*3.4. Infrared Spectra*

The coordination mode of azides to a transition metals is usually characterized by an intense IR band due to <sup>ν</sup>*as*(N3) at 2000–2055 cm<sup>−</sup><sup>1</sup> for a terminal and >2055 cm<sup>−</sup><sup>1</sup> 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<sup>−</sup><sup>1</sup> in the solid state spectrum of (**2**) (Figure S3) is attributed to the presence of both terminal and bridging azides.

### *3.5. 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 CuII 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 antiferromagnetic exchange. Such strong antiferromagnetic exchange within each Cu3(μ3-OH) triangle

leads to *S*Cu1-2-3 = 1/2 ground spin state. Therefore, the value of μeff/μ<sup>B</sup> ≈ 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 μeff below 50 K is then ascribed to weak magnetic interactions between two Cu3(μ3-OH) triangles and eventually between Cu3(μ3-OH) triangles and the central [Cu(4-Ph-pzH)4] complex units (see Figure 2). Moreover, another important origin of decrease of μeff below 50 K can be attributed to the antisymmetric exchange interactions (ASE, also named Dzyaloshinsky–Moriya interactions) within two Cu3(μ3-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 Cu3(μ3-OH) or Cu3(μ3-O) motifs, and its e ffects 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 data

$$\begin{aligned} H &= -l\_{12}(\mathbf{S}\_1 \cdot \mathbf{S}\_2 + \mathbf{S}\_1, \cdot \mathbf{S}\_2) - l\_{13}(\mathbf{S}\_1 \cdot \mathbf{S}\_3 + \mathbf{S}\_1, \cdot \mathbf{S}\_3) - l\_{23}(\mathbf{S}\_2 \cdot \mathbf{S}\_3 + \mathbf{S}\_2, \cdot \mathbf{S}\_3) - l\_{12}(\mathbf{S}\_1 \cdot \mathbf{S}\_2, + \mathbf{S}\_1, \cdot \mathbf{S}\_2) - l\_{14}(\mathbf{S}\_1 \cdot \mathbf{S}\_4 + \mathbf{S}\_1, \cdot \mathbf{S}\_4) \\ &+ \mathbf{d}\_{12} \cdot (\mathbf{S}\_1 \times \mathbf{S}\_2 + \mathbf{S}\_1, \times \mathbf{S}\_2) + \mathbf{d}\_{23} \cdot (\mathbf{S}\_2 \times \mathbf{S}\_3 + \mathbf{S}\_2, \times \mathbf{S}\_3) + \mathbf{d}\_{31} \cdot (\mathbf{S}\_3 \times \mathbf{S}\_1 + \mathbf{S}\_3, \times \mathbf{S}\_1) + \mu\_{\mathbf{B}} \sum\_{i=1}^{2} \mathbf{B} \cdot \mathbf{g} \cdot \mathbf{S}\_i \end{aligned} \tag{1}$$

where the isotropic exchange, Zeeman terms and ASE expressed by **d***ij* vectors, (*dx*, *dy*, *dz*)*ij*, are included. The application of Moriya symmetry rules [42] for the Cu3(<sup>μ</sup>3-OH) triangles results in only one non-zero component: **d***ij* = (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 **B***a* = *<sup>B</sup>*·(sin<sup>θ</sup>cosϕ, sinθsinϕ, cos<sup>θ</sup>) was calculated as

$$M\_{\rm al} = -N\_{\rm A}kT \frac{\partial \ln Z}{\partial B\_{\rm a}} \tag{2}$$

and since the magnetic data were acquired on a polycrystalline sample, the powder average of the molar magnetization was then calculated as

$$M\_{\rm mol} = -1/4\pi \int\_0^{2\pi} \int\_0^{\pi} M\_d \sin^{\circ}\theta d\theta d\phi \tag{3}$$

**Figure 5.** Temperature dependence of the effective magnetic moment for **1**. Empty circles—experimental data, full lines—calculated data with the spin Hamiltonian in Equation (1) and *J*12 = *J*23 = −281 cm<sup>−</sup>1, *J*13 = −226 cm<sup>−</sup>1, *J*12 = *J*14 = +19.7 cm<sup>−</sup>1, |*d*z| = 37.1 cm<sup>−</sup>1, *g* = 2.35.

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 Cu3(<sup>μ</sup>3-OH) triangles and between Cu3(<sup>μ</sup>3-OH) triangles and the central [Cu(4-Ph-pzH)4] complex unit is weakly ferromagnetic, whereas the strong antiferromagnetic exchange was expected within Cu3(<sup>μ</sup>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−<sup>1</sup> and |*<sup>d</sup>*z| = 37.1 cm−<sup>1</sup> with an isotropic *g*-factor *g* = 2.35 (Figure 5). The temperature-independent paramagnetism was also accounted for by adding a constant term χTIP = 5.23 × 10−<sup>9</sup> m<sup>3</sup> mol−<sup>1</sup> for seven copper atoms based on the generally accepted value for one CuII ion equal to 60 × 10−<sup>6</sup> cm<sup>3</sup> mol−<sup>1</sup> in cgs units [43], or 0.754 × 10−<sup>9</sup> m<sup>3</sup> mol−<sup>1</sup> in SI units. In summary, the strong antiferromagnetic exchange within the Cu3(<sup>μ</sup>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 Cu3(<sup>μ</sup>3-OH) triangles is comparable to those reported in the literature for similar CuII-pyrazolato/triazolato-bridged complexes containing <sup>μ</sup>3-OH group. It seems that in compound (**1**) reported herein, the antiferromagnetic exchange is one of the strongest (Table 1) [44].

