Molecular S = 2 High-Spin, S = 0 Low-Spin and S = 0 (cid:29) 2 Spin-Transition/-Crossover Nickel(II)-Bis(nitroxide) Coordination Compounds

: Heterospin systems have a great advantage in frontier orbital engineering since they utilize a wide diversity of paramagnetic chromophores and almost inﬁnite combinations and mutual geometries. Strong exchange couplings are expected in 3d–2p heterospin compounds, where the nitroxide (aminoxyl) oxygen atom has a direct coordination bond with a nickel(II) ion. Complex formation of nickel(II) salts and tert -butyl 2-pyridyl nitroxides afforded a discrete 2p–3d–2p triad. Ferromagnetic coupling is favored when the magnetic orbitals, nickel(II) d σ and radical π *, are arranged in a strictly orthogonal fashion, namely, a planar coordination structure is characterized. In contrast, a severe twist around the coordination bond gives an orbital overlap, resulting in antiferromagnetic coupling. Non-chelatable nitroxide ligands are available for highly twisted and practically diamagnetic complexes. Here, the Ni–O–N–C sp2 torsion (dihedral) angle is supposed to be a useful metric to describe the nickel ion dislocated out of the radical π * nodal plane. Spin-transition complexes exhibited a planar coordination structure in a high-temperature phase and a nonplanar structure in a low-temperature phase. The gradual spin transition is described as a spin equilibrium obeying the van’t Hoff law. Density functional theory calculation indicates that the energy level crossing of the high- and low-spin states. The optimized structures of diamagnetic and high-spin states well agreed with the experimental large and small torsions, respectively. The novel mechanism of the present spin transition lies in the ferro-/antiferromagnetic coupling switch. The entropy-driven mechanism is plausible after combining the results of the related copper(II)-nitroxide compounds. Attention must be paid to the coupling parameter J as a variable of temperature in the magnetic analysis of such spin-transition materials. For future work, the exchange coupling may be tuned by chemical modiﬁcation and external stimulus, because it has been clariﬁed that the parameter is sensitive to the coordination structure and actually varies from 2 J / k B = +400 K to − 1400 K. Ar ring improves persistency of the radicals under ambient conditions.


Introduction
Various magnetic switches operative in solid states are of great interest for applications to display, memory, sensor, and related smart devices [1][2][3][4][5][6][7][8]. Structural transformations in solid states often induce a change of a number of physical properties, including magnetic, chromic, and electric properties, associated with a change of the unit cell volume, crystal/molecular symmetry and chirality, electronic state, and spin states. Heterospin systems have a great advantage in frontier orbital engineering since they utilize a wide diversity of paramagnetic (open-shell) chromophores and almost infinite combinations and mutual geometries. Organic radical species can work as ligands [6][7][8], and Gatteschi et al. have proposed the versatile "metal-radical approach," where considerable magnetic exchange interaction occurs through direct metal-radical coordination bonds [9,10]. Resultant short spin-spin distances and paramagnetically dense systems are favorable for magnetic exchange interaction occurs through direct metal-radical coordination bonds [9,10]. Resultant short spin-spin distances and paramagnetically dense systems are favor able for constructing strongly exchange-coupled materials and magnets. Recent works on metal-organic frameworks are making progress in materials involving a radical hos and/or guest [11,12]. Multi-nuclearity and -dimensionality are important keywords in the field of molecule-based materials chemistry [13][14][15][16][17].
In spin-transition phenomenon, LS states are favored for the enthalpy control in a low-temperature phase, whereas HS states for the entropy control in a high-temperature phase [34,35]. As Figure 1 depicts, the Gibbs energy of a HS state tends to be low-lying in a high-temperature phase due to an enhanced entropy term in G = H − TS. Entropy as a coefficient of temperature becomes larger when a spin multiplicity is higher, because the degeneracy 2S + 1 contributes to the entropy by nR ln(2S + 1). The critical temperature T is defined with the energy-level crossing between the HS and LS states. Spin-transition behavior would take place only under limited conditions, where the energy levels of HS and LS states are close to each other. A major subject of this review is to describe a successful application of the magneto structural correlation to development of molecular HS, LS, and novel spin-transition com pounds in nickel(II)(3d 8 )-bis(nitroxide) heterospin systems. While exotic spin-transition/ crossover systems have been explored extensively [6,36,37], we will report here the S = 0 ⇄ 2 spin-transition system other than iron(II) complexes. We have utilized nitroxides o aminoxyls as a 2p spin source, because nitroxides are persistent enough when sterically bulky and/or π-conjugate substituents are attached at appropriate positions [38,39]. Ni troxides are highly accessible and chemically modifiable in many ways [40][41][42][43][44][45], and actu ally various spin label agents, such as TEMPO and PROXYL, are commercially available and derivatized by users [39,40,46,47]. The new nickel(II)-bis(nitroxide) coordination com pounds of the present work were synthesized in a rational manner, since the molecules are designable. The chelate ring size is programmable in particular. After overviewing the various ground states in nickel(II)-bis(nitroxides), the transition can be assumed just as an entropy-driven SCO phenomenon, which is highlighted in this review. A major subject of this review is to describe a successful application of the magnetostructural correlation to development of molecular HS, LS, and novel spin-transition compounds in nickel(II)(3d 8 )-bis(nitroxide) heterospin systems. While exotic spin-transition/crossover systems have been explored extensively [6,36,37], we will report here the S = 0 2 spin-transition system other than iron(II) complexes. We have utilized nitroxides or aminoxyls as a 2p spin source, because nitroxides are persistent enough when sterically bulky and/or π-conjugate substituents are attached at appropriate positions [38,39]. Nitroxides are highly accessible and chemically modifiable in many ways [40][41][42][43][44][45], and actually various spin label agents, such as TEMPO and PROXYL, are commercially available and derivatized by users [39,40,46,47]. The new nickel(II)-bis(nitroxide) coordination compounds of the present work were synthesized in a rational manner, since the molecules are designable. The chelate ring size is programmable in particular. After overviewing the various ground states in nickel(II)-bis(nitroxides), the transition can be assumed just as an entropy-driven SCO phenomenon, which is highlighted in this review.
There are a few reports on related spin-transition in 3d-2p heterospin systems. Though the present review is focused on nickel(II)-nitroxide systems, some relevant copper(II)nitroxide systems have already been known, and we have to check them out. Ovcharenko et al. intensively explored the spin-transition materials in copper(II)(3d 9 )-nitroxide compounds as named "breathing crystals" [48][49][50]. The mechanism has been originally proposed by Rey et al., which involves a switch of the role of axial and equatorial coordinations [51,52]. It works only in octahedral copper(II) systems having the magnetic orbital in a basal plane. In contrast, our group focused on octahedral nickel(II) complexes, where the magnetic orbitals are localized both in 3d z 2 and 3d x 2 −y 2 . A coupling switch actually takes place at any coordination sites, axial or equatorial. Another advantage of our system is strong ferromagnetic coupling, often stronger than the order of a thermal energy at room temperature.
Rey et al. also reported another type of spin transition in copper(II)-nitroxide materials [53]. The copper(II) coordination environment is changed between a trigonal bipyramid and a square pyramid. This mechanism utilized the five-coordinate environment, and it would be limited practically only for copper(II) compounds. Their compounds were regarded as a "pseudo-spin-transition" material displaying an alteration between strong and weak ferromagnetic couplings. According to their classification, "genuine spin-transition" materials that would serve a ferro-/antiferromagnetic coupling switch are the target of our project.

Advantage of Nitroxides
Heterospin strategy takes advantage of a variety of the symmetry and energy level of magnetic orbitals. The exchange interactions in heterospin compounds have been intensively investigated in connection with molecular structures [9,10,[54][55][56][57][58], because they are regulated as well with their mutual spatial arrangement. McConnell has proposed that the exchange interaction is proportional to the spin densities at the interacting atoms [59]. Accordingly, a paramagnetic center atom is directly bonded to a metal center, giving rise to considerable exchange coupling.
