A Pyrazolate-Supported Fe₃(μ₃-O)-Core; Structural, Spectroscopic, Electrochemical and Magnetic Study

Synopsis

A comparison is made between the structural, spectroscopic and magnetic properties of pyrazolate versus carboxylate complexes containing the Fe₃(μ₃-O)-motif.

Introduction

Carboxylates constitute one of the widest families of transition-metal complexes and have been associated with numerous studies in all aspects of coordination chemistry. Their ubiquitous presence in Nature makes them an essential ligand in bioinorganic chemistry and an obvious choice when a chelating or bridging ligand is required. Since some early investigations of metal-metal interactions and magnetic exchange,¹ carboxylate complexes have an uninterrupted history as well in what has now become known as materials chemistry. In recent years, elegant studies of electron transfer and ground-breaking work in the new field of single molecule magnets have been carried out using transition metal carboxylates.^2,3

In the course of our investigations of transition-metal pyrazolate chemistry, we became aware of the existence of a structural parallel between carboxylate and pyrazolate complexes of the same nuclearity: quite similar Pd-Pd distances are found in the trinuclear [Pd(μ-O₂CR)₂]₃ and [Pd(μ-pz)₂]₃ complexes (pz = pyrazolato, C₃H₃N₂^—, or substituted pyrazolato anion).^4,5 Additional examples exist in the literature, as between the tetranuclear Cu^I-carboxylates [Cu(μ-O₂CPh)]₄ and [Cu(μ-O₂CCF₃)]₄ on one hand and the pyrazolate [Cu(μ-3,5-Ph₂-pz)]₄ on the other.^6,7 Replacement of one ligand by another, while the metal-core motif remains mostly unperturbed, can have significant effects on the physical properties of the metal centers, as both their electronic structure, as well as their electronic and magnetic communication are influenced by the donor-acceptor properties and orbital symmetry of the ligands. Perlepes et al. have shown that substitution of a hydroxide or cyanide by an azide bridge inverts the sign of magnetic exchange in nonanuclear Ni²⁺, Co²⁺ and Fe²⁺ clusters.⁸ Considering the central role of carboxylates as ligands in Coordination and Materials Chemistry -- particularly in the fast expanding field of single-molecule magnets ³ -- the development of a parallel class of structurally related pyrazolates would open-up a number of new possibilities. In order to investigate further this structural parallel and its accompanying effects, we turned our attention to one of the best known motifs in carboxylate chemistry, namely the M₃(μ₃-O)- core, which includes examples of most transition metals.⁹

A variety of [Fe₃(μ₃-O)(μ-O₂CR)₆L₃] complexes have been studied with regard to the magnetic and electronic interactions of their three paramagnetic metal centers.¹⁰ The long metal-metal distances within the Fe₃(μ₃-O)-unit preclude direct metal-metal bonding and the magnitude of the O-mediated antiferromagnetic exchange among them is determined by the Fe-O bond lengths.¹¹ Trinuclear [Fe₃(μ₃-O)(μ-O₂CR)₆L₃] complexes have proven excellent starting materials for the synthesis of higher nuclearity clusters, taking advantage of the lability of carboxylate ligands.¹²

Here we report on the synthesis, characterization, X-ray crystal structure, infrared and electrochemical study of the trinuclear anion [Fe₃(μ₃-O)(μ-4-O₂N-pz)₆Cl₃]²⁻ (1), (Figure 1), as its Et₃NH⁺ (a), Bu₄N⁺ (b) or PPh₄⁺ (c) salts, along with the Electron Paramagnetic Resonance (EPR), the Mössbauer spectroscopy, magnetic susceptibility and magnetization studies for 1a. We present a comparison among the best studied [Fe₃(μ₃-O)(μ-LL)₆L₃] complexes with LL = carboxylate on one hand and the analogous LL = pyrazolate complexes reported here on the other, in order to better elucidate the relationship between the physical properties and the structural environment of the Fe₃O-motif.

Figure 1.

Ball-and stick diagram of anions 1.

Experimental Section

Synthesis

Reagents were purchased from Sigma-Aldrich and used without further purification. The anhydrous Fe^III salts were stored in a glove box compartment under argon. The ligand 4- O₂N-pzH was synthesized according to a literature method.¹³ Infrared, ¹H NMR, and UV-vis spectra were recorded on a Nicolet FT-IR 6000, Bruker ADVANCE DRX-500, and Varian CARY 500 Scan, respectively.

