Supramolecular Assemblies of Trinuclear Copper(II)-Pyrazolato Units: A Structural, Magnetic and EPR Study

Two anionic complexes, {[Cu3(μ3-OH)(μ-4-Ph-pz)3Cl3]2[Cu(4-Ph-pzH)4](μ-Cl)2}2− (1) and [Cu3(μ3-OH)(μ-pz)3(μ1,1-N3)2(N3)]− (2), crystallize as one-dimensional polymers, held together by weak Cu-(μ-Cl) and Cu-(μ-N3) interactions, respectively. Variable temperature magnetic susceptibility analyses determined the dominant antiferromagnetic intra-Cu3 exchange parameters in the solid state for both complexes, whereas the weak ferromagnetic inter-Cu3 interactions manifested also in the solid state EPR spectra, are absent in the corresponding frozen solution spectra. DFT calculations were employed to support the results of the magnetic susceptibility analyses.


Introduction
Herein, we present a structural, magnetic susceptibility and EPR study of two supramolecular assemblies of metallacyclic Cu II pyrazolates with Cu 3 (µ 3 -OH) cores. The focus of this work is the elucidation of weak intermolecular interactions manifested in the magnetic properties and EPR spectra of the supramolecular assemblies.
Supramolecular interactions, such as H-bonding, dipolar, metallophilic and π-π interactions, are important not only for the structural organization of molecules in 3D, but because they often play a crucial role in determining the physical and spectroscopic properties of the assemblies. A corollary of the latter statement is that, in the absence of structural data, the detection of such spectroscopic "signatures" reveals the presence of supramolecular interactions-e.g., in biological systems. Magnetic exchange is among the properties that can be modulated by supramolecular interactions, thereby introducing new functionality into a system [1]. For instance, in the layered Ni(H 2 O) 2 [Ni(CN) 4 ]·xH 2 O solid, H-bonding in the interlayer regions is shown to mediate weak ferromagnetic interactions, but when the coordinated water molecules were replaced by 3-halopyridine ligands, removing H-bonding, anti-ferromagnetic interactions through π-clouds became dominant [2]. Weak intramolecular antiferromagnetic exchange is active within a molecule containing two isolated Cu II centers separated by a K + ion, whereas relatively strong ferromagnetic interactions were found between adjacent units, along a supramolecular pathway [3]. In yet another dinuclear Cu II complex with chelating 2-hydroxy-1,10-phenanthroline and bridging thiocyanate ligands, it was shown that an intermolecular ferromagnetic exchange was facilitated by π-π interactions between phenanthroline ligands [4][5][6].
The antiferromagnetic exchange among the Cu II centers of the triangular Cu 3 (µ 3 -O/OH) units has been studied extensively by us and others [7][8][9][10][11][12]. We have recently turned our attention to interactions between weakly-coupled Cu 3 (µ 3 -O/OH) species and shown that the presence of weak dipolar interactions str evident in the magnetic susceptibility and EPR spectra of H-bonded Cu 3 (µ 3 -OH) units [13]. Continuing along the same lines, we report here the structure and magnetochemical studies of a heptanuclear Cu II assembly employing 4-phenyl-pyrazole ligands and of a polymeric structure containing Cu 3 N 6 metallacycles with terminal and bridging azido ligands.

Materials
4-Phenyl-pyrazole (4-Ph-pzH) was prepared according to a procedure from the literature [14]. All other reagents were purchased from commercial sources and used as received. Solvents were purified using standard techniques [15].

X-Ray Crystallography
Single crystal X-ray diffraction data were collected on a Bruker D8 QUEST CMOS system equipped with a TRIUMPH curved-crystal monochromator and a fine-focus X-ray tube with graphite monochromated Mo-Kα radiation (λ = 0.71073 Å) at ambient or low temperature using the APEX3 or APEX2 suite [16]. Crystal data, data collection and structure refinement details are listed in Supplementary Material (Table S1). Frames were integrated with the Bruker SAINT software package using a narrow-frame algorithm. Absorption effects were corrected using the multi-scan method (SADABS) [17]. Structures were solved by intrinsic phasing methods with ShelXT [18] and refined with ShelXL [19] using full-matrix least-squares minimization using Olex2 [20]. All non-hydrogen atoms were refined anisotropically. H atoms were included in calculated positions riding on the C atoms to which they are bonded, with C-H = 0.93 Å and Uiso(H) = 1.2 Ueq(C). Electron densities of poorly ordered lattice solvent molecules could not be modeled satisfactorily, and they were removed by using the SQUEEZE routine in PLATON [21]. In (1), the C47 and C48 atoms were constrained to have equivalent atomic displacement parameters and the relatively large thermal ellipsoids of C atoms of one of the phenyl rings (C46-C51) were restrained with enhanced rigid bond restraint [22].

