17, g = 2.05 (a) D = -1.6, E = -0.4 (d) Fe(L1 NMe3 )(NCS)2]2[Fe(NCS)5(H2O)] 5/2 |D| = 1.57, |E| = 0.16, g = 1.98 (a) D = -1.6/-1.5, E/D = 0.23 (d) 61 (a) EPR in solid state; (b) EPR in solution; (c) magnetic behavior; (d) theoretical calculations; quinol-NO3: 8carboxymethoxy-2-quinolinecarboxylate

Figure 5 .

 5 Figure 5.[Fe(H2L1 Ph )Cl2] with its magnetic axes; easy-axis is depicted in blue, x and y are green and red, respectively (Reproduced from reference[START_REF] Bar | Pentagonal Bipyramid FeII Complexes: Robust Ising-Spin Units towards Heteropolynuclear Nanomagnets[END_REF] with permission from Wiley-VCH, copyright 2022), and sketch showing the first three excited states which coupling with ground state give strongest contributions to D for PBP Fe II complexes.

Figure 6 .

 6 Figure 6. The two lowest molecular orbitals (optimized at the CAS(6,5)SCF level 13 ) showing the ligand-Fe π-interactions for [Fe(L1 Ph )Cl2] (left) and [Fe(L1 Ph )(MeOH)H2O](BF4)2 (right) and their energy difference in cm -1 .

68 (

 68 a) from magnetic behavior; (b) EPR data available; (c) CASSCF/NEVPT2 calculations ; (d) multiprocess relaxation analysis; tpa: 6,6'-(pyridin-2-ylmethylazanediyl)bis-(methylene)bis(N-tert-butylpicolinamide); n.a.: not available.

Figure 7 .

 7 Figure 7. Crystal structure and temperature dependence of the relaxation time (τ) for 1D-[FeL1 Ph {Ni(CN)4}] (adapted from ref. 70 with permission from The Royal Society of Chemistry).

23

 23

Figure 8 .

 8 Figure 8. SCM involving PBP Fe II centres as the source of magnetic anisotropy. (top) 1D-[Fe(H2L1 NH2 ){Cr(L1 Ph )(CN)2}]•PF6 with local easy magnetic axes depicted as blue arrows (Fe in green, Cr in light-blue. Reprinted with permission from Ref.[START_REF] Pichon | Cyano-Bridged Fe(II)-Cr(III) Single-Chain Magnet Based on Pentagonal Bipyramid Units: On the Added Value of Aligned Axial Anisotropy[END_REF] , Copyright 2022 American Chemical Society), (bottom) 1D-azido-bridged [Fe(L5 H )(N3)]•ClO4 , the red arrows represents the easy axis of magnetization of a Fe II center positioned along Nazido-Fe-Nazido axis, thus highlighting the tilt angle at the origin of weak ferromagnetism and SCM behavior (Adapted with permission from Ref.[START_REF] Drahoš | Single-Chain Magnet Based on 1D Polymeric Azido-Bridged Seven-Coordinate Fe(II) Complex with a Pyridine-Based Macrocyclic Ligand[END_REF] , copyright 2021 American Chemical Society).

Figure 9 .

 9 Figure 9. [Co(H2L1 Ph )(H2O)NO3]•NO3: (left) molecular complex, and (right) the three main positive contributions to the overall ab initio calculated ZFS parameters. 10

Figure 10 .

 10 Figure 10. PBP Co II in polynuclear complexes: (a) [Co(L1 CMeN2HCONH2 )Ln(NO3)2]NO3 derivatives obtained by ligand design, 92 (b) pentanuclear [{Co(H2L1 Ph )}3{W(CN)8}2] formed by building-block approach.[START_REF] Bar | Pentagonal Bipyramid FeII Complexes: Robust Ising-Spin Units towards Heteropolynuclear Nanomagnets[END_REF]

  from magnetic behavior; (b) EPR data available; (c) CASSCF/NEVPT2 calculations ; (d) multi-process relaxation analysis; (e) DFT calculations;(f) τ = τ0exp(Ueff/kBT); (g) τ -1 = AT n ; (h) τ -1 = BH[START_REF] Gómez-Coca | Large magnetic anisotropy in mononuclear metal complexes[END_REF] T (H in Oe; exponent is 2 due to the hyperfine interactions applying for this Kramers ion); DEF: diethylformamide; n.a.: not available; L1' stands for methyl pyrinide-4carboxylate derivative.