(Et₃NH)₄[Fe₃(μ₃-O)(μ-4-NO₂-pz)₆Cl₃]Cl₂, 1a

A flask is charged with 0.750 g (4.62 mmol) anhydrous FeCl₃, 30 ml CH₂Cl₂ and 1.569 g (13.87 mmol) of 4-O₂N-pzH under an argon atmosphere, forming a partially soluble yellow solid. Dropwise addition of NEt₃ (1.611 ml, 11.5 mmol) to the reaction mixture under air, changes the solution color to dark red. X-ray quality single crystals were obtained by slow Et₂O vapor diffusion into the CH₂Cl₂ solution; yield, 52%, m.p. = 192 °C. Elemental analysis, found (calc.) for 1a: C 34.82 (34.98), H 5.21 (5.31), N 21.23 (21.37); UV/Vis (CH₂Cl₂): λ_max = 291 nm; IR (KBr disk, cm⁻¹): ν = 1489 (s), 1407 (s), 1279 (s), 1163 (s), 1035 (s), 1008 (s), 976 (m), 888 (m), 837 (w), 815 (s), 759 (s), 682 (w), 626 (s), 600 (s), 551 (m), 476 (s); ¹H-NMR (CDCl₃) 30.87 ppm. The sample of 1a used for magnetic susceptibility measurements was prepared from 99.99% FeCl₃.

(Bu₄N)₂[Fe₃(μ₃-O)(μ-4-NO₂-pz)₆Cl₃]·0.5MeOH·H₂O, 1b

Complex 1b is prepared similarly to 1a in thf solvent, using a 1M Bu₄NOH/MeOH solution instead of NEt₃. X-ray quality single crystals are obtained by slow Et₂O vapor diffusion into a CH₂Cl₂ solution of the dark red reaction product; yield >20%, mp = 245 °C. Elemental analysis, found (calc.) for 1b: C 41.29 (40.94), H 5.84 (5.99), N 19.13 (18.92).

(Ph₄P)₂[Fe₃(μ₃-O)(μ-4-NO₂-pz)₆Cl₃], 1c

A flask is charged with 0.189g (0.35 mmol) [Ph₄P][FeCl₄], 15 ml CH₂Cl₂ and 0.132 g (1.17 mmol) 4-O₂N-pzH. Drop wise addition of NEt₃ (0.162 ml, 1.16 mmol) turns the mixture to a dark red solution. X-ray quality single crystals were obtained by slow Et₂O diffusion into the CH₂Cl₂ solution; yield > 40%. m.p. = 277°C. Elemental analysis, found (calc.) for 1c: C 48.63 (49.02), H 3.69 (3.64), N 14.51 (14.70).

X-Ray Crystallography

X-ray diffraction data, taken from a single crystal mounted atop a glass fiber with a Siemens SMART-CCD diffractometer (298 K, λ = 0.71073 Å), were collected on a Bruker AXS SMART 1K CCD, area detector with graphite monochromated Mo-Kα radiation (λ = 0.71073 Å) at room temperature using the program SMART-NT¹⁴ and processed by SAINT-NT.¹⁵ An empirical absorption correction was applied by the program SADABS. The structures were solved by direct method and refined by full-matrix least-squares methods on F².¹⁶ All non-hydrogen atoms were refined anisotropically, while H-atoms were placed in calculated positions with their thermal parameters riding on those of their C-atoms. Crystallographic details for 1a, 1b and 1c are summarized in Table 1.

Table 1.

Crystallographic data for 1a, 1b and 1c.

	1a	1b	1c
Empirical formula	C42H76Cl5Fe3N22O13	C50.5H88Cl3Fe3N20O14.5	C66H52Cl3Fe3N18O13P2
Fw	1442.05	1481.31	1641.10
Temp (K)	298	299	298(2)
Wavelength (Å)	0.71073	0.71073	0.71073
Cryst syst	Orthorhombic	Monoclinic	Monoclinic
Space group	Pbcn	P21/c	P21/n
a(Å)	24.344(4)	17.811(3)	17.532(3)
b(Å)	10.672(2)	15.399(2)	18.109(3)
c(Å)	25.978(4)	26.573(4)	24.150(4)
β(deg)	90	101.809(3)	106.755(3)
V(Å)	6748.7(2)	7134.0(2)	7342(2)
Z	4	4	4
Density (cal) (Mg m−3)	1.419	1.379	1.485
Abs coeff (mm−1)	0.904	0.785	0.811
Cryst size (mm)	0.14 × 0.10 × 0.10	0.29 × 0.22 × 0.15	0.16 × 0.14 × 0.14
Independent reflns/ I >2σ(I)	4852 / 3055	15937 / 9304	12952 / 6696
R / Rw	0.0497 / 01183	0.0677 / 0.1451	0.0472 / 0.0846
F(000)	2996	3104	3348
GoF	1.003	1.044	0.902

Electrochemical experiments were performed with a BAS CV 50-W Voltammetric Analyzer, using non-aqueous Ag/AgNO₃ reference electrode for which the ferrrocene/ferricinium couple occurs at 0.200 V, Pt auxiliary electrode, and Pt working electrode. Magnetic functions were measured with a SQUID apparatus (Quantum Design) at B = 0.1 T from 2.0 to 300 K and the isothermal magnetization at T = 1.8 and 4.5 K, respectively. A correction to the underlying diamagnetism was estimated on the basis of Pascal constants as λ_dia = −9.91 10⁻⁹ m³ mol⁻¹ for 1a. X-band EPR measurements were performed with powdered samples or acetone solutions of 1a with a Bruker ER 200D instrument equipped with an ESR-9 Oxford cryostat and an Anristsu microwave frequency counter. Mössbauer measurements were recorded on a constant acceleration conventional spectrometer with a ⁵⁷Co (Rh matrix) source. Variable-temperature spectra were obtained by using Oxford cryostats, operating at 4.2 – 300 K. Isomer shift values (δ) are quoted relative to iron foil at 293 K.