EPR Spectroscopy
X-band spectra were recorded on a Bruker ESP300 spectrometer using a 4102ST rectangular cavity operating in the TE 102 mode. For variable-temperature experiments the cavity was fitted in an ESR900 dynamic continuous flow cryostat and the temperature was regulated with an Oxford ITC4 servocontrol. Q-band spectra were recorded on an EMXplus spectrometer fitted with an EMX premiumQ microwave bridge and an ER5106QTW microwave resonator operating in the TE 012 mode and controlled by the Bruker Xenon software. For variable-temperature experiments the resonator was fitted in an Oxford CF935 dynamic continuous flow cryostat and the temperature was regulated with an Oxford ITC503 servocontrol. The magnetic field was applied by a Bruker BE25 electromagnet using a Bruker ER082(155/45)Z power supply allowing a field sweep between −5 to 16,000 G.

Infrared Spectra
The coordination mode of azides to a transition metals is usually characterized by an intense IR band due to νas(N3) at 2000-2055 cm −1 for a terminal and >2055 cm −1 for a bridging N3 -; the larger values correspond to anions with unsymmetrical N-N-N bonding [39]. A broad trifurcated band with peaks at 2034, 2046 and 2060 cm −1 in the solid state spectrum of (2) ( Figure S3) is attributed to the presence of both terminal and bridging azides.

Magnetic Susceptibility of (1)
The temperature dependence of the effective magnetic moment and the molar magnetization data for (1) are shown in Figure 5. The effective magnetic moment at room temperature is 4.3 µB and is rapidly decreasing, reaching a plateau of 3.6 µB at ca. 100 K, and then further decreasing below 30 K to 3.1 µB at 1.9 K. The theoretical spin-only value for seven non-interacting Cu II ions with g = 2.0 is 4.58 µB, but usually the g-factor for this ion is much larger due to the angular orbital momentum contribution, so an even larger theoretical spin-only value is expected. The lower room temperature value of µeff together with its sharp decrease on subsequent cooling thus reflect strong

Infrared Spectra
The coordination mode of azides to a transition metals is usually characterized by an intense IR band due to ν as (N 3 ) at 2000-2055 cm −1 for a terminal and >2055 cm −1 for a bridging N 3 -; the larger values correspond to anions with unsymmetrical N-N-N bonding [39]. A broad trifurcated band with peaks at 2034, 2046 and 2060 cm −1 in the solid state spectrum of (2) ( Figure S3) is attributed to the presence of both terminal and bridging azides.