Figure 11 .

 11 Figure 11. PBP Ni II in [Ni(L7 Me )(H2O)2]•2BF4 (anions are not depicted), 33, 109 and sketch of the first three excited triplet states having main contributions to D.

Table 8 :

 8 Main perturbative contributions of the triplet excited states to D for a selection of PBP Ni II complexes. PBP Ni II as building unit: Pentanuclear [Ni3W2] compounds were obtained by assembling [Ni(H2L1 R )(H2O)2] 2+ and [W(CN)8] 3-. 111 They are characterized by substantial ferromagnetic Ni-W interactions (up to 30 cm -1 ) and the derivative with R = Ph was found to exhibit SMM-type behavior with an energy barrier for spin reversal of Ueff/kB = 30 K. [Ni(L7 Me )(H2O)2] 2+ and [Cr(L1 Ph )(CN)2] -resulted in the formation a 1D ferromagnetic coordination polymer behaving as an SCM with Ueff/kB = 54 K (Figure

Figure 12 .

 12 Figure 12. (a) Molecular arrangement in Single-Chain magnet [Ni(L7 Me ){Cr(L1 Ph )(CN)2}].ClO4; 33 (b) trinuclear complex featuring a central Ni II with PBP coordination sphere (drawn from ref. 117 ).

Figure 13 .

 13 Figure 13. Hexacoordinated Ni-dimer formed by reorganization of PBP [Ni(H2L1 R )(H2O)2] 2+ (redrawn from ref. 33 ).•

Table 9 .

 9 ,N-bis(2-aminobenzyl)-1,10-diaza-15C5) 2.035 vs 2.220 (N atoms) PBP Cu II complexes.

Figure 15 .

 15 Figure 15. Molecular structures of the cationic complex [Dy(Me(C6F5)CHO)2(THF)5] + . Colour code: orange, Dy; red, O; grey, C; green, F. Hydrogen atoms and the [BPh4] -moieties have been omitted for clarity. (Reprinted from ref. 143 with permission from Royal Society of Chemistry).

  The same arguments hold for the two Dy-based complexes [Dy(cy3PO)2(H2O)5]Cl3•(cy3PO)•H2O•EtOH and [Dy(cy3PO)2(H2O)5]Br3•2(cy3PO)•2H2O•2EtOH.

Figure 16 .

 16 Figure 16. Coordination environment of Dy III and outer coordination sphere connected with hydrogen bonds, in (top) [Dy(cy3PO)2(H2O)5]Cl3•(cy3PO)•H2O•EtOH and (bottom) [Dy(cy3PO)2(H2O)5]Br3•2(cy3PO)•2H2O•2EtOH. H atoms of the ligands are omitted for clarity. Color codes: Dy, cyan; P, purple; Br, orange; Cl, green; O, red; C, gray; H, light gray. (Reprinted with permission from ref. 150 , copyright 2022 American Chemical Society)

Figure 17 (

 17 Figure 17 (left) Molecular structure for [Dy(bbpen)Br]. The equatorial plane of pentagonal bipyramidal coordination sphere is highlighted. Dy, yellow; Br, brown; O, red; N, blue; C, gray. Hydrogen atoms are omitted for clarity. (right) Variable-temperature molar magnetic susceptibility data for [Dy(bbpen)Br] and [Dy(bbpen)Cl]. Solid lines correspond to the ab initio calculation results. Inset: plot of magnetic susceptibility vs temperature during FC (blue) and ZFC (red) measurements for [Dy(bbpen)Br] (left) and [Dy(bbpen)Cl] (right) (Adapted with permission from ref. 168 , copyright 2022 American Chemical Society).

-

  (a) Ueff/kB is reported for HDC = 0 Oe unless mentioned; (b) TB is the temperature of the maximum of the zero field cooled (ZFC) susceptibility unless marked *, which corresponds to the highest temperature, TH, with magnetic hysteresis cycle; (c) deviation parameter obtained by the Continuous Shape Measures (CShM) method compared to the ideal D5h symmetry configuration.

Figure 18 .