The discovery of the ferromagnetic coupling in copper(II)-and nickel(II)-SQ compounds by Kahn [69] and Benelli [70] is recognized as a pioneering work. These works are important for the progress of ferromagnetic heterospin systems in materials chemistry and also for comprehension of the nature of exchange interaction in terms of theoretical quantum chemistry. Moreover, SQ derivatives and their aza analogues have established the foundation for the development of valence tautomeric compounds [71][72][73]. The spin density at the ligating atom is reduced owing to spin delocalization onto the wide heteroatomic system: N 2 O 2 in NN, N 2 O 1 in IN, N 4 in VD, N 2 S 2 in DTDA, and N 3 in BT. Compared with these radicals, we assume that aryl tert-butyl nitroxides (Ar-NO; the tert-butyl nitroxide group is abbreviated as NO hereafter) would have an advantage; the nitroxide group has a relatively large spin density on the ligating oxygen atom [74], as proven with the ESR, NMR, and polarized neutron diffraction experiments. Iwamura et al. have explored the bulk magnets comprising HS di-and trinitroxides and magnetic transition metal ions [8]. The coordination ability of nitroxide oxygen atoms has been noticed since 1970's [9]. The discovery of the ferromagnetic coupling in copper(II)-and nickel(II)-SQ compounds by Kahn [69] and Benelli [70] is recognized as a pioneering work. These works are important for the progress of ferromagnetic heterospin systems in materials chemistry and also for comprehension of the nature of exchange interaction in terms of theoretical quantum chemistry. Moreover, SQ derivatives and their aza analogues have established the foundation for the development of valence tautomeric compounds [71][72][73]. The spin density at the ligating atom is reduced owing to spin delocalization onto the wide heteroatomic system: N2O2 in NN, N2O1 in IN, N4 in VD, N2S2 in DTDA, and N3 in BT. Compared with these radicals, we assume that aryl tert-butyl nitroxides (Ar-NO; the tert-butyl nitroxide group is abbreviated as NO hereafter) would have an advantage; the nitroxide group has a relatively large spin density on the ligating oxygen atom [74], as proven with the ESR, NMR, and polarized neutron diffraction experiments. Iwamura et al. have explored the bulk magnets comprising HS di-and trinitroxides and magnetic transition metal ions [8]. The coordination ability of nitroxide oxygen atoms has been noticed since 1970's [9].

Magneto-Structural Relationship and Molecular Design
Copper(II)-and nickel(II)-radical complexes having a direct radical coordination bond are the best documented in the 3d-2p heterospin systems [9,[60][61][62][63][64][65][66][67][68][69][70]. There have been an increasing number of compounds showing a ferromagnetic 3d-2p coupling [75][76][77][78][79][80][81]. It is believed for a long time that axial coordination in copper(II)-nitroxide complexes displays relatively weak ferromagnetic interaction whilst equatorial coordination strong antiferromagnetic interaction [9]. However, after the accumulation of experimental results, it becomes familiar that ferromagnetic interaction is possible in equatorial coordination [60][61][62]. On the contrary, the magnitude of the coupling interactions often exceeds the order of thermal energy of room temperature, even in the ferromagnetic case. The following explanation is plausible [69,74]. Strictly orthogonal arrangement of two magnetic orbitals (metal dσ and radical π*) favors ferromagnetic coupling (Figure 3a,c). In contrast, severe twist around the coordination bond gives rise to an orbital overlap between magnetic orbitals and consequently antiferromagnetic interaction (Figure 3b,d). This mechanism is operative, regardless of the equatorial or axial sites of nickel(II) coordination environments, which is different from that of some other copper(II)-radical case regulated with a different mechanism [48][49][50][51][52][53] (see Section 1). . The Ni ions are (a,c) located on the π* nodal plane and (b,d) dislocated out of the plane. This picture is also applicable to other conventional organic radical ligands having a well-defined π* nodal plane.
Depending on whether the interaction is antiferro-or ferromagnetic, the molecular spin state is called HS (the magnetic moments add up) or LS (the magnetic moments compensate each other). In this review, the local metallic spin states are unchanged; SNi 2+ = 1 and SCu 2+ = 1/2 in the HS and LS states and throughout possible spin transition.
Five-membered chelate rings seem to have advantage for the planar conformation over 6-membered ones. A 5-membered chelate has a relatively open bite angle with respect to ligating atoms and force to flatten the chelate ring. In fact, as Luneau et al. reported [61], the copper(II) and 2pyIN complex possessed a 5-membered chelate ring and ferromagnetic coupling with 2J/kB = +420 K, and the planar conformation is indicated with the Cu-N-C-Csp 2 torsion (φ) of 1.0°. Here, the exchange coupling parameter J is defined in the = −2J 1• 2 convention. In this regard, we have to stress that 2-azaaryl-NO ligands would be one of the best candidates for exploring ferromagnetic complexes, because coordination compounds with 2-azaaryl-NO always involve a 5-membered chelate ring. In Depending on whether the interaction is antiferro-or ferromagnetic, the molecular spin state is called HS (the magnetic moments add up) or LS (the magnetic moments compensate each other). In this review, the local metallic spin states are unchanged; S Ni 2+ = 1 and S Cu 2+ = 1/2 in the HS and LS states and throughout possible spin transition. Five-membered chelate rings seem to have advantage for the planar conformation over 6-membered ones. A 5-membered chelate has a relatively open bite angle with respect to ligating atoms and force to flatten the chelate ring. In fact, as Luneau et al. reported [61], the copper(II) and 2pyIN complex possessed a 5-membered chelate ring and ferromagnetic coupling with 2J/k B = +420 K, and the planar conformation is indicated with the Cu-N-Inorganics 2021, 9, 10 5 of 28 C-C sp 2 torsion (ϕ) of 1.0 • . Here, the exchange coupling parameter J is defined in thê H = −2JŜ 1 ·Ŝ 2 convention. In this regard, we have to stress that 2-azaaryl-NO ligands would be one of the best candidates for exploring ferromagnetic complexes, because coordination compounds with 2-azaaryl-NO always involve a 5-membered chelate ring. In contrast, the corresponding 2pyNN derivative having a 6-membered chelate ring is likely to undergo out-of-plane distortion and actually displays antiferromagnetic couplings [82,83]. Some exceptions have been reported; the complex from nickel(II) and 4-imidazolyl-NN exhibited a ferromagnetic coupling of 2J/k B = +85(3) K [84,85]. In that case, the small imidazole ring may force the O and N bite angle open in the 6-membered ring. Thus, the relatively planar chelate indicated with the Ni-O-N-C sp 2 torsion angle of 6.3(4) • is reasonably acceptable. A quite similar synthetic strategy has been adopted to the copper(II) perchlorate and 2-imidazolyl-NN complex, which showed 2J/k B = +216 K [86,87]. The nickel(II) analogue was also reported to show ferromagnetic coupling [87]. Another type of exception is found in the nickel(II)-2,2 -bipyridine-6,6 -diylbis(NN) complex [60]. The highly planar structure may be associated with the presence of three tandem chelate rings, one of which is a 5-membered ring involving a bpy (2,2 -bipyridine) moiety.
The choice of a geometrical parameter is key to easy comprehension of the mutual spatial arrangement of magnetic orbitals. Based on the above experimental results, |ϕ (M-O-N-C sp 2 )| is chosen as a handy metric [74,88,89]. Here, the torsion angle is defined by a dihedral angle between the M-O-N and O-N-C sp 2 planes, as depicted in the inset of Figure 4. A plot of J vs. |ϕ| for the octahedral copper(II) and nickel(II) complexes was drawn, and a distinct correlation appears ( Figure 4).   Figure 2). The source of these data has appeared in References [74,[88][89][90]. A solid line stands for a linear fit. Inset shows a schematic drawing of φ defined in the atomic sequence 1-2-3-4.
The φ parameter in M-O-N-Csp 2 implies the degree of the out-of-plane dislocation of M from the π*nodal plane defined by three sp 2 -hybridized atoms O, N, and adjacent Csp 2 in the ligand. Syn-and antiperiplanar limits correspond to φ = 0 and ±180°, respectively, as ideal in-plane coordination structures. We can simply call this to be "planar." The plus/minus sign of φ means a chirality on the torsion. The absolute values are important in the discussion of the following sections. Eventually, this formalism ( Figure 4) entirely satisfies the exchange mechanism proposed (Figure 3). The critical |φC|, where the sign of J alters from positive to negative, is optimized to 12.8(8)° [74,89]. After the data on the copper(II) and nickel(II) complexes are separated, |φ| for the nickel(II) category became 21(1)° from the linear fit or 26(3)° from the cos(2φ) fit [91,92]. Thus, the magnetic coupling becomes predictable from the molecular structure.