Magnetic Susceptibility of (1)
The temperature dependence of the effective magnetic moment and the molar magnetization data for (1) are shown in Figure 5. The effective magnetic moment at room temperature is 4.3 µ B and is rapidly decreasing, reaching a plateau of 3.6 µ B at ca. 100 K, and then further decreasing below 30 K to 3.1 µ B at 1.9 K. The theoretical spin-only value for seven non-interacting Cu II ions with g = 2.0 is 4.58 µ B , but usually the g-factor for this ion is much larger due to the angular orbital momentum contribution, so an even larger theoretical spin-only value is expected. The lower room temperature value of µ eff together with its sharp decrease on subsequent cooling thus reflect strong antiferromagnetic exchange. Such strong antiferromagnetic exchange within each Cu 3 (µ 3 -OH) triangle Chemistry 2020, 2 632 leads to S Cu1-2-3 = 1/2 ground spin state. Therefore, the value of µ eff /µ B ≈ 3.6 in the temperature interval 50-120 K can be explained by considering coexistence of two S Cu1-2-3 = 1/2 and one S Cu4 = 1/2 spin levels. A further decrease of µ eff below 50 K is then ascribed to weak magnetic interactions between two Cu 3 (µ 3 -OH) triangles and eventually between Cu 3 (µ 3 -OH) triangles and the central [Cu(4-Ph-pzH) 4 ] complex units (see Figure 2). Moreover, another important origin of decrease of µ eff below 50 K can be attributed to the antisymmetric exchange interactions (ASE, also named Dzyaloshinsky-Moriya interactions) within two Cu 3 (µ 3 -OH) triangles, as this kind of interaction is typical of triangular molecular systems based on Kramers ions coupled with strong antiferromagnetic exchange [40]. Moreover, an ASE has been identified and quantified in similar coordination compounds with individual Cu 3 (µ 3 -OH) or Cu 3 (µ 3 -O) motifs, and its effects on magnetic and spectroscopic properties have been demonstrated [7,41]. Additionally, the presence of ASE in (1) was evidenced by low temperature EPR spectroscopy, as discussed in the following section. Therefore, the following spin Hamiltonian has been postulated in order to quantitatively analyze the experimental magnetic datâ where the isotropic exchange, Zeeman terms and ASE expressed by The application of Moriya symmetry rules [42] for the Cu 3 (µ 3 -OH) triangles results in only one non-zero component: d ij = (0, 0, d z ) ij and it was assumed that (d z ) ij are equal for all pairs. Next, the molar magnetization in the direction of the magnetic field B a = B·(sinθcosϕ, sinθsinϕ, cosθ) was calculated as and since the magnetic data were acquired on a polycrystalline sample, the powder average of the molar magnetization was then calculated as where the isotropic exchange, Zeeman terms and ASE expressed by dij vectors, (dx, dy, dz)ij, are included. The application of Moriya symmetry rules [42] for the Cu3(µ3-OH) triangles results in only one non-zero component: dij = (0, 0, dz)ij and it was assumed that (dz)ij are equal for all pairs. Next, the molar magnetization in the direction of the magnetic field Ba = B•(sinθcosφ, sinθsinφ, cosθ) was calculated as and since the magnetic data were acquired on a polycrystalline sample, the powder average of the molar magnetization was then calculated as In order to reduce the number of free parameters, DFT calculations were employed (vide infra) from which we may assume J12 ≈ J23, |J12|, |J23| > |J13| and J12′ ≈ J14, and J12′ ,J14 > 0. Thus, magnetic data were fitted under the assumption that magnetic coupling through µ-Cl-ligands between two Cu3(µ3-OH) triangles and between Cu3(µ3-OH) triangles and the central [Cu(4-Ph-pzH)4] complex unit is In order to reduce the number of free parameters, DFT calculations were employed (vide infra) from which we may assume J 12 ≈ J 23 , |J 12 |, |J 23 | > |J 13 | and J 12 ≈ J 14 , and J 12 , J 14 > 0. Thus, magnetic data were fitted under the assumption that magnetic coupling through µ-Cl-ligands between two Cu 3 (µ 3 -OH) triangles and between Cu 3 (µ 3 -OH) triangles and the central [Cu(4-Ph-pzH) 4 ] complex unit is weakly ferromagnetic, whereas the strong antiferromagnetic exchange was expected within Cu 3 (µ 3 -OH) triangles. Such analysis resulted in best-fit values of J 12 = J 23 = −281 cm −1 , J 13 = −226 cm −1 , J 12 = J 14 = +19.7 cm −1 and |d z | = 37.1 cm −1 with an isotropic g-factor g = 2.35 ( Figure 5). The temperature-independent paramagnetism was also accounted for by adding a constant term χ TIP = 5.23 × 10 −9 m 3 mol −1 for seven copper atoms based on the generally accepted value for one Cu II ion equal to 60 × 10 −6 cm 3 mol −1 in cgs units [43], or 0.754 × 10 −9 m 3 mol −1 in SI units. In summary, the strong antiferromagnetic exchange within the Cu 3 (µ 3 -OH) triangles was confirmed together with the antisymmetric non-Heisenberg interaction, and the overall analysis was impossible without the introduction of a weak inter-triangle magnetic exchange.
The value of the magnetic exchange within the Cu 3 (µ 3 -OH) triangles is comparable to those reported in the literature for similar Cu II -pyrazolato/triazolato-bridged complexes containing µ 3 -OH group. It seems that in compound (1) reported herein, the antiferromagnetic exchange is one of the strongest (Table 1) [44]. 3.6. EPR Spectroscopy of (1) Solid state X-band EPR spectra of (1) at 4.2 K showed a complex derivative signal centered around 3000 G, with broad linewidths and a broad resonance around 3800 G (g~1.8), all characteristic of an exchange-coupled system ( Figure 6). Upon heating, part of the signal decreased in intensity, leaving an axial signal, which persisted unchanged up to 290 K, and was assigned to the central [Cu(4-Ph-pzH) 4 ] 2+ complex, which appears not to be exchange-coupled to the two Cu 3 triangles. This is in agreement with the crystal structure, showing that the main coupling pathway between [Cu(4-Ph-pzH) 4 ] and the trinuclear units-Cl-counterions at axial sites on either side of the Cu 3 -units-involves non-magnetic orbitals (d z 2 ) and consistent with the analysis of magnetic susceptibility data, where J 14 was shown to be the weakest interaction (vide supra, Section 3.5). Whereas the relaxation rate of the intradoublet signal of the Cu 3 accelerates rapidly with increasing temperature, the signal intensity of the mononuclear complex follows a Curie dependence, masking the contribution of the exchange-coupled system above 12 K. Attempts to increase the signal of the exchange-coupled system by exploiting the relaxation differences of the two components, in particular by increasing the microwave power at the low-temperature limit of the apparatus, failed; experiments at 4.0 K with microwave power of 20 mW did not selectively increase the signal intensity of that component. The above assignment is further corroborated by EPR studies in a frozen THF solution ( Figure  7) showing significant differences between the signal attributed to the two components: one axial signal exhibited hyperfine features and the other exhibited a very broad g⊥ < 2 feature. The latter feature is characteristic of half-integer trinuclear clusters and is due to the presence of magnetic asymmetries operating in tandem with antisymmetric exchange [52,53]. These characteristic features allowed simulations assuming two axial subcomponents. For the former, an S = 1/2 spin, described  The presence of the hyperfine signals in solution and not in the solid state for the mononuclear component suggests the presence of dipolar interactions that are removed upon dissolution. To test this hypothesis and better understand the solid-state spectra of (1), complementary Q-band studies were carried out. The solid-state Q-band spectra ( Figure S4) were by and large similar to the X-band ones, but they revealed additional features of the two subcomponents ( Figure 8). In particular, the The above assignment is further corroborated by EPR studies in a frozen THF solution (Figure 7) showing significant differences between the signal attributed to the two components: one axial signal exhibited hyperfine features and the other exhibited a very broad g ⊥ < 2 feature. The latter feature is characteristic of half-integer trinuclear clusters and is due to the presence of magnetic asymmetries operating in tandem with antisymmetric exchange [52,53]. These characteristic features allowed simulations assuming two axial subcomponents. For the former, an S = 1/2 spin, described by theĤ = βH gŜ +Î AŜ Hamiltonian, and for the latter an effective S = 1/2 spin, described by a simple Zeeman Hamiltonian, were assumed. Simulations with parameters g 1⊥ = 2.145, g 1|| = 2.334, A 1|| = 527 (MHz), g 2⊥ = 1.82 (g-strain = 0.37 FWHM) and g 2|| = 2.268 (relative intensities I 2 :I 1 = 0.91:1) gave a satisfactory agreement to the experimental spectrum. Due to the large number of variables, the above parameter set is indicative, as far as line widths and g-strain parameters are concerned. The above assignment is further corroborated by EPR studies in a frozen THF solution ( Figure  7) showing significant differences between the signal attributed to the two components: one axial signal exhibited hyperfine features and the other exhibited a very broad g⊥ < 2 feature. The latter feature is characteristic of half-integer trinuclear clusters and is due to the presence of magnetic asymmetries operating in tandem with antisymmetric exchange [52,53]. These characteristic features allowed simulations assuming two axial subcomponents. For the former, an S = 1/2 spin, described  The presence of the hyperfine signals in solution and not in the solid state for the mononuclear component suggests the presence of dipolar interactions that are removed upon dissolution. To test this hypothesis and better understand the solid-state spectra of (1), complementary Q-band studies were carried out. The solid-state Q-band spectra ( Figure S4) were by and large similar to the X-band The presence of the hyperfine signals in solution and not in the solid state for the mononuclear component suggests the presence of dipolar interactions that are removed upon dissolution. To test this hypothesis and better understand the solid-state spectra of (1), complementary Q-band studies were carried out. The solid-state Q-band spectra ( Figure S4) were by and large similar to the X-band ones, but they revealed additional features of the two subcomponents ( Figure 8). In particular, the signal attributed to [Cu(4-Ph-pzH) 4 ] was found to be rhombic, with a small split in its x and y components, indiscernible in the X-band experiments. The overall behavior observed in the X-band spectra was confirmed, with a composite spectrum at 5 K. spectra was confirmed, with a composite spectrum at 5 K.
The solid-state structure is characterized by a network of possible dipolar interactions along the chains formed by the trinuclear and mononuclear complexes previously described ( Figure S5). Depending on their magnetic symmetry, i.e., |J| > |J′| versus |J| < |J′|, the spin densities of the triangles may be spread out over all three metal sites, or concentrated on one of them, respectively [13]. Our tentative conclusion from DFT calculation points toward the former case, which is also consistent with the magnetic susceptibility analysis, negating the applicability of the point-dipole approximation and hindering a straightforward analysis of dipolar interactions. Moreover, the nontrivial symmetry of the structure, combined with the extended nature of the system, seriously complicated any such analysis. Therefore, a detailed analysis of the dipole-dipole interactions was not pursued in this case.  (1) The complexity of magnetic interactions in (1) demands some theoretical insight guiding the analysis of the experimental magnetic data. Therefore, the isotropic exchange parameters Ji were calculated with the help of broken-symmetry calculations using several molecular fragments derived from experimental X-ray data ( Figure 9). First, the triangular moiety was extracted and energies of high-spin state (HS) and broken-symmetry spin states (BS) were calculated with B3LYP to derive Jparameters for spin Hamiltonian