 18 Figure 18. [{Dy(bbpen)}2{M(CN)6}]•PPh4: Molecular structure and magnetic hysteresis loops at various temperatures for the complexes with M = Fe III (left) and Co III (right). (Adapted with permission from ref. 167 , copyright 2022 American Chemical Society) [Dy2Cu10(quinha)10(sal)2(OH)(py)9]•3CF3SO3 has been obtain by assembling two Dy[15-MCCu-5] metallacrowns by an hydroxyl group (Figure 19, Table11 entry 38).165 Each Dy III is located in the cavity of a metallocrown of five Cu II centers and exhibits a PBP coordination sphere where the bridging hydroxyl group occupies an apical position. This double-decker arrangement leads the anisotropy axes of the two Dy centers to be almost collinear, and to a ferromagnetic Dy-Dy interaction. This 3d-4f SMM is characterized by a Ueff/kB = 837 K, and a magnetic hysteresis up to 6 K.

Figure 19 :

 19 Figure 19: [Dy2Cu10(quinha)10(sal)2(OH)(py)9]•3CF3SO3: a) molecular structure of the double-decker [Dy{15-MCCu-5}]2 metallacrown complex. Yellow drawing shows the [15-MCCu-5] metallacrown. The green arrows represent the orientations of the anisotropy axes for each of the Dy III ions as calculated by the MAGELLAN program. b) Coordination environment of the Dy III ions. H atoms are

Figure 20 .

 20 Figure 20. Selective geometrical criterion allowing to discriminate neutral versus deprotonated hydrazide moieties in (H2-XL1 R ) x-ligands; (right) example for mono-deprotonated ligand in complex [Cr(HL1 Ph )(NCS)2].[START_REF] Pichon | From Heptacoordinated CrIII Complexes with Cyanide or Isothiocyanate Apical Groups to 1D Heterometallic Assemblages with All-Pentagonal-Bipyramid Coordination Geometries[END_REF]

Table 1 .

 1 Magnetic anisotropy in d 2 metal complexes

I.3 d 3 ions (Cr III , Mo III , W III , Re IV )

Table 2 .

 2 Magnetic anisotropy in d 3 metal complexes.

		3/2	-	-	45, 46
	[Cr(L8 EtOH )(H2O)2] 3+	3/2	-	-	47
	[Cr(HL1 Ph )(H2O)2] 2+	3/2	|2.2|		22
	[Cr(HL1 Ph )(NCS)2]	3/2	1.3		22
	[Cr(L1 Ph )(CN)2] -	3/2	-0.88 (b,c,d)	D = -0.99(0.23) to +0.92(0.27)	22-24
	[Cr(HL1 PhOMe )Cl2]	3/2	-1.8	-1.06	21
				EPR
	NaK3[Mo III (CN)7]	1/2		g|| = 3.89, g⊥ = 1.77 (e)
	cis-[W(CN)5(CO)2] 2-	1/2	gx = 1.92, gy = 1.89, gz = 1.82 (f)	29
	(NBu4)3[Re IV (CN)7]	1/2		g|| = 3.66, g⊥ = 1.759 (e)

27 (a) from HF-EPR data; (b) from magnetic susceptibility data; (c) from magnetization data; (d) unpublished results, (e) in solid state, (f) in solution, (g) CASSCF/NEVPT2 calculations

Table 3 .

 3 Magnetic anisotropy in d 5 metal complexes.

Table 4 .

 4 Magnetic anisotropy in high-spin d[START_REF] Ivanovic-Burmazovic | Advances in Inorganic Chemistry[END_REF] Fe II complexes and their SMM characteristics.

Table 5 .