Results and Discussion

The reactions of FeCl₃, (or PPh₄FeCl₄) with excess 4-O₂N-pzH and base (NEt₃, or Bu₄NOH) give the corresponding salts of 1, which are recrystallized from CH₂Cl₂/Et₂O yielding analytically pure samples. A ~50% excess of pyrazole in the reaction mixture improves the crystalline product yield. The X-ray crystallographic analyses show that the all three dianions 1 contain six-coordinate Fe^III-centers forming an Fe₃(μ₃-O)-core, supported by six bridging pyrazolates and three terminal chlorides (Fig. 1). Table 2 summarizes important bond lengths and angles for 1a–c, respectively. While the molecular symmetry of anion 1 is D_3h, consistent with the presence of a single resonance for all 12 protons in the ¹H-NMR/CDCl³ spectrum, its crystallographic symmetry is two fold (1a), or lower (1b,c): Complex 1a crystallizes on two-fold axis running along an Fe-O bond, with one short (3.269(1) Å) and two long (3.287(1) Å) Fe•••Fe distances. Whole trinuclear complex dianions are present in the asymmetric units of 1b and 1c. The trinuclear complex dianion 1 packs efficiently with two PPh₄⁺ counter ions in the crystal lattice, while the lattices of the Bu₄N⁺ salt 1b include interstitial solvent molecules. When the smaller NEt₃H⁺ counter ion is employed, the crystal lattice of 1a includes two interstitial [NEt₃H]Cl, besides the Fe₃-dianion. Inspection of packing diagrams shows that the shortest intermolecular contact in 1a is an O•••O distance of 2.951 Å between two NO₂-groups, while the shortest intermolecular Fe•••Fe approach is of 7.995 Å. Similarly, the shortest intermolecular contacts, also between NO₂-groups, are O•••O of 3.301 Å in 1b and 2.949 Å in 1c, while the shortest intermolecular Fe•••Fe contacts for 1b and 1c are 9.882 and 10.307 Å, respectively.

Table 2.

Selected bond lengths (Å) and angles (deg) for 1a–c.

	1a	1b	1c
	C42H76Cl5Fe3N22O13	C50.5H88Cl3Fe3N20O14.5	C66H52Cl3Fe3N18O13P2
Fe…Fe	3.269(1), 3.287(1)	3.269(4) – 3.287(1)	3.265(1) – 3.292(2)
Fe-O	1.885(4), 1.894(2)	1.889(3) – 1.898(3)	1.878(2) – 1.904(2)
Fe-N	2.129(3) – 2.152(4)	2.116(3) – 2.161(4)	2.116(4) – 2.149(3)
Fe-X	2.280(2), 2.284(2)	2.272(1) – 2.294(1)	2.263(1) – 2.291(1)
Fe-O-Fe	120.4(1), 119.1(2)	120.6(1) – 119.4(1)	119.7(1) – 120.3(1)
O-Fe-X	177.7(1), 180.000(1)	177.63(9) – 178.98(9)	177.51(8) – 179.9(1)

The Fe-O and Fe•••Fe distances of 1 (Table 2) fall within the narrow ranges of the corresponding distances reported for analogous Fe₃(μ₃-O)-complexes of carboxylate or oxime ligands – 1.855 to 1.944 and 3.251 to 3.327 Å, respectively (Table 3).¹⁰ Similarly, the infrared ν_as(Fe-O) bands for 1 occur at 626 cm⁻¹ (598 cm⁻¹ for ν_as(Fe-¹⁸O)), also comparable to those reported for carboxylate analogues, 595 – 635 cm⁻¹ (Table 4).10 d, i–j

Table 3.

Fe-˜O and Fe•••Fe distances for selected [Fe₃(μ₃-O)(μ-LL)₆X₃] complexes.

	Fe-O (Å)	Fe…Fe (Å)	Ref.
[Fe3O(O2CCH3)6(isoxazole)3]ClO4	1.901, 1.894	3.286, 3.284	10f
		3.274,
[Fe3O(O2CPh)6(CH3OH)3]NO3	1.890, 1.907	3.300, 3.284	10b
	1.855, 1.882,	3.254,
[Fe3O(O2CPh)5(salox)(MeOH)2]	1.944	3.251, 3.327	10h
[Fe3O(O2CPh)6(py)3]NO3	1.9084	3.306	10c
[Fe3O(bamen)3]+	1.898, 1.911	3.299, 3.301	10g
[Fe3O(piv)6(MeOH)3]+	1.905	3.274	10a
	1.897, 1.917,	3.283,
[NaFe3O(O2CPh)5(pic)2(EtOH)2(H2O)]2(ClO4)2	1.933	3.285, 3.371	10n

Table 4.