Theoretical DFT Calculations of
As a result, the energies Δ1 = −245.197 cm −1 , Δ2 = −323.346 cm −1 and Δ3 = −251.072 cm −1 were calculated, where Δi = εBS,i − εHS. From these energies, J-values were calculated by Ruiz's approach [54,55], resulting in J12 = −159 cm −1 , J13 = −86.5 cm −1 and J23 = −165 cm −1 . It must be noted that this approach is based on the so-called strong interaction limit, whereas the weak interaction limit treatment of Noodleman would have resulted in J-values generally twice larger [56]. Next, the hexanuclear molecular fragment was extracted in order to estimate the magnetic exchange mediated by chlorido-ligands between two trimeric units: The solid-state structure is characterized by a network of possible dipolar interactions along the chains formed by the trinuclear and mononuclear complexes previously described ( Figure S5). Depending on their magnetic symmetry, i.e., |J| > |J | versus |J| < |J |, the spin densities of the triangles may be spread out over all three metal sites, or concentrated on one of them, respectively [13]. Our tentative conclusion from DFT calculation points toward the former case, which is also consistent with the magnetic susceptibility analysis, negating the applicability of the point-dipole approximation and hindering a straightforward analysis of dipolar interactions. Moreover, the non-trivial symmetry of the structure, combined with the extended nature of the system, seriously complicated any such analysis. Therefore, a detailed analysis of the dipole-dipole interactions was not pursued in this case.