Theoretical background for the magneto-structural relationship is as follows. The observable exchange interaction comprises ferro-and antiferromagnetic contributions as written in Equation (1), according to Kahn's approach [54]. The JF term arises from the two-electron exchange integral (Equation (2)), which is always positive. The JAF term is regulated with the overlap and transfer integrals between the two magnetic orbitals (Equation (3)), which is negative [93][94][95].  Figure 2). The source of these data has appeared in References [74,[88][89][90]. A solid line stands for a linear fit. Inset shows a schematic drawing of ϕ defined in the atomic sequence 1-2-3-4.
The ϕ parameter in M-O-N-C sp 2 implies the degree of the out-of-plane dislocation of M from the π*nodal plane defined by three sp 2 -hybridized atoms O, N, and adjacent C sp 2 in the ligand. Syn-and antiperiplanar limits correspond to ϕ = 0 and ±180 • , respectively, as ideal in-plane coordination structures. We can simply call this to be "planar." The plus/minus sign of ϕ means a chirality on the torsion. The absolute values are important in the discussion of the following sections. Eventually, this formalism ( Figure 4) entirely satisfies the exchange mechanism proposed (Figure 3). The critical |ϕ C |, where the sign of J alters from positive to negative, is optimized to 12.8(8) • [74,89]. After the data on the copper(II) and nickel(II) complexes are separated, |ϕ| for the nickel(II) category became 21(1) • from the linear fit or 26(3) • from the cos(2ϕ) fit [91,92]. Thus, the magnetic coupling becomes predictable from the molecular structure.
Theoretical background for the magneto-structural relationship is as follows. The observable exchange interaction comprises ferro-and antiferromagnetic contributions as written in Equation (1), according to Kahn's approach [54]. The J F term arises from the two-electron exchange integral (Equation (2)), which is always positive. The J AF term is regulated with the overlap and transfer integrals between the two magnetic orbitals (Equation (3)), which is negative [93][94][95].
An intercept at ϕ = 0 ( Figure 4) stands for the J F term as a ferromagnetic limit, and a decrease accompanied by a slope for the J AF term as an angular dependence. This is why both ferro-and antiferromagnetic cases can be discussed on the same ground. The magnitude of orbital overlap is sensitive to the torsional configuration, and antiferromagnetic contribution is overwhelmingly large in general. As a result, ferromagnetic coupling would survive only when the magnetic orbitals are arranged in a strictly or very closely orthogonal manner.
In the following sections, we will describe several kinds of nickel(II)-nitroxide coordination complexes developed by our group. The 3d and 2p spins are correlated within a molecule, but the molecules are magnetically isolated in a crystal. First, ground HS molecules are demonstrated as a successful example according to the molecular design described here. Almost ideal planar coordination structures give a ferromagnetic limit (Section 2.3). Second, spin-transition (Section 2.4) and unfinished ("pseudo") spintransition molecules (Section 2.5) are elaborated, and a co-ligand dependence on the transition temperature will be discussed. Finally, ground LS molecules are shown as an almost ideal antiferromagnetic limit (Sections 2.6 and 2.7).

High-Spin Molecules
Complex formation of nickel(II) salts with aryl tert-butyl nitroxides afforded a 2p-3d-2p triad as a discrete molecule. Figure 5 shows the structural formulas of several 2pyNO-based derivatives. A bulky substituent on the Ar ring improves persistency of the radicals under ambient conditions. Inorganics 2021, 9, x FOR PEER REVIEW 7 of 28 molecules (Section 2.5) are elaborated, and a co-ligand dependence on the transition temperature will be discussed. Finally, ground LS molecules are shown as an almost ideal antiferromagnetic limit (Sections 2.6 and 2.7).

High-Spin Molecules
Complex formation of nickel(II) salts with aryl tert-butyl nitroxides afforded a 2p-3d-2p triad as a discrete molecule. Figure 5 shows the structural formulas of several 2pyNO-based derivatives. A bulky substituent on the Ar ring improves persistency of the radicals under ambient conditions.    meridional 6pbyNO ligands. The two ligands are crystallographically independent. Furthermore, there are two independent molecules in a unit cell. The Ni-O and Ni-N distances in 2.084(3)-2.100(3) and 1.965(3)-2.086(4) Å, respectively, form an octahedral environment around the nickel(II) ion, guaranteeing that each nickel ion has SNi 2+ = 1. The Ni-O-N-Csp 2 torsion angles were 4.8(4), 5.5(5), 4.6(5), and 4.9(5)°. These small torsion angles imply the planar structure of the chelate ring. The tandem 5-membered chelates are supposed to be just suitable for the coplanar coordination structure. The mother ligand 2pyNO is known to be unisolable [98], so that the complexes were synthesized immediately after the formation of 2pyNO without isolation. The chelate rings involving 2pyNO in [Ni(2pyNO)2(H2O)2](ClO4)2 [97] are depicted in Figure 6b. A two-fold axis is located at Ni1. Two water molecules occupy the axial positions, and an octahedron is characterized with the Ni-O and Ni-N distances of 2.008(2)-2.080(4) Å. The The mother ligand 2pyNO is known to be unisolable [98], so that the complexes were synthesized immediately after the formation of 2pyNO without isolation. The chelate rings involving 2pyNO in [Ni(2pyNO) 2 (H 2 O) 2 ](ClO 4 ) 2 [97] are depicted in Figure 6b. A two-fold axis is located at Ni1. Two water molecules occupy the axial positions, and an octahedron is characterized with the Ni-O and Ni-N distances of 2.008(2)-2.080(4) Å. The small Ni1-O1-N2-C1 torsion angle (3.9(3) • ) was recorded. Even a single 5-membered chelate ring can afford a planar structure, and this finding allows us a variety of chemical modification on the 2py ring (see below).
The outline on how to comprehend the magnetic behavior is depicted in Figure 7. The theoretical χ m T value, the product of the molar magnetic susceptibility and temperature, or the Curie constant is calculated from the spin quantum number S according to Equation (4), where the symbols have the following meanings; N A , the Avogadro constant; µ B , the Bohr magneton; k B , the Boltzmann constant; g, the Landé g factor. The spin-only value with g = 2 can approximately be rephrased as Equation (5) in the conventional unit of the Curie constant, cm 3 K mol −1 [99][100][101]. The paramagnetic limit of multi-spin systems, where each spin center is magnetically isolated, can also be calculated. For example, a molecule comprising an octahedral nickel(II) ion (3d 8 ; S Ni 2+ = 1) and two radicals (S rad = 1/2) has 1.75 cm 3 K mol −1 in total. In contrast, the HS S total = 2 state displays 3.0 cm 3 K mol −1 . When g is deviated from 2, it would be helpful to recall that χ m T is proportional to g 2 .
Inorganics 2021, 9, 10 8 of 28 When g is deviated from 2, it would be helpful to recall that χmT is proportional to g 2 . From the magnetic study on these compounds (Figure 6c), the χmT values increased upon cooling from 300 to 100 K. This finding indicates the presence of intramolecular ferromagnetic interactions in both compounds, giving the ground spin structures drawn as ↑-↑↑-↑. The χmT values increased up to 3.2 cm 3 K mol −1 , which is close to the value 3.0 cm 3 K mol −1 for an Stotal = 2 species. At 300 K, the χmT values still exceed the spin-only paramagnetic limit (1.75 cm 3 K mol −1 ). A symmetrical linear arrayed 3-centered model (Equation (6)) was applied to the magnetic analysis. Fitting to the resultant van Vleck equation (equation (7)) [102] afforded the optimized parameters 2J/kB = +318(4) and +252(6) K for [Ni(6bpyNO)2](PF6)2 and [Ni II (2pyNO)2(H2O)2](ClO4)2, respectively, after possible contribution from intermolecular antiferromagnetic coupling and nickel(II) ion zero-field-splitting effect are taken into consideration. From the magnetic study on these compounds (Figure 6c), the χ m T values increased upon cooling from 300 to 100 K. This finding indicates the presence of intramolecular ferromagnetic interactions in both compounds, giving the ground spin structures drawn as ↑-↑↑-↑. The χ m T values increased up to 3.2 cm 3 K mol −1 , which is close to the value 3.0 cm 3 K mol −1 for an S total = 2 species. At 300 K, the χ m T values still exceed the spinonly paramagnetic limit (1.75 cm 3 K mol −1 ). A symmetrical linear arrayed 3-centered model (Equation (6)) was applied to the magnetic analysis. Fitting to the resultant van Vleck equation (equation (7)) [102] afforded the optimized parameters 2J/k B = +318(4) and +252(6) K for [Ni(6bpyNO) 2 ](PF 6 ) 2 and [Ni II (2pyNO) 2 (H 2 O) 2 ](ClO 4 ) 2 , respectively, after possible contribution from intermolecular antiferromagnetic coupling and nickel(II) ion zero-field-splitting effect are taken into consideration.