Infrared ν_(Fe-O) stretches for selected [Fe₃(μ₃-O)(μ-LL)₆X₃] complexes.

	νas(Fe3O)	Reference
1a	626 (18O; 598)	this work
[Fe3O(O2CH)6(H2O)3]NO3	595	10i
[Fe3O(O2CCH3)6(H2O)3]ClO4	609	10i
[Fe3O(O2CCH3)6(py)3]NO3	604	10i
[Fe3O(O2CCH3)6(γ-pic)]ClO4	605	10i
[Fe3O(O2CCH3)6(py)3][FeCl4]	600 (18O; 580)	10j
[Fe3O(O2CCH3)6(py)3]ClO4	635	10d
[Fe3O(O2CPh)6(py)3]ClO4	622	10e
[Fe3O(O2CCH3)6(H2O)3]ClO4	520	10k

Cyclic voltammetric analysis of 1b (Fig. 2) in the +1.000 to −1.440 V window shows one reversible reduction at E_1/2 = −0.703 V (vs. Fc⁺/Fc), followed by an irreversible one at − 1.246 V, which remains irreversible at 218 K. The voltammetric results are consistent with earlier studies of Fe₃(μ₃-O)-carboxylates showing a strongly ligand-dependent reversible reduction to the formally mixed-valent Fe^III₂Fe^II species at E_1/2 values between −0.09 and −0.76 V.^10c The E_1/2-values of the pyrazolate complex [Fe₃(μ₃-O)(μ-O₂Npz)) ₆Cl₃]²⁻ 1b are shifted negative compared to those of the isovalent carboxylates [Fe₃(μ₃-O)(μ-O₂CR)₆L₃]⁺. This is largely due to the charge difference between the dianionic 1 (with three terminal chlorides) and the monocationic carboxylate complexes (with three neutral terminal ligands, L).

Figure 2.

Cyclic voltammogram (0.03M Bu₄NPF₆/CH₂Cl₂, 295 K, Pt-working electrode, Ag/AgNO₃ reference, 100 mV/s sweep) of 1b from-200 mV to −1400 mV, vs Fc/Fc⁺.

Mössbauer spectra from powdered samples of 1a were recorded in the 4.2-300 K temperature range and zero external magnetic fields. Representative spectra are shown in Figure 3. At T > 20–30K the spectra comprise one relative symmetric quadrupole doublet with δ = 0.43 (1) mms⁻¹ and ΔE_Q = 1.02(2) mms⁻¹ at 78 K. No noticeable dependence of ΔE_Q on temperature is observed. On the other hand, the isomer shift decreases as the temperature increases (δ = 0.32(1) mms⁻¹, at 293 K). The temperature dependence of the isomer shift is attributed to the second-order Doppler effect.¹⁷ The value of isomer shift in the whole temperature range is consistent with high spin ferric ions in N/O coordination environment. For temperatures below 20 K, an asymmetric line broadening is observed and is attributed to the onset of relaxation effects. Magnetic susceptibility studies (see below) indicate that the ground state of 1a is characterized by S =1/2, which is the only thermally occupied state at liquid helium temperature. As the spin-lattice relaxation rate decreases at liquid helium temperatures, non-zero effective magnetic fields are induced at the iron nuclei, thus affecting the spectra.¹⁸ Because the line broadening is larger for the lower energy line, a negative sign for the largest component of the Electron Field Gradient (EFG) tensor is inferred.¹⁸ For complex 1a the isomer shift fall at the lower end of the Fe^III₃O-carboxylate range (Table 5), indicating an increased degree of covalency for the present compounds compared to typical carboxylates.¹⁰ On the other hand, the high quadrupole splitting value reflects the axial (locally C_4ν) ClN₄O-coordination environment of the Fe-atoms of 1a, compared to the pseudo-octahedral O₆-coordination of the carboxylate complexes listed in Table 5.

Figure 3.

Mössbauer spectra of 1a at 293 K, 78 K and 4.2 K.

Table 5.

Mössbauer isomer shift (δ) and quadrupole splitting (ΔE_Q) values for selected [Fe₃(μ₃-O)(μ-LL)₆Cl₃] complexes.