Theoretical DFT Calculations of (1)
The complexity of magnetic interactions in (1) demands some theoretical insight guiding the analysis of the experimental magnetic data. Therefore, the isotropic exchange parameters J i were calculated with the help of broken-symmetry calculations using several molecular fragments derived from experimental X-ray data ( Figure 9). First, the triangular moiety was extracted and energies of high-spin state (HS) and broken-symmetry spin states (BS) were calculated with B3LYP to derive J-parameters for spin Hamiltonian which J12′ equals +2.90 cm . Finally, the heptanuclear molecular fragment was investigated using spin Hamiltonian and HS and BS4 spin states were calculated, resulting in Δ123 = +1.723 cm −1 . Thus, also this interaction is weakly ferromagnetic, J14 = +0.86 cm −1 .
(a) (b) (c) Figure 9. The calculated spin density distribution using B3LYP of (1) for the HS states of Cu3 molecular fragment (a), Cu6 fragment (b) and Cu7 fragment (c). The spin density is represented by yellow As a result, the energies ∆ 1 = −245.197 cm −1 , ∆ 2 = −323.346 cm −1 and ∆ 3 = −251.072 cm −1 were calculated, where ∆ i = ε BS,i − ε HS . From these energies, J-values were calculated by Ruiz's approach [54,55], resulting in J 12 = −159 cm −1 , J 13 = −86.5 cm −1 and J 23 = −165 cm −1 . It must be noted that this approach is based on the so-called strong interaction limit, whereas the weak interaction limit treatment of Noodleman would have resulted in J-values generally twice larger [56]. Next, the hexanuclear molecular fragment was extracted in order to estimate the magnetic exchange mediated by chlorido-ligands between two trimeric units: Therefore, energies of HS and BS123 states were calculated, leading to ∆ 123 = +5.808 cm −1 , from which J 12 equals +2.90 cm −1 . Finally, the heptanuclear molecular fragment was investigated using spin Hamiltonian and HS and BS4 spin states were calculated, resulting in ∆ 123 = +1.723 cm −1 . Thus, also this interaction is weakly ferromagnetic, J 14 = +0.86 cm −1 .