 5 Polynuclear nanomagnets involving PBP Fe II units.

		Arrhenius parameters	Applied DC	Coercive
	SMMs	Ueff/kB (K)	τ0 (s)	field (kOe)	field (kOe) (T)	Ref.
	[Fe(tpa){ReCl4(CN)2}]	n.a.	n.a.	0		71
	[{Fe(L4)(H2O)}2{Cr(CN)6}]	44.3	1.4×10 -9		butterfly	79
	[{Fe(H2L1 NH2 )}{CrL1 Ph (CN)2}2]	22	3.8×10 -8	0		23
	[{Fe(H2L1 mand )}{CrL1 Ph (CN)2}2]	19	3.5×10 -7	0		24
		35	6.8×10 -8	1
	mand =
	[{Fe(H2L1 Cyclohex )}{Cr(L1 Ph )(CN)2}2]	n.a.				24
	[{Fe(H2L1 R )}3{W(CN)8}2]					13
	R = Ph	n.a.	n.a.
	R = biPh	35	4.6×10 -10	2
	SCMs
	[{Fe(L3)}2{Nb(CN)8}]	74	4.6×10 -11		4 (1 K)	67
	[{Fe(H2L1 NH2 )}{Cr(L1 Ph )(CN)2}]•PF6	113	1.6×10 -11		1.4 (2 K)	23
	[Fe(L3)CN]•BF4	35.9	5.6×10 -9	0	0.68 (2 K)	80
		39.1	1.9×10 -9	2.2
	[Fe(L4)CN]•ABSA	26.1	8.3×10 -10	0		73
	[Fe(L5 H )N3]•ClO4	87.5	5.2×10 -10	0	4.8 (2 K)

76 tpa: 6,6'-(pyridin-2-ylmethylazanediyl)bis-(methylene)bis(N-tert-butylpicolinamide); n.a.: not available

Table 7 .

 7 Magnetic anisotropy in PBP Ni II complexes.

		2.28	-14.5	-1.7	-	113
	1.6	2.22	-19.0	-1.8	-	113
	0.76	2.19	-32.8	1.0	2.26	112
	2.1 c	gx = 2.0 c			2.28
		gy = 2.1			2.48
		gz= 2.3

106

(a) distortion parameter with respect to PBP geometry calculated by SHAPE;

[START_REF] Casanova | Shape and symmetry of heptacoordinated transition-metal complexes: structural trends[END_REF] 114

(b) from magnetic behavior or as specified; (c) from EPR data; (d) CASSCF/NEVPT2 calculations ; (e) the asymmetric unit contains two Ni centers.

  ) with gz < gx, gy (i.e.

	g|| < g⊥) in agreement with singly-occupied	orbital. 119
	Complexes	Cu-L axial vs equatorial mean-distances (Å)	g factors (EPR) gx,y,z or g||, g⊥	Ref.
	[Cu(H2L N3O2R )(H2O)2]•2NO3
	R = NH2	1.922 vs 2.296		108
	R = Ph	1.942 vs 2.246		120
	R = Me	1.942 vs 2.229		121
	[CuL N7 ]•2ClO4	1.99 vs 2.356	2.02, 2.22 (b)	122
	[Cu(L terpy )(imidazole)2] 2+	2.038 vs 2.206	2.26, 2.06 (a)	123
	[Co(L COO )]	1.925 vs 2.345	2.043, 2.106, 2.307 (a)	107, 124
	[Cu(benzo15C5)Cl2]	2.248 vs 2.284	1.995, 2.294	125, 126
				2.321, 2.321, 1.995	119
	[Cu(15C5)Y2]•2X
	Y = Cl -			2.372, 2.265, 2.00 (a)
	Y = H2O, X = NO3 -	1.93 vs 2.25

Table 10 .

 10 Oe unless mentioned. b TB is the temperature of the maximum of the zero field cooled (ZFC) susceptibility unless marked *, which corresponds to the highest temperature, TH, with magnetic hysteresis cycle. c Deviation parameter obtained by the Continuous Shape Measures (CShM) method compared to the ideal D5h symmetry configuration; n.a. PBP Ln SMMs formed from mono-dentate ligands with a selection of relevant magnetic (SMM characteristics) and structural information.

	Structural information

Table 11

 11 Finally, it can be noticed that the complexes involving polydentate ligands often exhibit slightly more distorted D5h symmetry than those constructed with monodentate ligands. This is revealed by larger Shape parameters for the former (up to 2.327, Table11entry 15) while the same parameter does not exceed 0.801 (entry 26, Table10) for the latter.

	entry 39) versus [Dy(HBpen)Cl3] 174 (entry 43), and

Table 11 .

 11 PBP

Ln SMMs involving polydentate ligands with a selection of relevant magnetic (SMM characteristics) and structural information.

[Mo(L1 Ph )Cl2] - 1/2 -25

SMM relaxation characteristics Structural information

Entry Complex

Ueff/kB (a) (K) τ0 (s) Ucal/kB (K) Hysteresis (field sweep Ts -1 )