	δ, mm s−1		ΔEQ, mm s−1		Reference
1a	0.43(1)		1.02(2)		This work,	T = 78 K
		0.32(1)		1.04(2)	This work,	T = 300K
[Fe3O(O2CCH3)6(H2O)3]ClO4	0.53		0.74		10k, T = 21 K
		0.42		0.58		T = 295 K
[Fe3O(O2CCH2CO2)3(H2O)3]ClO4	0.52		0.72		10k, T = 21 K
		0.41		0.58		T = 295 K
[Fe3O(O2CCH2CH2CO2)3(H2O)3]ClO4	0.53		0.81		10k, T = 22 K
		0.42		0.67		T = 295 K
[Fe3O(O2CCHCHCO2)3(H2O)3]ClO4	0.51		0.88		10k, T = 20 K
		0.42		0.79		T = 295 K
[Fe3O(o-phthalate)3(H2O)3](o-phthalate)0.5	0.52		0.82		10k, T = 22K
		0.41		0.81		T = 295 K
[Fe3O(m-phthalate)3(H2O)3(m-phthalate)	0.53		0.93		10k, T = 22 K
		0.42		0.79		T = 295 K
[Fe3O(ditetrazole)3]NO3	0.44		1.10		10m, T = 4.2 K
[Fe3O(O2CPh)6(CH3OH)3]NO3		0.31		0.346	10b,	T = room temp.
[NaFe3O(O2CPh)5(pic)2(EtOH)2(H2O)]2(ClO4)2	0.51		0.70		10n, T = 78 K
		0.40		0.59		T = 298 K

The overall temperature dependence of the effective magnetic moment for 1a (Figure 4, Figure 5) indicates a sizable antiferromagnetic exchange. However, the low-temperature data reach a μ_eff value of 1.3 μ_B, lower than the theoretical limit of 1.7 μ_B for an S = 1/2 molecular spin predicted by isotropic exchange. In addition, the magnetization curve deviates progressively from the theoretical prediction when only the isotropic exchange is taken into account. The analysis of the magnetic susceptibility data (both χ vs. T and M vs. H) as well as the EPR spectra (below), require the presence of non-Heisenberg interactions. These could be (a) single ion anisotropy, (zero field splitting D_i) (b) asymmetric (pseudodipolar) interaction D_ij, (c) antisymmetric interaction (d_ij).^19,20 With regard to the magnetic properties, the three terms induce the same effects, namely lowering of the g_eff for the S = 1/2 ground state and axial EPR signals with extremely low g_⊥ values. Consequently, the EPR results cannot be used as an argument for favoring one term over the other two. Rather, antisymmetric exchange (AE) is favored here on the basis of quantitative considerations based on the different effects that the terms (a), (b), and (c) have on the exchange coupling scheme of 1a. Both D_i and D_ij mix states with higher S-values into the ground S = 1/2 state, inducing the aforementioned phenomena (low g_eff and g_⊥). Therefore, to a first approximation, the effects of these terms on the magnetic properties depend on the ratios D_i/J and D_ij/J respectively (J is the average value of the J_ij’s). The J_ij values can be accurately estimated from the fitting of the χ vs. T data. However, in order to achieve a good fitting of the magnetic data, unreasonably large D_i or D_ij values had to be assumed (because the magnitude of J leads to relatively large energy separation between the ground S = 1/2 states and the S > 1/2 states). Antisymmetric exchange, on the other hand, mixes the two S = 1/2 ground states; the effects on the magnetic properties of 1a depend approximately on the ratio d_ij/δ, where δ is a measure of the non-equivalence between the J_ij values (lowering of the D_3h symmetry). As a result, the effects of AE are more pronounced for more symmetric triangles, where δ is close to zero and even a small value of d_ij can induce large anisotropies. Apart from the point-dipolar interaction (which has the same effects as the D_ij term) all the other terms arise from spin-orbit coupling, which is small (albeit non-zero) for Fe³⁺(S=5/2) ions.

Figure 4.

Temperature dependence of the effective magnetic moment (left, B = 0.1 T) and magnetization (right, T = 1.8 and 4.5 K) for 1a. Inset: Temperature dependence of the molar magnetization. Open circles, experimental data; red solid line – best-fit for J₁/hc = −80 1 cm⁻¹, J₂/hc = −72.4 cm⁻¹, |d_z|/hc = 5.09 cm⁻¹ and zj/hc = −0.326 cm⁻¹.

Figure 5.

Temperature dependence of the effective magnetic moment (left, B = 0.1 T) and magnetization (right, T = 1.8 and 4.5 K) for 1a. Open circles, experimental data; solid line, best-fit for J₁/hc = −70 6 cm⁻¹, J₂/hc = 80 8 cm⁻¹, |d_z|/hc = 9.87 cm⁻¹ and zj/hc = −0.325 cm⁻¹.