Hence, we have clarified the first examples of nickel(II) complexes that possess highly planar Ar-NO chelate rings and at the same time show considerably strong ferromagnetic interactions ( Figure 6). The exchange mechanism based on the coordination geometry ( Figure 4) is plausible, and molecular design seems to be promising.
There have now been a number of instances of ferromagnetic nickel(II)-radical complexes. We have designed novel paramagnetic ligands phpyNO and meopyNO ( Figure 5), in which Ph and MeO groups are introduced at the "para" position with respect to the nitroxide group for improving stability of the ligands themselves under ambient conditions. The experimental results using them are entirely compatible with the results and discussion on the mother 2pyNO complexes. From the X-ray crystallographic analysis of [NiL 2 (H 2 O) 2 ](ClO 4 ) 2 , the torsion angles are 1.5(3) and 4.2(3) • for L = phpyNO ( Figure 8a) and meopyNO (Figure 8b), respectively. From the magnetic study, the metal-radical ferromagnetic exchange couplings were quantified as 2J/k B = +409(10) and +288(5) K, respectively [74,88]. In fact, [Ni(phpyNO) 2 (H 2 O) 2 ](ClO 4 ) 2 enjoys the status of the record holder for the strongest nickel(II)-radical ferromagnetic coupling [91].

Spin-Transition Molecules
Upon these backgrounds described in Sections 2.1-2.3, we developed a novel spintransition behavior in heterospin 2p-3d-2p triads [Ni(phpyNO) 2 X 2 ]; X = Cl [103], Br [89]). In this section, the Cl derivative is focused (Figure 9), taking for an example. From the crystallographic study on [Ni(phpyNO)2Cl2], the nickel(II) ion forms an octahedral geometry, indicating SNi 2+ = 1 (Figure 9a). On cooling, the space group P21/c retained, and the Ni1-O1, Ni1-O2, and other bond lengths were almost unchanged. The coordination sphere can be characterized by means of the SHAPE analysis [104], and the continuous shape measures (CShM values) are a sensitive structural indicator in many conventional one-centered SCO complexes [26,30,105,106]. The CShM values to the ideal octahedron were 1.749 at 400 K and 1.970 at 85 K for [Ni(phpyNO)2Cl2], indicating that the crystal field hardly changes. This feature is characteristic of the spin transition materials of the present type. In contrast, the Ni-O-N-Csp 2 torsions are sensitively enhanced as a function of temperature (Figure 9b). The Ni-O-N-Csp 2 torsion angles are 13.0(4) and 25.8(3)° at 400 K while 29.2(2) and 38.9(2)° at 85 K. Namely, these torsions move from the "ferromagnetic region" to the "antiferromagnetic region" (Figure 4). The breakdown of the dσ(Ni)−π*(nitroxide) orthogonal geometry will lead to antiferromagnetic interaction. Figure 9c displays the magnetic susceptibility result of [Ni(phpyNO)2Cl2]. The χmT value at 400 K was 2.14 cm 3 K mol -1 , and the positive slope remained here. The extrapo-3 -1 From the crystallographic study on [Ni(phpyNO) 2 Cl 2 ], the nickel(II) ion forms an octahedral geometry, indicating S Ni 2+ = 1 (Figure 9a). On cooling, the space group P2 1 /c retained, and the Ni1-O1, Ni1-O2, and other bond lengths were almost unchanged. The coordination sphere can be characterized by means of the SHAPE analysis [104], and the continuous shape measures (CShM values) are a sensitive structural indicator in many conventional one-centered SCO complexes [26,30,105,106]. The CShM values to the ideal octahedron were 1.749 at 400 K and 1.970 at 85 K for [Ni(phpyNO) 2 Cl 2 ], indicating that the crystal field hardly changes. This feature is characteristic of the spin transition materials of the present type. In contrast, the Ni-O-N-C sp 2 torsions are sensitively enhanced as a function of temperature (Figure 9b). The Ni-O-N-C sp 2 torsion angles are 13.0(4) and 25.8(3) • at 400 K while 29.2(2) and 38.9(2) • at 85 K. Namely, these torsions move from the "ferromagnetic region" to the "antiferromagnetic region" (Figure 4). The breakdown of the dσ(Ni)−π*(nitroxide) orthogonal geometry will lead to antiferromagnetic interaction. Figure 9c displays the magnetic susceptibility result of [Ni(phpyNO) 2 Cl 2 ]. The χ m T value at 400 K was 2.14 cm 3 K mol -1 , and the positive slope remained here. The extrapolated χ m T value at the HS limit was 2.38(2) cm 3 K mol -1 at 400 K, which is larger than the paramagnetic limit from one nickel(II) ion and two radicals (2.14 cm 3 K mol -1 from g Ni 2+ = 2.36 determined from the ESR experiments). This finding implies the ground spin structure of ↑-↑↑-↑ in the high-temperature phase. On cooling, the χ m T value monotonically decreased, indicating the presence of strong antiferromagnetic interaction. The temperature range of this behavior coincides with that of the structural deformation (Figure 9b). The crystallographic study also rejects possibility of any intermolecular antiferromagnetic coupling. Below 50 K the specimen was practically diamagnetic (S total = 0). The spin structure becomes ↓-↑↑-↓. Therefore, we can conclude that the intramolecular 3d-2p interactions undergo an exchange-coupling switch. In other words, a spin transition occurs as the whole [Ni(phpyNO) 2 Cl 2 ] molecule. The variable-temperature X-band ESR study on polycrystalline [Ni(phpyNO) 2 Cl 2 ] clearly supports the spin-transition behavior.
Owing to the molecular structure deformation, the exchange coupling parameter J is supposed to be a function of temperature. Therefore, the van Vleck analysis with constant exchange coupling is inappropriate and actually did not work. Although the magnetic analysis involving temperature-dependent coupling parameter was reported [53,107], no suitable expression of J(T) is known for the present case. Instead, the magnetic data were found to perfectly obey the van't Hoff law (Figure 9c). The observed behavior is best described as equilibrium in a solid-state chemical reaction.
A question arises here whether the observed structure is an identical geometry or an average in time or space [108]. As the animated picture deposited as a supporting information file shows [103], the thermal ellipsoids of the oxygen atoms are normal during the transition. In the present case, every structure has an identical geometry, and magnetic properties are associated with each structure. The equilibrium model can be applied to the two terminal states.
The van't Hoff analysis is a popular method to quantify SCO behavior [34,54,109]. The original van't Hoff equation is given by Equation (8). The equilibrium constant is rewritten by using molar HS and LS fractions, γ HS and γ LS , respectively (Equation (9)). Putting Equation (9) into Equation (8) leads to Equation (10). The transition entropy change is related with Equation (11) because ∆G vanishes at equilibrium. The spin-transition temperature T 1/2 is defined as the temperature satisfying γ HS = γ LS , and in this treatment the phase transition temperature T C has the same meaning of T 1/2 . The χ m T data set is converted to γ HS by Equation (12), where C is the Curie constant of the HS species. Thus, the SCO temperature of [Ni(phpyNO) 2 Cl 2 ] was calculated as T 1/2 = 173.7(8) K. Note that the error bar seems to be considerably reduced, thanks to many data points from the entire temperature range used in the statistical analysis.