Magnetic Susceptibility Studies of (2)
The temperature dependence of effective magnetic moment data for compound (2) is depicted in Figure 10. The room temperature effective magnetic moment has value 3.1 µ B , which is relatively close to the theoretical value 3.0 µ B for three non-interacting spins S 1 = S 2 = S 3 = 1/2 with g = 2.0. Upon lowering the temperature, the effective magnetic moment continually decreases down to a value of 0.1 µ B at 1.9 K, indicating the presence of strong antiferromagnetic exchange interactions. The observed magnetic behavior of (2) can be rationalized on a qualitative level by assuming dominant antiferromagnetic exchange within each triangle, which leads to S eff = 1/2 ground spin state similarly to (1) and also supported by DFT (vide infra). These Cu 3 -triangles are then coupled within the infinite chain by azido ligands, which also mediate a weak antiferromagnetic exchange. Established magnetostructural correlations [57,58] also suggest that the Cu-N-Cu angles of 115.0(2) and 105.9(2) • should mediate an antiferromagnetic exchange. Thus, from the magnetic point of view, the coordination polymer of (2) can be simplified to 1D chain of the antiferromagnetically coupled S eff = 1/2 spins with this spin Hamiltonian: where S i = S eff = 1/2. Fortunately, the analytical equation of the molar susceptibility for said system has already been derived by Johnston et al. [59] and the fitting procedure applied to the temperature dependence of the molar susceptibility of (2) resulted in J = −53 cm −1 with g = 2.2. The negative value of J confirms the antiferromagnetic exchange among the trinuclear building block within the coordination polymer in contrast to DFT calculations, which suggest ferromagnetic exchange mediated by azido ligands. Moreover, the deviation of calculated values of the effective magnetic moment at temperatures higher than ca 60 K is attributed to fact that at such high temperature, the proposed approximation of S eff = 1/2 for each Cu 3 -triangle loses its validity, because the excited S eff = 3/2 state is also populated, explaining the higher values of the effective magnetic moment in comparison to the calculated ones. It must be noted that we have tried to employ spin Hamiltonian analogous to Equation1 also for (2), but the agreement with the experimental data was not achieved. Most probably, the case of both intra and inter Cu 3 -triangle antiferromagnetic exchange would demand expanding the spin Hamiltonian to contain more spin centers to better simulate the polymeric character of the compound, which is unfortunately prohibited by large dimension of the respective Hilbert space.  (2) The 4.2 K solid-state X-band EPR spectrum of (2) is characterized by a main derivative signal at g = 2.05, and a secondary half-field transition at g = 4.06; the latter transition was attributed to magnetic interactions with neighboring complexes of the polymeric structure ( Figure 11). Due to the magnetic interaction pathway mediated by the bridging azides, which passes through non-magnetic orbitals of the copper(II) ions, this interaction may not be of exchange but of dipolar origins [60].

EPR Spectroscopy of
In frozen CH2Cl2 solutions this half-field transition disappears, in line with a disruption of the polymeric network in solution. In turn, the solution spectrum exhibits a downfield shifted feature (g = 1.74), which is a characteristic signature of magnetic anisotropy induced by the combined operation of a moderate magnetic asymmetry (J ≠ J′) and antisymmetric exchange interactions ( Figure 10) [13,52,53].

EPR Spectroscopy of (2)
The 4.2 K solid-state X-band EPR spectrum of (2) is characterized by a main derivative signal at g = 2.05, and a secondary half-field transition at g = 4.06; the latter transition was attributed to magnetic interactions with neighboring complexes of the polymeric structure ( Figure 11). Due to the magnetic interaction pathway mediated by the bridging azides, which passes through non-magnetic orbitals of the copper(II) ions, this interaction may not be of exchange but of dipolar origins [60].  (2) The 4.2 K solid-state X-band EPR spectrum of (2) is characterized by a main derivative signal at g = 2.05, and a secondary half-field transition at g = 4.06; the latter transition was attributed to magnetic interactions with neighboring complexes of the polymeric structure ( Figure 11). Due to the magnetic interaction pathway mediated by the bridging azides, which passes through non-magnetic orbitals of the copper(II) ions, this interaction may not be of exchange but of dipolar origins [60].