Therefore, a spin-Hamiltonian for an isosceles triangle with the isotropic, AE and molecular-field correction (Equation 1) has been postulated.

$$\begin{array}{c}\widehat{H}=-J_1({\mathbf{S}}_1\cdot {\mathbf{S}}_2+{\mathbf{S}}_2\cdot {\mathbf{S}}_3)-J_2({\mathbf{S}}_1\cdot S_3)+{\mathbf{d}}_{12}\cdot ({\mathbf{S}}_1\times {\mathbf{S}}_2)+{\mathbf{d}}_{23}\cdot ({\mathbf{S}}_2\times {\mathbf{S}}_3)+{\mathbf{d}}_{31}\cdot ({\mathbf{S}}_3\times {\mathbf{S}}_1)\hfill \\ +{\mu }_B{B}_{a}g({\widehat{S}}_{1a}+{\widehat{S}}_{2a}+{\widehat{S}}_{3a})-zj{\langle {\widehat{S}}_a\rangle }_T({\widehat{S}}_{1a}+{\widehat{S}}_{2a}+{\widehat{S}}_{3a})\hfill \end{array}$$ (1)

where J_i are the isotropic exchange interaction parameters, d_ij are corresponding antisymmetric vectors, zj is a common molecular-field parameter, and <S_a>_T is a thermal average of the spin projection in the a-direction. For the magnetic field vector in the polar coordinates defined as B⃗_a = B(sin θ cos φ, sin θ sin φ, cos θ) the molar magnetization was calculated as

$$M_{a,mol}=-N_A\frac{{\displaystyle \sum _i\left({\displaystyle \sum _k{\displaystyle \sum _l{C}_{ik}^{+}{(Z_a)}_{kl}{C}_{li}}}\right)}\text{exp}(-{\epsilon }_{a,i}/KT)}{{\displaystyle \sum _i\text{exp}(-{\epsilon }_{a,i}/KT)}}$$ (2)

where Z_a is the matrix element of the Zeeman term for the a-direction of the magnetic field and C are the eigenvectors resulting from the diagonalization of the complete spin Hamiltonian matrix in local basis set of uncoupled kets (spin S_i = 5/2 for each center). Since a powder sample was used, the averaged molar magnetization was calculated as an orientational average using the qromb subroutine.²¹

$$M_{mol}=1/4\pi {\displaystyle {\int }_0^{2\pi }{\displaystyle {\int }_0^{\pi }{M}_{a,mol}\sin \theta d\theta d\phi }}$$ (3)

Since the averaged spin in Equation 1 needs eigenvectors, the equation has been solved by an iterative, time demanding procedure. The data were fitted simultaneously for the temperature-dependence and the field-dependence of the magnetization with the assumptions that: (a) The antisymmetric vector is equal for each pair, d⃗₁₂ = d⃗₂₃ = d⃗₃₁ = d⃗ and only the z-component was assumed to be non-zero, d_x = d_y = 0. (b) The g-factors for Fe_III are fixed at g_x = g_y = g_z = 2.0. This leaves four free parameters, namely J₁, J₂, d_z and zj. Two different parameter sets were found for 1a, which is a common feature.^10n,22 First, for J₁ > J₂: J₁/hc = −80.1 cm⁻¹, J₂/hc = −72.4cm⁻¹, |d_z|/hc = 5.09 cm⁻¹ and zj/hc = − 0.326 cm⁻¹ (Figure 4) and second for J₁ < J₂: J₁/hc = −70.6 cm⁻¹, J₂/hc = −80.8 cm⁻¹, |d_z|/hc = 9.87 cm⁻¹ and zj/hc = −0.325 cm⁻¹ (Figure 5). The average values for the isotropic exchange are in both cases quite similar, J_av/hc = −77.5 cm⁻¹ and J_av/hc = −74.0 cm⁻¹, respectively. The intermolecular interaction zj was found to be of antiferromagnetic nature and of the same value in both cases. The plots of the lowest energy levels for both parameter sets (S5) reveal that the ground state is S = 1/2 with effective g-factors g_‖,eff = 2.0 and g_⊥eff = 0.84 (for both fits). Such a low value for g_⊥eff is the result of the antisymmetric exchange.

The analyses of magnetic data for several analogous to 1 carboxylate complexes containing the Fe₃(μ₃-O)-motif have yielded J-values in the range of −34.3 to −64.4 cm⁻¹, while a complex of a polydentate-N₅ ligand gave J/hc = −82.0 cm⁻¹ (Table 6).10b,f–h,l,n

Table 6.

Magnetic exchange coupling constants^* for selected [Fe₃(μ₃-O)(μ-LL)₆X₃] complexes.

	J/hc, cm−1	Reference
1a	−80.1, −72.4
	−70.6, −80.8	This work
[Fe3O(O2CCH3)6(isoxazole)3]ClO4	−58.8, −34.3	10f
[Fe3O(O2CPh)6(CH3OH)3]NO3	−54.12	10b
[Fe3O(O2CPh)5(salox)(MeOH)2]	−54.6	10h
[Fe3O(bamen)3]+	−82.0	10g
[Fe3O(O2CCH3)6(pyz)3]ClO4	−64.6	10l
[Fe3O(O2CCH3)6(H2O)3]NO3	−54	10l
[NaFe3O(O2CPh)5(pic)2(EtOH)2(H2O)]2(ClO4)2	−54.8, −41.8
	−45.4, −63.2	10n

^*J-values calculated with the -2JS_iS_j Hamiltonian have been doubled for direct comparison with the ones determined here.