The experimental results on the bromide analogue [Ni(phpyNO) 2 Br 2 ] [89] are similar. The variable-temperature crystallographic analysis indicates the structural transformation. The magnetic data obeyed the van't Hoff model, clarifying T 1/2 = 134(1) K. However, it is a dissimilar point that the χ m T vs. T profile exhibited a monotonic increase to the paramagnetic limit and not to the high-spin limit on heating. The χ m T value was only 1.96 cm 3 K mol -1 at 400 K. In short, the HS nature is buried by a possible thermal depopulation from the HS state, even though the spin transition is almost finished. The experimental χ m T value approaches the non-interacting limit. Therefore, we named this behavior an apparent "incomplete spin transition" (Figure 7). The origin of "incomplete" is different from that of typical iron(II) SCO materials; incomplete SCO usually takes place in a low-temperature phase [1,110]. The theoretical calculation supports this conclusion (see the next section). Thus, the new scenario of the spin transition based on the solid-phase equilibrium reaction has been established for the X = Cl and Br compounds.
We have to refer a closely related spin-transition behavior found in the corresponding copper(II) version. The mechanism includes torsional deformation around the coordination bond just like the above nickel(II) compounds. The magnetic study of [Cu(phpyNO) 2 (H 2 O) 2 ] (BF 4 ) 2 [111] (Figure 10a) revealed the presence of the ferromagnetic coupling on both wings in a high-temperature region, leading to the spin structure of ↑-↑-↑ (S total = 3/2). After a spin transition at 175 K, the S total = 1/2 state appeared. The crystallographic analysis clarified that an out-of-plane chelate ring deformation occurred around 175 K only on one side (31.1(3) • at 94 K for Cu1-O2-N4-C16), breaking the crystal symmetry: the space groups P2 1 2 1 2 1 and C222 1 in the LS and HS phases, respectively. The spin structure of the low-temperature phase is not ↑-↓-↑, but ↑-↑-↓. Only one side transition is enough for minimization of S total to 1/2.  (Figure 10b) behaved in a different manner. Despite a 4-centered dimerized structure, the magnetic behavior can be understood as a 2-centered monomer. A spin transition took place at 64 K. The spin structures of the low-and high-temperature phases are drawn as ↑-↑ and ↑-↓, respectively, for every spin pair. The space group remains Pbca across the transition, and the dimeric molecule keeps a centrosymmetry. In this case all the chelate ring deformations are synchronized, because Stotal could be minimized to 0.
After combining the results on the nickel(II)-and copper(II)-nitroxide compounds, we obtain a clue to a driving force of this spin transition. The two Ni-O-N-Csp 2 angular deformations in [Ni(phpyNO)2X2] are synchronized, and both interactions alter from ferro-to antiferromagnetic on lowering temperature, because the spin multiplicity could reach the minimum with Stotal = 0. The present transition seems to be entropy-driven [71,113]; i.e., driven under the control of the change of spin entropy. The paramagnetic ligands play a crucial role in the motivation of the molecular deformation. It is a feasible Another example [{Cu 2+ (2pyNO·)(µ-2pyNO -)} 2 ](BF 4 -) 2 [112] (Figure 10b) behaved in a different manner. Despite a 4-centered dimerized structure, the magnetic behavior can be understood as a 2-centered monomer. A spin transition took place at 64 K. The spin structures of the low-and high-temperature phases are drawn as ↑-↑ and ↑-↓, respectively, for every spin pair. The space group remains Pbca across the transition, and the dimeric molecule keeps a centrosymmetry. In this case all the chelate ring deformations are synchronized, because S total could be minimized to 0.
After combining the results on the nickel(II)-and copper(II)-nitroxide compounds, we obtain a clue to a driving force of this spin transition. The two Ni-O-N-C sp 2 angular deformations in [Ni(phpyNO) 2 X 2 ] are synchronized, and both interactions alter from ferroto antiferromagnetic on lowering temperature, because the spin multiplicity could reach the minimum with S total = 0. The present transition seems to be entropy-driven [71,113]; i.e., driven under the control of the change of spin entropy. The paramagnetic ligands play a crucial role in the motivation of the molecular deformation. It is a feasible experiment to mask the paramagnetic center by substituting a nitroxide group with a diamagnetic ketone group. In fact, Ovcharenko's group has clarified that the copper(II)-nitroxide complex showed the molecular spin transition while no structural rearrangement took place in the corresponding ketone analogue [114].
For detailed structural studies, a single-crystal-to-single-crystal-type transformation is welcomed [115], and such conditions are often realized in the present study. The entropy change due to the spin multiplicity change is generally small, and the spin entropy regulates the enthalpy term by Equation (11), leading to minimal atomic dislocation [116,117]. The plasticity of organic-based crystals is also important in accommodation of such structural modification.
In theory [35,118,119], the entropy difference of SCO can be calculated as a sum of contributions of electronic, vibrational, rotational, and translational terms (Equation (13)). In the solid state, two last terms are excluded. The electronic contribution comes from the degeneracy of each state as shown in Equation (14). When singlet and quintet states are involved, the electronic contribution is given as R ln 5 = 13.38 J K −1 mol −1 .
The experimental ∆S values are 26.3(1) and 24.0(7) J K −1 mol −1 for the Cl and Br compounds, respectively. These values are somewhat smaller than typical values for the iron(II) compounds similarly showing S = 0 2 SCO [1,120]. The vibrational entropy contribution for the present compounds is almost negligible because the structural change is only the torsional deformation. This situation is completely different from that of the conventional one-centered SCO materials causing the drastic bond length change.
Consequently, the small but substantial spin entropy change of the present compounds suffices the small enthalpy change of the structural transition.
The combined work from detailed magnetochemistry and structural chemistry afforded the evidence for the spin transition observed as an equilibrated solid-state reaction. Such reactions involve an intersystem-crossing nature and usually accompany the structural isomerization where the internal atomic geometries struggle to satisfy the spin state of each species.

Unfinished Spin-Transition Molecules
The stabilization of HS states raises T 1/2 while that of LS states lowers T 1/2 (Figure 1). The study on the chemical modification varying T 1/2 is important not only for exploring new materials but also for checking the validity of the molecular design and discussing the steric and electronic substituent effects which regulates the energy level of each state. The purpose of this section is to explain what happens in the pseudohalide case: X = NCS [121] and NCO [122]. The topic is focused on [Ni(phpyNO) 2 (NCO) 2 ] (Figure 11).
The stabilization of HS states raises T1/2 while that of LS states lowers T1/2 ( Figure 1). The study on the chemical modification varying T1/2 is important not only for exploring new materials but also for checking the validity of the molecular design and discussing the steric and electronic substituent effects which regulates the energy level of each state. The purpose of this section is to explain what happens in the pseudohalide case: X = NCS [121] and NCO [122]. The topic is focused on [Ni(phpyNO)2(NCO)2] (Figure 11). The torsion angles around Ni-O-N-Csp 2 in [Ni(phpyNO)2(NCO)2] are 25.7(10) and 32.3(11)° at 400 K, indicating appreciable overlaps of the magnetic orbitals even at such a high temperature. On cooling, the torsion was enhanced as indicated with 33.5(5) and 36.2(4)° at 100 K (Figure 11a). However, the variation width is relatively narrow (Figure  11b), in comparison with those of the Cl and Br analogues (Section 2.4). All the observed torsion values 25.7(10)-36.2(4)° fell in the "antiferromagnetic region" in Figure 4.
The χmT value of [Ni(phpyNO)2(NCO)2] was practically null below ca. 100 K and gradually increased to 1.04 cm 3 K mol −1 on heating to 400 K (Figure 11c). A van't Hoff analysis was satisfactory like the X = Cl and Br derivatives, but T1/2 was estimated as high as ≫ 400 K. The relatively large error of T1/2 is unavoidable because it was derived only from the onset χmT data (the solid line in Figure 11c). Though T1/2 seems to be somewhat The torsion angles around Ni-O-N-C sp 2 in [Ni(phpyNO) 2 (NCO) 2 ] are 25.7(10) and 32.3(11) • at 400 K, indicating appreciable overlaps of the magnetic orbitals even at such a high temperature. On cooling, the torsion was enhanced as indicated with 33.5(5) and 36.2(4) • at 100 K (Figure 11a). However, the variation width is relatively narrow (Figure 11b), in comparison with those of the Cl and Br analogues (Section 2.4). All the observed torsion values 25.7(10)-36.2(4) • fell in the "antiferromagnetic region" in Figure 4.