**Table 1.** Selected magnetostructural data for various Cu3(μ3-O(H/R)) systems.


*a* aat = 3-acetylamino-1,2,4-triazolate; Haaat = 3-acetylamino-5-amino-1,2,4-triazolate; admtrz = 4-amino-3,5- dimethyl-1,2,4-triazole.

### *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 Cu3 triangles. This is in agreemen<sup>t</sup> 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 Cu3-units—involves non-magnetic orbitals (dz 2) and consistent with the analysis of magnetic susceptibility data, where *J14* was shown to be the weakest interaction (*vide supra*, Section 3.5). Whereas the relaxation rate of the intradoublet signal of the Cu3 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 di fferences 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.

**Figure 6.** Solid-state X-band EPR spectra of (**1**) between 4.2 and 290 K. Experimental conditions: *f* EPR = 9.43 GHz, MA = 2 Gpp (6–290 K) and 1 Gpp (4.2 K), *PMW* = 2 mW (6–290 K) and 0.2 mW (4.2 K).

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 the *H*ˆ = β**HgS**<sup>ˆ</sup> + ˆ**IAS**<sup>ˆ</sup> Hamiltonian, and for the latter an effective *S* = 1/2 spin, described by a simple Zeeman Hamiltonian, were assumed. Simulations with parameters *g*<sup>1</sup>⊥ = 2.145, *g*1|| = 2.334, *<sup>A</sup>*1|| = 527 (MHz), *g*<sup>2</sup>⊥ = 1.82 (*g*-strain = 0.37 FWHM) and *g*2|| = 2.268 (relative intensities *I*2:*I*1 = 0.91:1) gave a satisfactory agreemen<sup>t</sup> 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.

**Figure 7.** X-band EPR spectra of (**1**) in a frozen THF solution (black line) and calculated curve according to the discussion in the text (red line). The blue and green lines correspond to the two components. Experimental conditions: *f* EPR = 9.42 GHz, MA = 2 Gpp, *PMW* = 2 mW.

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.

**Figure 8.** Q-band EPR spectra of (**1**) in a frozen THF solution (black line) and calculated curve according to the discussion in the text (red line). The blue and green lines correspond to the two components. Experimental conditions: *f* EPR = 33.96 GHz, MA = 2 Gpp, *PMW* = 0.29 mW (5 K) and 1.1 mW (295 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 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.

### *3.7. 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 *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 *J*-parameters for spin Hamiltonian

$$
\hat{H} \quad \text{---} \quad -l\_{12}(\mathbf{S}\_1 \cdot \mathbf{S}\_2 + \mathbf{S}\_{1\nu} \cdot \mathbf{S}\_{2\nu}) - l\_{13}(\mathbf{S}\_1 \cdot \mathbf{S}\_3 + \mathbf{S}\_{1\nu} \cdot \mathbf{S}\_{3\nu}) - l\_{23}(\mathbf{S}\_2 \cdot \mathbf{S}\_3 + \mathbf{S}\_{2\nu} \cdot \mathbf{S}\_{3\nu}) \tag{4}$$

**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 surfaces. The isodensity surfaces are plotted with the cut-off value of 0.005 *ea*0<sup>−</sup>3. Hydrogen atoms are omitted for clarity.

As a result, the energies Δ1 = −245.197 cm−1, Δ2 = −323.346 cm−<sup>1</sup> and Δ3 = −251.072 cm−<sup>1</sup> were calculated, where Δ*i* = <sup>ε</sup>BS,i − εHS. 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−<sup>1</sup> 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:

$$\hat{H} \quad \text{---} \quad -I\_{12}(\mathbf{S}\_1 \cdot \mathbf{S}\_2 + \mathbf{S}\_{1\nu} \cdot \mathbf{S}\_{2\nu}) - I\_{13}(\mathbf{S}\_1 \cdot \mathbf{S}\_3 + \mathbf{S}\_{1\nu} \cdot \mathbf{S}\_{3\nu}) - I\_{23}(\mathbf{S}\_2 \cdot \mathbf{S}\_3 + \mathbf{S}\_{2\nu} \cdot \mathbf{S}\_{3\nu}) - I\_{12}(\mathbf{S}\_1 \cdot \mathbf{S}\_2 + \mathbf{S}\_{1\nu} \cdot \mathbf{S}\_2) \tag{5}$$