X-band EPR spectroscopy

From the analysis of the magnetic susceptibility data, an isolated S = 1/2 ground state was deduced for 1a. The analysis also indicated the presence of AE interaction. Further evidence for the presence of AE comes from X-band EPR studies (Figure 6). In the absence of AE the S = 1/2 state is expected to be characterized by the intrinsic g₀- tensor of the transition metal ion. High spin ferric ions are characterized by a fairly isotropic intrinsic g₀-tensor. Therefore the EPR signal from the S = 1/2 ground state should consist of a symmetric derivative feature at g_eff ~ 2.0. Indeed, such signals have been observed in the case of acetone solutions of [Fe₃(μ₃-O)(μ-O₂CPh)₅(salox)L₁L₂] (L₁ = L₂ = MeOH or L₁ = EtOH, L₂ = H₂O, H₂salox= Salicylaldoxime).^10h However, the EPR spectra of several trinuclear ferric complexes, either in the solid state or in solution, deviate significantly from this case. In general, the spectra comprise one relatively sharp peak at g_eff ~ 2.0 and a broad tail at higher magnetic fields.²³ Such behavior is also found for Cr₃ and Cu₃ complexes.^24,25

Figure 6.

X-band (9.4 GHz) EPR spectra from powdered sample of 1a (A) and from an acetone glass (B). The vertical arrows indicate the g~4.3 signal attributed to ferric impurities. The asterisk in A indicates the broad signal at g~2.0 which is absent in B. EPR conditions: (A) Temperature, 4.2 K; microwave power, 10 mW; modulation amplitude 25 Gpp; (B) Temperature, 5.1 K, microwave power, 2 mW, modulation amplitude 25 G_pp.

This characteristic EPR behavior has been successfully explained on the grounds of AE. Briefly, the AE term mixes the lowest two S = 1/2 states inducing an axial anisotropy in the g-tensor. The parallel component, g_‖, of the g-tensor lies along the direction of the antisymmetric pseudovector d, assumed perpendicularly to the triangle plane. Because the g_‖ component is not affected by the AE term, the EPR feature from this component consists of a rather sharp peak at a g-value, which coincides with the intrinsic g₀-tensor. The axial component, however, strongly depends on this parameter. To a first approximation, for a high spin triferric complex:^{23a, 26}

$$g_{\perp }=g_0{\left[\frac{{\delta }^2-{(h\nu )}^2}{{\mathrm{\Delta }}^2-{(h\nu )}^2}\right]}^{1/2}$$ (4)

where $\mathrm{\Delta }=\sqrt{{\delta }^2+243d^2},$ h ν is the energy of the microwave quantum (ca. 0.3 cm⁻¹ at X-band) and g₀ the g-value of the intrinsic g-tensor of the high spin ferric ion (ca. 2.0). In this equation δ is the separation of the two lowest S = 1/2 doublets in the absence of AE. For a strictly equilateral configuration (all three isotropic exchange parameters, J_ij’s, equal) δ = 0. In this case the transition probability for an EPR signal at X-band vanishes.^23a For a lower symmetry (i.e., isosceles configuration) δ ≠0 and then EPR transitions are possible. Therefore, observation of an EPR signal from the S = 1/2 ground state constitutes evidence for non-equivalent exchange coupling constants, J_ij’s.

From Equation 4, g_⊥ is expected to be lower than g₀ and indeed signals corresponding to g_eff ≪ 2.0 are observed in trinuclear complexes.²³ Inspection of Equation 4 indicates that g_⊥ is extremely sensitive in the parameters d and δ. This has the consequence that distributions in these parameters induce large distribution in g_⊥. The broad high field tails observed in these systems have been attributed to such distributions.^{23c,d, 26}

In Figure 6A, we show the EPR spectrum of a powdered sample of 1a recorded at liquid helium temperatures. The spectrum exhibits a strong peak at g~2.0 superimposed on a broad signal. Careful inspection of the spectrum reveals also the presence of broad features at higher magnetic fields. These signals are shown in a different scale. The broad spectrum on which the sharp peak is superimposed is attributed to inter-molecular interactions present in the solid state. Such interactions have been considered in the analysis of the magnetic susceptibility data and have been observed in solid samples of other triferric complexes.^{10h, 24e, 27}

In the present case, in order to minimize solid-state effects, we recorded a second EPR spectrum of 1a dissolved in acetone (Figure 6B). The broad signal present in the solid sample is not observed in the acetone solution. Mononuclear high-spin ferric species usually give rise to characteristic signals at g~4.3. The weakness of the g~4.3 signal (which actually originates from impurities of the cavity) strongly suggests that no iron release in the form of high spin ferric mononuclear takes place upon dissolution. On the other hand, the sharp g~2.0 peak and the broad features at high magnetic fields are clearly retained in solution.