The χ m T value of [Ni(phpyNO) 2 (NCO) 2 ] was practically null below ca. 100 K and gradually increased to 1.04 cm 3 K mol −1 on heating to 400 K (Figure 11c). A van't Hoff analysis was satisfactory like the X = Cl and Br derivatives, but T 1/2 was estimated as high as 400 K. The relatively large error of T 1/2 is unavoidable because it was derived only from the onset χ m T data (the solid line in Figure 11c). Though T 1/2 seems to be somewhat overestimated, owing to a depopulation effect, [Ni(phpyNO) 2 (NCO) 2 ] would undergo a possible spin transition at T 1/2 400 K. The parallel experiment and analysis on the NCS derivative, [Ni(phpyNO) 2 (NCS) 2 ], indicated a spin transition with T 1/2 = 530(20) K [121]. The molecule crystallizes in an orthorhombic Pbca with Z = 8, but the space group was changed to a monoclinic P2 1 /n with Z = 8 in the low-temperature phase. The molecules are differentiated into two morphs on cooling. Such an order-disorder-type structural transition [123][124][125] as well as a molecular packing motif change [111,126] might certify the substantial spin transition.
It is convincing that the low-temperature phase is diamagnetic, but one may wonder if the high-temperature phase has the ground state of S total = 2 or 1. The following notices strongly suggest that the ground state should be S total = 2 in the high-temperature phase: (1) The driving force is needed for structural modification on both wings. (2) The estimated χ m T value of the high-temperature phase was close to the S total = 2 limit value.
To check the structure-dependence of the exchange coupling, the density functional theory (DFT) calculation was performed in Gaussian16 [127], using the determined atomic coordinates of [Ni(phpyNO) 2 (NCO) 2 ]. The self-consistent field energies were calculated on the 100, 200, 300, and 400 K structures with the unrestricted B3LYP (Beck three-parameter hybrid functional combined with Lee-Yang-Parr correlation functional [128][129][130]) protocol and 6-311+G(2d,p) basis set. The B3LYP functional has been well-established for calculation of exchange couplings [131,132]. The broken symmetry method [133][134][135] was applied. According to this method, the ground state of the 100 K structure (Figure 11a) was singlet. The highest one was quintet with the singlet-quintet gap of −2196 K. Two triplet states, ↓-↑↑-↑ and ↑-↑↑-↓, intervene them. The ground state remained singlet at 400 K, but the gap was decreased. At the same time, the gap between the ground and first excited triplet states also became as narrow as the thermal energy of the temperatures of magnetic measurements. All the calculation results are compatible with the experiments.
Full geometry optimization calculation provided a strong support for the exchangecoupling switch. The optimization on the diamagnetic LS and S total = 2 HS states was conducted with the same protocol except for the 6-31+G(d) basis for organic elements. A model ligand methyl 2-pyridyl nitroxide (abbreviated as L') was introduced to reduce calculation cost. As Figure 12a,b shows, the Ni-O-N-C sp 2 torsion angles of diamagnetic [NiL' 2 (NCO) 2 ] are 32.7 • , and those of the S total = 2 state are decreased to 11.9 • . The calculation on the diamagnetic phase well reproduced the experimental values at 100 K, but the value of 11.9 • was not found even at 400 K. This finding is acceptable by thinking that the 400 K form is transient toward the HS form.
Another calculation was performed on a model [NiL' 2 Cl 2 ] for the spin-transition compound [Ni(phpyNO) 2 Cl 2 ] [103] (Section 2.4). The geometries of the diamagnetic and S total = 2 states were optimized on the same approximation and calculation level (Figure 12c,d, respectively). The former has ϕ = 35.4 and −27.2 • , while the latter has ϕ = −9.3 • . The calculation well reproduced the experimental LS geometries (38.9(2) and -29.2(2) at 85 K, Figure 9b) but still left a discrepancy from the experimental HS values (25.8(3) and 13.0(4) at 400 K, Figure 9b). The 400 K structure is a nearly but not ideal HS form.
protocol and 6-311+G(2d,p) basis set. The B3LYP functional has been well-established for calculation of exchange couplings [131,132]. The broken symmetry method [133][134][135] was applied. According to this method, the ground state of the 100 K structure (Figure 11a) was singlet. The highest one was quintet with the singlet-quintet gap of −2196 K. Two triplet states, ↓-↑↑-↑ and ↑-↑↑-↓, intervene them. The ground state remained singlet at 400 K, but the gap was decreased. At the same time, the gap between the ground and first excited triplet states also became as narrow as the thermal energy of the temperatures of magnetic measurements. All the calculation results are compatible with the experiments.
Full geometry optimization calculation provided a strong support for the exchangecoupling switch. The optimization on the diamagnetic LS and Stotal = 2 HS states was conducted with the same protocol except for the 6-31+G(d) basis for organic elements. A model ligand methyl 2-pyridyl nitroxide (abbreviated as L') was introduced to reduce calculation cost. As Figure 12a,b shows, the Ni-O-N-Csp 2 torsion angles of diamagnetic [NiL'2(NCO)2] are 32.7°, and those of the Stotal = 2 state are decreased to 11.9°. The calculation on the diamagnetic phase well reproduced the experimental values at 100 K, but the value of 11.9° was not found even at 400 K. This finding is acceptable by thinking that the 400 K form is transient toward the HS form.
Another calculation was performed on a model  Figure 13a summarizes the DFT calculation results of the energy gaps on the X = NCO and NCS derivatives (this section) together with those of the X = Cl and Br analogues (Section 2.4). The singlet-quintet energy gaps were +102 and +141 K for the Cl and Br derivatives, respectively. In sharp contrast to the results on the NCO and NCS derivatives, the ground spin state of the Cl and Br ones was calculated as HS at 400 K.  Figure 13a summarizes the DFT calculation results of the energy gaps on the X = NCO and NCS derivatives (this section) together with those of the X = Cl and Br analogues (Section 2.4). The singlet-quintet energy gaps were +102 and +141 K for the Cl and Br derivatives, respectively. In sharp contrast to the results on the NCO and NCS derivatives, the ground spin state of the Cl and Br ones was calculated as HS at 400 K. light green. Adapted from [122], published by MDPI, 2020. Figure 13a summarizes the DFT calculation results of the energy gaps on the X = NCO and NCS derivatives (this section) together with those of the X = Cl and Br analogues (Section 2.4). The singlet-quintet energy gaps were +102 and +141 K for the Cl and Br derivatives, respectively. In sharp contrast to the results on the NCO and NCS derivatives, the ground spin state of the Cl and Br ones was calculated as HS at 400 K. Overall, the four compounds are described in a common phase diagram (Figure 13b). The Cl and Br compounds undergo the energy level crossing, but the NCS and NCO compounds do not. The X = NCO and NCS derivatives are assumed to be a "pseudo spintransition" material [52], or more correctly an "unfinished spin-transition" material, as a result of T1/2 located beyond the upper limit of the experimental temperature (Figure 7). The spin transition is registered but unfinished to give a small HS fraction value. As for the Cl and Br compounds, T1/2 is located inside the experimental temperature window, and "genuine spin-transition" compounds are materialized. In any case, when heated above T1/2, the experimental susceptibility hardly reached the theoretical HS value but approached the paramagnetic one, due to the depopulation effect pronounced in high temperatures. We have to stress that a single-point X-ray crystallographic analysis could not reveal such a hidden structural transition.
In comparison among the four [Ni(phpyNO)2X2] derivatives, the order is summarized as T1/2(Br) < T1/2(Cl) < T1/2(NCS) < T1/2(NCO) (Figure 13b). The van der Waals radii of Br, Cl, and N have an inverse order [136], suggesting that the ligating atom mainly affects the steric congestion. Bulky coligands cannot accommodate out-of-plane displacement of Overall, the four compounds are described in a common phase diagram (Figure 13b). The Cl and Br compounds undergo the energy level crossing, but the NCS and NCO compounds do not. The X = NCO and NCS derivatives are assumed to be a "pseudo spin-transition" material [52], or more correctly an "unfinished spin-transition" material, as a result of T 1/2 located beyond the upper limit of the experimental temperature (Figure 7). The spin transition is registered but unfinished to give a small HS fraction value. As for the Cl and Br compounds, T 1/2 is located inside the experimental temperature window, and "genuine spin-transition" compounds are materialized. In any case, when heated above T 1/2 , the experimental susceptibility hardly reached the theoretical HS value but approached the paramagnetic one, due to the depopulation effect pronounced in high temperatures. We have to stress that a single-point X-ray crystallographic analysis could not reveal such a hidden structural transition.