EPR Spectroscopy of
In frozen CH2Cl2 solutions this half-field transition disappears, in line with a disruption of the polymeric network in solution. In turn, the solution spectrum exhibits a downfield shifted feature (g = 1.74), which is a characteristic signature of magnetic anisotropy induced by the combined operation of a moderate magnetic asymmetry (J ≠ J′) and antisymmetric exchange interactions ( Figure 10) [13,52,53].  In frozen CH 2 Cl 2 solutions this half-field transition disappears, in line with a disruption of the polymeric network in solution. In turn, the solution spectrum exhibits a downfield shifted feature (g = 1.74), which is a characteristic signature of magnetic anisotropy induced by the combined operation of a moderate magnetic asymmetry (J J ) and antisymmetric exchange interactions ( Figure 10) [13,52,53].

Theoretical DFT Calculations of (2)
The magnetic interactions in (2) were also analyzed with the broken-symmetry calculations using two molecular fragments derived from experimental X-ray data ( Figure 12). First, the triangular moiety was extracted and energies of high-spin state (HS) and broken-symmetry spin states (BS) were calculated with B3LYP to derive J-parameters for spin Hamiltonian  (2) The magnetic interactions in (2) were also analyzed with the broken-symmetry calculations using two molecular fragments derived from experimental X-ray data ( Figure 12). First, the triangular moiety was extracted and energies of high-spin state (HS) and broken-symmetry spin states (BS) were calculated with B3LYP to derive J-parameters for spin Hamiltonian  (1), resulting in J12 = −176 cm −1 , J13 = −162 cm −1 and J23 = −187 cm −1 . It should also be stressed that in weak interactions, limit J-values would have been two times larger. Afterwards, the hexamer molecular fragment was extracted in order to estimate the magnetic exchange mediated by azido-ligands between two trimeric units: Thus, energies of HS and BS123 states were calculated, leading to Δ123 = +10.644 cm −1 , from which J23′ equals +5.32 cm −1 .
(a) (b) Figure 12. The calculated spin density distribution using B3LYP of (2) for the HS states of Cu3 molecular fragment (a) and Cu6 fragment (b). The spin density is represented by yellow surfaces. The isodensity surfaces are plotted with the cut-off value of 0.005 ea0 −3 . Hydrogen atoms are omitted for clarity. Figure 12. The calculated spin density distribution using B3LYP of (2) for the HS states of Cu 3 molecular fragment (a) and Cu 6 fragment (b). The spin density is represented by yellow surfaces. The isodensity surfaces are plotted with the cut-off value of 0.005 ea 0 −3 . Hydrogen atoms are omitted for clarity.

Conclusions
The one-dimensional solid state structures of (1) and (2) are held together by weak interactions via bridging anions-chlorides and azides, respectively-which are disrupted in solution. Because of the polymeric nature and low symmetry of these materials, the analysis of the magnetic properties has been supported by DFT calculations, suggesting strong antiferromagnetic exchange within Cu 3 units and weak ferromagnetic interactions among these units. The predominant antiferromagnetic exchange within the Cu 3 units has been unequivocally determined in both cases by the analysis of magnetic susceptibility characteristics. In addition, the operation of an antisymmetric exchange in (1) was evident by both magnetometry and EPR spectroscopy. The much weaker inter-Cu 3 exchange, ferromagnetic in (1) and antiferromagnetic in (2), is attributed to the fact that non-magnetic Cu-orbitals are involved at one or both ends. EPR spectroscopy determined the magnitude of dipolar interaction in solid state (1), while the possible dipolar interaction between Cu 3 -units of (2) cannot be determined with certainty. The solution EPR spectra of both compounds are clearly distinguished from those in the solid state and are straightforwardly attributed to individual Cu 3 (µ 3 -OH) species of (2), and to the presence of isolated mononuclear and trinuclear species in the case of (1). Two new reports, describing the magnetic susceptibilities and (in one case) the EPR spectrum of polymeric supramolecular assemblies of copper(II) complexes, appeared in the literature recently [61,62].