The EPR spectra of 1a, either in the solid state or in solution, are attributed to the S = 1/2 ground state of the complex and are considered as evidence for the presence of AE interaction. Specifically, the sharp peak observed at g~2.0 is attributed to the g_‖ component. The broad features observed at higher fields are attributed to the g_⊥ part of the axial signal. As discussed earlier, only a lower than equilateral symmetry would lead to an EPR active ground state. Therefore, observation of these signals is in line with the analysis of the magnetic susceptibility data, which was based on an isosceles rather than on an equilateral configuration. Application of the analytical Equation 4 using the parameters of the exchange coupling constants and the magnitude of the antisymmetric parameter d derived from the magnetic susceptibility data, yield a value of ca. 0.57 for g_⊥. The EPR spectra at the high magnetic field region, however, do not exhibit a feature corresponding to a well-defined g_⊥ value. Instead, the broad high field signals indicate a rather broad distribution with g_⊥ < 1.1 – 1.2, which is in reasonable agreement with the value (g_{⊥, eff} = 0.84) derived from the magnetization data. As discussed above, the distribution in g_⊥ are interpreted on the basis of distribution in J_ij’s and/or d. The slight line-shape differences observed in the high magnetic field signals in 5A and 5B may result from differences in the distribution profiles between solid and solution phases.

Evidence for the presence of AE is provided on the basis of magnetic susceptibility measurements and X-band EPR spectroscopy. Moreover, EPR spectroscopy suggests also distributions in J_ij and/or the parameter d. Such distributions are probably not discernible in the magnetic susceptibility measurements, which under the above discussion reflect a mean over an unknown distribution.

Conclusion

Complexes of formula [Fe₃(μ₃-O)(μ-LL)₆L₃] have been described for a variety of bridging LL ligands, including carboxylate, oxime, linked-pyridine/tetrazole and now 4-nitropyrazole, as well. With regard to the Fe₃(μ₃-O)-motif, both the Fe-O bond lengths and the Fe•••Fe separations of 1 are quite similar to those of the previously published structures (Table 3).¹⁰ Comparison of the spectroscopic (IR, Mössbauer) data (vide supra) also indicates that the Fe₃(μ₃-O)-motif is not significantly affected by the replacement of carboxylate by pyrazolate ligands, with the pyrazolate data resembling closer those of the benzoate.10b,e,h In contrast, the magnetic data differ significantly between the pyrazolate and carboxylate materials (Table 6) with the former having a larger antiferromagnetic exchange value than the latter. The value of antiferromagnetic exchange constant of 1a falls close to those predicted by the models of Gorun and Lippard on the basis of the Fe - O distances, as well as by that of Christou et al. on the basis of Fe – O distances and Fe – O – Fe angles.^11,28 Both models predict accurately J-values in polynuclear Fe^III-systems that involve negligible contribution by a secondary magnetic exchange pathway. The J-value predicted by the Gorun and Lippard relatioship for 1 is approximately −70 cm⁻¹, while that of Christou et al. is −69.7 cm⁻¹, both > 5% lower than the actual J-value determined here (average J-values of 1a are −77.5 cm⁻¹ and −74.0 cm⁻¹). The latter are lower than the values calculated for and measured in Fe₄(μ₃-O)₂ “butterfly”-type complexes by Ruiz et al.²⁹ and the dioxime complex [Fe₃O(bamen)₃]⁺.^10g While the principal magnetic exchange path, Fe-O-Fe (a two-bond path), is practically identical in the pyrazolate and carboxylate complexes discussed here, the corresponding contributions of the secondary 3-bond (pyrazolate) versus the 4-bond (carboxylate) paths are evidently different. Pyrazolates have been known for a long time as efficient mediators of antiferromagnetic exchange,³⁰ and an important contribution of μ-pyrazolato ligands has recently been invoked for the interpretation of magnetic exchange among Cu^II-centers.³¹ As a result, the overall antiferromagnetic exchange increases in magnitude in the case of the pyrazolate complex 1a compared to its analogous carboxylates. This is also consistent with the higher degree of covalency of 1a compared to its carboxylate analogues revealed by Mössbauer spectroscopy. Consequently, polynuclear pyrazolato complexes of open-shell metals are expected to show different magnetic properties than those of the corresponding carboxylates. Apart from the magnitude of the isotropic exchange interaction, the present complexes are also characterized by significant antisymmetric exchange.

Supplementary Material

1File002

Supporting Information Available: ORTEP diagrams (S1), X-ray data in CIF format (S2–4) for 1a–c, fit of magnetic data for 1a with the second parameter set and reconstruction of energy levels for 1a (S5). This material is available free of charge via the Internet at http://pubs.acs.org.