In comparison among the four [Ni(phpyNO) 2 X 2 ] derivatives, the order is summarized as T 1/2 (Br) < T 1/2 (Cl) < T 1/2 (NCS) < T 1/2 (NCO) (Figure 13b). The van der Waals radii of Br, Cl, and N have an inverse order [136], suggesting that the ligating atom mainly affects the steric congestion. Bulky coligands cannot accommodate out-of-plane displacement of the adjacent chelate ring atoms, so that bulkiness stabilizes the HS state and consequently reduces T 1/2 .
The following will be of interest from the viewpoint of supramolecular chemistry. Another ground-low-spin example is relatively rare M/L = 3/6 compounds, [Ni 3 (pzNN) 6 ] and [Ni 3 (pzIN) 6 ] [143], where HpzNN and HpzIN are 3-pyrazolyl NN and 3-pyrazolyl IN, respectively (Figure 14a,b). A meso-helicate [144,145] (or mesocate [146]) structure is characterized. Namely, the opposite chirality around the inversion center at the central ion leads to a meso-helical symmetry as the whole molecule. For the pzNN compound, a half molecule is a crystallographically independent in a monoclinic P2 1 /n space group. The averaged ϕ(Ni-O-N-C sp 2 ) was 35.0(7) • . For the pzIN compound, the IN oxygen atom is ligated to the nickel ion, giving a 6-membered chelate structure. There are two polymorphs. One morph has an intrinsic three-fold symmetry with respect to the molecular long axis in a cubic Pa3 space group. A sixth molecule is crystallographically independent, and the unique ϕ was 38.0(5) • . The other morph is practically isomorphous to the pzNN derivative. The averaged ϕ was 43(5) • .
The magnetic susceptibility data ( Figure 14c) were analyzed after inter-site interaction was approximately introduced as a mean-field approximation, giving the 3d-2p couplings, 2J/k B = −80(2) and −106(6) K, for the pzNN and pzIN compounds, respectively. The χ m T vs. T profiles show a considerable convex, being consistent with the relatively small antiferromagnetic couplings. The stronger exchange interaction is observed in the latter than in the former, in good agreement with the larger ϕ of the latter. The finding is again reasonable, according to the magneto-structural relationship ( Figure 4). This supramolecular architecture was reproduced after replacing paramagnetic ligands with diamagnetic ones [114,[147][148][149]. This method simplifies the magnetic analysis. Using a diamagnetic ligand HpzNTR (N-tert-butyl-α-3-pyrazolylnitrone), the trinuclear nickel(II,II,II) as well as iron(II,III,II) compounds were prepared, and their magnetic properties including triply pyrazolate-bridged superexchange interaction were investigated in detail [150]. This supramolecular architecture was reproduced after replacing paramagnetic ligands with diamagnetic ones [114,[147][148][149]. This method simplifies the magnetic analysis. Using a diamagnetic ligand HpzNTR (N-tert-butyl-α-3-pyrazolylnitrone), the trinuclear nickel(II,II,II) as well as iron(II,III,II) compounds were prepared, and their magnetic properties including triply pyrazolate-bridged superexchange interaction were investigated in detail [150].

Diamagnetic Molecules
Non-chelatable ligands are available, which would give rise to further twisted coordination structures. Taking a model complex of phNO ( Figure 5) for example, a large angular torsion is expected from the steric repulsion between the nickel(II) ion and adjacent phenyl ortho-CH group (Figure 15a). A problem occurs in the stability of coordination compounds consisting of a monodentate ligand as well as the ligand itself. To solve these issues, we have employed a biradical ligand, tbpbNO ( Figure 5), known as a ground triplet molecule [151]. The novelty of this work is that [{Ni(µ-tbpbNO)(hfac) 2 } 2 ] showed a record strong exchange coupling [152], though the molecular skeleton is already known for the manganese(II) [153,154] and cobalt(II) complexes [155]. The hfac coligand was utilized because of a powerful accepting nature capable of coordinating the nitroxide oxygen atom. for the manganese(II) [153,154] and cobalt(II) complexes [155]. The hfac coligand was utilized because of a powerful accepting nature capable of coordinating the nitroxide oxygen atom. Note that the right angle is ideal for the overlapped arrangement of the metal dσ and radical π* magnetic orbitals. As Figure 15c displays, the magnetic study clarified the almost diamagnetic nature. The experimental χmT value was essentially null below 300 K and reached to a 5.6% level of the theoretical spin-only value (3.50 cm 3 K mol −1 from two SNi 2+ and four Srad centers) at 400 K.
For estimation of J, a simple extrapolation in Figure 4 is risky because the slope is related with a bonding contribution due to the magnetic orbital overlap, partly regulated by a cos(2φ) law [91]. Instead, a simulation work was performed. Each magnetic exchange coupling constant was estimated by means of DFT calculation [127] on the UB3LYP/6-311+G(2d,p) level. A simulated χmT vs. T curve was drawn on the MAGPACK program [156], using the spin Hamiltonian defined as a 6-centered macrocyclic model (Equation (15)). The simulation curve approximately reproduced the experimental data, indicating 2JNi-rad/kB = ca. −1300 to −1400 K.
Thus, we have found the largest-class torsion angles and antiferromagnetic coupling Note that the right angle is ideal for the overlapped arrangement of the metal dσ and radical π* magnetic orbitals. As Figure 15c displays, the magnetic study clarified the almost diamagnetic nature. The experimental χ m T value was essentially null below 300 K and reached to a 5.6% level of the theoretical spin-only value (3.50 cm 3 K mol −1 from two S Ni 2+ and four S rad centers) at 400 K. For estimation of J, a simple extrapolation in Figure 4 is risky because the slope is related with a bonding contribution due to the magnetic orbital overlap, partly regulated by a cos(2ϕ) law [91]. Instead, a simulation work was performed. Each magnetic exchange coupling constant was estimated by means of DFT calculation [127] on the UB3LYP/6-311+G(2d,p) level. A simulated χ m T vs. T curve was drawn on the MAGPACK program [156], using the spin Hamiltonian defined as a 6-centered macrocyclic model (Equation (15)). The simulation curve approximately reproduced the experimental data, indicating 2J Ni-rad /k B = ca. −1300 to −1400 K.
Thus, we have found the largest-class torsion angles and antiferromagnetic coupling parameters in [{Ni(µ-tbpbNO)(hfac) 2 } 2 ]. As described in Section 2.2, antiferromagnetic contribution in Equation (1) is overwhelmingly large in general. From Figures 14 and 15, the nickel(II)-nitroxide compounds showing moderate to very strong antiferromagnetic coupling can be realized according to the common logic as depicted in Figures 3 and 4. The open ligation (non-chelate) compounds are good examples for testing an antiferromagnetic extreme case. When the coupling is antiferromagnetic, a ferrimagnetic approach would be promising by using large and small spins.
The nickel(II) ion in [Ni(phpyNO) 2 ] is square planar. The valence of the nickel ion in [Ni(phpyNO) 2 ]I 3 is suggested to be +3.25 from the bond valence sum analysis [166], and accordingly, the charge balance is satisfied as [Ni 3+ (phpyNO -) 2 ]I 3 -. At this stage, it is concluded that the nitroxide ligands can be reduced with iodide according to Equation (16).
The nickel(II) ion in [Ni(phpyNO)2] is square planar. The valence of the nickel ion in [Ni(phpyNO)2]I3 is suggested to be +3.25 from the bond valence sum analysis [166], and accordingly, the charge balance is satisfied as [Ni 3+ (phpyNO -)2]I3 -. At this stage, it is concluded that the nitroxide ligands can be reduced with iodide according to Equation (16). (16) When tfpyNO [167] carrying a trifluoromethyl group ( Figure 5) was applied, the reaction with nickel(II) chloride gave [Ni(tfpyNO)2] (Figure 16c). The N-O bond length is 1.394(8) Å, which is close to that of [Ni(phpyNO)2] and characterized to be anionic. Even after the purge of a reductant iodide, the electron-accepting trifluoromethyl group facilitates the reduction of the nitroxide group.