Therefore, energies of HS and BS123 states were calculated, leading to Δ123 = +5.808 cm−1, from which *J*12 equals +2.90 cm−1. Finally, the heptanuclear molecular fragment was investigated using spin Hamiltonian

$$\hat{H} \quad = -\|\mathbf{1}\rangle \mathbf{S}\_1 \cdot \mathbf{S}\_2 + \mathbf{S}\_{1\prime} \cdot \mathbf{S}\_{2\prime}\rangle - \|\mathbf{1}\rangle (\mathbf{S}\_1 \cdot \mathbf{S}\_3 + \mathbf{S}\_{1\prime} \cdot \mathbf{S}\_{3\prime}) - \|\mathbf{1}\rangle (\mathbf{S}\_2 \cdot \mathbf{S}\_3 + \mathbf{S}\_{2\prime} \cdot \mathbf{S}\_{3\prime}) - \|\mathbf{1}\| (\mathbf{S}\_1 \cdot \mathbf{S}\_4 + \mathbf{S}\_{1\prime} \cdot \mathbf{S}\_4) \tag{6}$$

and HS and BS4 spin states were calculated, resulting in Δ123 = +1.723 cm−1. Thus, also this interaction is weakly ferromagnetic, *J*14 = +0.86 cm−1.

### *3.8. 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 μB, which is relatively close to the theoretical value 3.0 μB 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 μB 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 Cu3-triangles are then coupled within the infinite chain by azido ligands, which also mediate a weak antiferromagnetic exchange. Established magnetostructural correlations [57,58] also sugges<sup>t</sup> 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:

$$\hat{H} = -\mathfrak{J}\sum\_{i=1}^{\infty} \mathbf{S}\_{i} \cdot \mathbf{S}\_{i+1} + \mu\_{\text{B}} \sum\_{i=1}^{\infty} \mathbf{B} \cdot \mathbf{g}\_{i} \cdot \mathbf{S}\_{i} \tag{7}$$

where *Si* = *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−<sup>1</sup> 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 sugges<sup>t</sup> 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 Cu3-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 agreemen<sup>t</sup> with the experimental data was not achieved. Most probably, the case of both intra and inter Cu3-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.

**Figure 10.** Temperature dependence of the effective magnetic moment for (**2**). The empty symbols—experimental data, the red line—calculated data with *J* = −53 cm<sup>−</sup><sup>1</sup> and *g* = 2.2 using spin Hamiltonian in Equation (2).

### *3.9. 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].

**Figure 11.** X-band EPR spectra of (**2**) in the solid state (black) and a frozen CH2Cl2 solution. Experimental parameters: *f* EPR = 9.429 GHz, *PMW* = 2 mW, MA = 5 Gpp (powder); and *f* EPR = 9.425 GHz, *PMW* = 2 mW, MA = 2 Gpp (solution).

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].

### *3.10. 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

$$H \quad \text{---} \quad -l\_{12}(\mathbf{S}\_1 \cdot \mathbf{S}\_2 + \mathbf{S}\_{1\nu} \cdot \mathbf{S}\_{2\nu}) - l\_{13}(\mathbf{S}\_1 \cdot \mathbf{S}\_3 + \mathbf{S}\_{1\nu} \cdot \mathbf{S}\_{3\nu}) - l\_{23}(\mathbf{S}\_2 \cdot \mathbf{S}\_3 + \mathbf{S}\_{2\nu} \cdot \mathbf{S}\_{3\nu}) \tag{8}$$

**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 *ea*0<sup>−</sup>3. Hydrogen atoms are omitted for clarity.

As a result, the energies Δ1 = −337.724 cm−1, Δ2 = −362.944 cm−<sup>1</sup> and Δ3 = −349.454 cm−<sup>1</sup> were computed. Next, *J*-values were calculated by Ruiz's approach, as for (**1**), resulting in *J*12 = −176 cm−1, *J*13 = −162 cm−<sup>1</sup> and *J*23 = −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:

$$H \quad = -\mathbf{I}\_{12}(\mathbf{S}\_1 \cdot \mathbf{S}\_2 + \mathbf{S}\_{1\prime} \cdot \mathbf{S}\_{2\prime}) - \mathbf{I}\_{13}(\mathbf{S}\_1 \cdot \mathbf{S}\_3 + \mathbf{S}\_{1\prime} \cdot \mathbf{S}\_{3\prime}) - \mathbf{I}\_{23}(\mathbf{S}\_2 \cdot \mathbf{S}\_3 + \mathbf{S}\_{2\prime} \cdot \mathbf{S}\_{3\prime}) - \mathbf{I}\_{23\prime}(\mathbf{S}\_2 \cdot \mathbf{S}\_{3\prime} + \mathbf{S}\_{2\prime} \cdot \mathbf{S}\_3) \tag{9}$$

Thus, energies of HS and BS123 states were calculated, leading to Δ123 = +10.644 cm−1, from which *J*23 equals +5.32 cm−1.