When tfpyNO [167] carrying a trifluoromethyl group ( Figure 5) was applied, the reaction with nickel(II) chloride gave [Ni(tfpyNO) 2 ] (Figure 16c). The N-O bond length is 1.394(8) Å, which is close to that of [Ni(phpyNO) 2 ] and characterized to be anionic. Even after the purge of a reductant iodide, the electron-accepting trifluoromethyl group facilitates the reduction of the nitroxide group.
When tfpyNO [167] carrying a trifluoromethyl group ( Figure 5) was applied, the reaction with nickel(II) chloride gave [Ni(tfpyNO)2] (Figure 16c). The N-O bond length is 1.394(8) Å, which is close to that of [Ni(phpyNO)2] and characterized to be anionic. Even after the purge of a reductant iodide, the electron-accepting trifluoromethyl group facilitates the reduction of the nitroxide group. The redox ability of the tert-butyl pyridyl nitroxides has been well investigated [161][162][163][164][165] and actually confirmed here. Charge-transfer-triggered switching materials, like valencetautomeric cobalt(II)-SQ compounds [71][72][73] would be a next target of interest. It will be more promising to use manganese(II) instead of cobalt(II). Redox active Mn 2+ -nitroxide complexes of this type have recently been described [168,169], but such properties have not yet been found for cobalt(II)-nitroxides, possibly because the value of the Mn 2+/3+ redox potential is more suitable for converting nitroxides into aminoxylates than that of Co 2+/3+ .
Finally, a variety of the Ar-NO type ligands are briefly noted for possible applications in many directions. The 2py substituents can be replaced with diazaaromatic rings, and paramagnetic bridging ligands were designed and actually synthesized. Pyrimidine-4,6bis(NO) (Figure 17) was proven to be a ground triplet molecule and applied to a linear trinuclear prototype for metal organic frameworks [170]. 4-X-Substituted pyridine-2,6bis(NO) was a ground triplet molecule with 2J/k B +300 K (X = mesityl [171], 9-anthryl, tert-butoxy [172]). A bulky stabilizing substituent X is required to be treated under ambient conditions. The pyridine bridge can be elongated with bi-and terpyridines, thus giving tetradentate bpy-bis(NO) [173,174] and pentadentate tpy-bis(NO) [175]. By using these paramagnetic ligands as a host, an exchange-coupling switch has been investigated with diamagnetic as well as paramagnetic guest ions. For pursuing ground triplet bridges, one of isomeric bpy-bis(NO) ligands, 3,4 -bipyridine-6,2 -diyl bis(tert-butyl nitroxide) (34bpybis(NO)), was synthesized [176]. The spin polarization mechanism [8,115,116,[177][178][179][180] seems to hold for azaaromatic-and oligopyridine-bis(NO) systems. ent conditions. The pyridine bridge can be elongated with bi-and terpyridines, thus giving tetradentate bpy-bis(NO) [173,174] and pentadentate tpy-bis(NO) [175]. By using these paramagnetic ligands as a host, an exchange-coupling switch has been investigated with diamagnetic as well as paramagnetic guest ions. For pursuing ground triplet bridges, one of isomeric bpy-bis(NO) ligands, 3,4′-bipyridine-6,2′-diyl bis(tert-butyl nitroxide) (34bpy-bis(NO)), was synthesized [176]. The spin polarization mechanism [8,115,116,[177][178][179][180] seems to hold for azaaromatic-and oligopyridine-bis(NO) systems. Lahti et al. have exploited benzimidazole-and benzothiazole-based isolable tert-butyl nitroxide compounds, bzimNO [181] and bzthNO [182], respectively, thanks to the stabilization from the electron delocalization. The imidazole and thiazole rings are smaller than the pyridine ring. This feature seems to be attracting, because, on chelate formation, the N and O bite angle of bzimNO and bzthNO might be open, being favorable for strong 3d-2p ferromagnetic coupling. Very recently, Luneau explained the spin-transition phenomenon of [CuL2(ClO4)2] (L = 2-imidazolyl-NN) [87] in terms of a magnetic coupling switch accompanied by the coordination structure modification [169]. This mechanism is quite similar to the present one and in particular to that of [Cu(phpyNO)2(H2O)2](BF4)2 ( Figure 10a) [111]. The small aromatic substituent seems to be beneficial for approaching the energy levels of the HS and LS states each other (see Section 2.2), even though it has a six-membered chelate ring. Lahti et al. have exploited benzimidazole-and benzothiazole-based isolable tertbutyl nitroxide compounds, bzimNO [181] and bzthNO [182], respectively, thanks to the stabilization from the electron delocalization. The imidazole and thiazole rings are smaller than the pyridine ring. This feature seems to be attracting, because, on chelate formation, the N and O bite angle of bzimNO and bzthNO might be open, being favorable for strong 3d-2p ferromagnetic coupling. Very recently, Luneau explained the spin-transition phenomenon of [CuL 2 (ClO 4 ) 2 ] (L = 2-imidazolyl-NN) [87] in terms of a magnetic coupling switch accompanied by the coordination structure modification [169]. This mechanism is quite similar to the present one and in particular to that of [Cu(phpyNO) 2 (H 2 O) 2 ](BF 4 ) 2 (Figure 10a) [111]. The small aromatic substituent seems to be beneficial for approaching the energy levels of the HS and LS states each other (see Section 2.2), even though it has a six-membered chelate ring.

Concluding Remarks
We have described a number of nickel(II)-nitroxide coordination complexes which show a broad spectrum from the ground HS molecules (Section 2.3) to the ground LS molecules (Sections 2.6 and 2.7) via the transient spin-transition molecules (Sections 2.4 and 2.5). Furthermore, the extensive researches on the ligand modification are concisely summarized (Section 2.8).
Molecular design must be provided on the basis of the reliable magneto-structural relationship, and the proposed relationship has been established by the cautious structural characterization and physical property analysis. The selection of a torsion angle ϕ (M-O-N-C sp 2 ) is key to comprehend the geometry, propose a relationship, predict physical properties, and apply to molecular/crystal design and material production strategy. The torsion angle table is usually listed up in a crystallographic information file (.cif), and no recalculation is needed to assess ϕ. The ϕ parameter is handy, so that the plot of J vs. ϕ has also been applied to 4f-2p heterospin systems; for example, the Gd- [183][184][185][186][187][188][189][190][191][192], Tb- [193,194], and Dy-nitroxide compounds [195,196].
The ground HS (LS) molecules with a wide energy gap are characterized to be HS (LS) in the experimental temperature window. When the two energy levels are accidentally nearly degenerate, there is a chance of level crossing. The present structural transition or structural crossover originates in the equilibrated system regulated with the spin entropy. We almost always encountered the single-crystal-to-single-crystal structural transition/crossover in this project, thanks to the small atomic dislocation as well as the soft character of organic-based crystalline materials [197]. Though the structural change is small, the exchange coupling change is substantial because of the sensitive structure dependence. The single-point X-ray diffraction study cannot reveal a hidden transition. Combining work from magnetochemistry and structural chemistry as well as computational chemistry can tackle these problems.
The novelty of the present spin-transition mechanism lies in the ferro-/antiferromagnetic exchange-coupling switch, which is fully understood in terms of an equilibrated system ( Figure 1). The spin state is determined by antiferro-/ferromagnetic contribution balance in multi-centered systems, in place of the aufbau/Hund balance in the conventional onecentered systems. In a molecular orbital picture, the aufbau principle works in gapped d-orbitals perturbed by a ligand field. Similarly, the aufbau principle also is operative in gapped bonding and antibonding orbitals caused by an orbital interaction. The HS electron configuration is favored under the control of Hund's rule in the one-centered SCO. This effect is also called intra-site ferromagnetic interaction or potential exchange [135,198,199]. The present spin-transition phenomena can be regarded as a multi-centered SCO.
As stated in the Introduction section, an advantage of our system is the use of strong ferromagnetic coupling, often stronger than the order of 300 K. It has been realized according to an appropriate molecular design based on the magneto-structural relationship. The large spin density at the ligating atom plays a crucial role to enhance the exchange coupling and sensitize the structural dependence of the exchange coupling, thus leading to the development of the multi-centered SCO materials. The structure-sensitive magnetic coupling is noticeable by referring a ferromagnetic limit (2J/k B = +409 K [74]) to an antiferromagnetic extreme (2J/k B ≈ -1400 K [152]). For future work, this potential will be adopted to tuning of exchange coupling in 3d-2p heterospin materials by means of external stimulus.