Structural, Spectroscopic, and Theoretical Investigation of a T-Shaped

Article pubs.acs.org/IC

Structural, Spectroscopic, and Theoretical Investigation of a T‑Shaped [Fe3(μ3‑O)] Cluster Sebastian A. Stoian,*,† Yi-Ru Peng,‡ Christopher C. Beedle,† Yi-Jung Chung,‡ Gene-Hsiang Lee,§ En-Che Yang,*,‡ and Stephen Hill*,†,∥ †

National High Magnetic Field Laboratory and ∥Department of Physics, Florida State University, Tallahassee, Florida 32310, United States ‡ Department of Chemistry, Fu Jen Catholic University, Hsinchuang, New Taipei City, 24205 Taiwan, Republic of China § Instrumentation Centre, College of Science, National Taiwan University, Taipei, 106 Taiwan, Republic of China S Supporting Information *

ABSTRACT: The synthesis, X-ray crystal and electronic structures of [Fe3(μ3-O)(mpmae)2(OAc)2 Cl3], 1, where mpmae-H = 2-(N-methyl-N-((pyridine-2-yl)methyl)amino)ethanol, are described. This cluster comprises three high-spin ferric ions and exhibits a T-shaped site topology. Variable-frequency electron paramagnetic resonance measurements performed on single crystals of 1 demonstrate a total spin ST = 5/2 ground state, characterized by a small, negative, and nearly axial zero-field splitting tensor D = −0.49 cm−1, E/D ≈ 0.055. Analysis of magnetic susceptibility, magnetization, and magneto-structural correlations further corroborate the presence of a sextet ground-spin state. The observed ground state originates from the strong antiferromagnetic interaction of two iron(III) spins, with J = 115(5) cm−1, that, in turn, are only weakly coupled to the spin of the third site, with j = 7(1) cm−1. These exchange interactions lead to a ground state with magnetic properties that are essentially entirely determined by the weakly coupled site. The contributions of the individual spins to the total ground state of the cluster were monitored using variable-field 57Fe Mössbauer spectroscopy. Field-dependent spectra reveal that, while one of the iron sites exhibits a large negative internal field, typical of ferric ions, the other two sites exhibit small, but not null, negative and positive internal fields. A theoretical analysis reveals that these small internal fields originate from the mixing of the lowest ST = 5/2 excited state into the ground state which, in turn, is induced by a minute structural distortion. protein hemerythrin,4 purple acid phosphatase,5 ribonucleotide reductase,6 soluble methane monooxygenase,7 and the ferroxidation site of ferritins.8 In contrast, trinuclear iron(III) clusters are considerably less common with only a handful of examples having been identified so far, such as the iron−sulfur clusters of ferredoxins and aconitase enzymes,9 the oxo-bridged cluster of ferreascidin,10 and the ferroxidase site of some bacterial ferritins.11,12 T-shaped clusters such as [Fe3(μ3-O)(mpmae)2(OAc)2 Cl3], 1, where mpmae-H = 2-(N-methyl-N-((pyridine-2-yl)methyl)amino)ethanol, as well as linear clusters, represent a specific subset of [FeIII3] compounds that exhibit an effective isosceles

1. INTRODUCTION Polynuclear metal clusters comprised of oxo- and hydroxobridged high-spin ferric ions are widespread throughout mineralogy and biology. 1 Furthermore, some synthetic examples that have a nonzero ground-spin state have been shown to exhibit single molecule magnet (SMM) behavior; that is, their magnetization exhibits slow relaxation at low temperatures.2 Consequently, the quest for high-spin iron(III) clusters that exhibit unusual magnetic properties or function as enzymatic model complexes is an active area of research and, to date, has led to the characterization of numerous polynuclear ferric complexes with interesting chemistry, spin topologies, magnetic, and electronic structures.3 In biological systems, diferric clusters are abundant and often encountered in the resting state of nonheme enzymes, such as the oxygen transport © XXXX American Chemical Society

Received: February 21, 2017

A

DOI: 10.1021/acs.inorgchem.7b00455 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry triangle topology of the iron spins as opposed to Y-shaped clusters, which are in the equilateral class; see Scheme 1.13 A

properties [FeIII3] clusters, such as 1, can be analyzed to assess the presence of specific structural distortions.

Scheme 1. Prevalent Topologies of Hitherto Characterized [Fe3] Clusters: (A) equilateral (Y-shaped), (B) isosceles (Tshaped), and (C) linear clusters

2. MATERIALS AND METHODS

literature survey revealed that only five examples of (μ3-O)bridged T-shaped [FeIII3] clusters have been characterized so far.14−18 Similarly, there are only a few examples of linear clusters.19 When it comes to their magnetic properties the behavior of these compounds can be described in terms of two exchange coupling constants. Thus, for linear clusters we expect the near-neighbor interactions J to be considerably larger than the interaction between the two outer sites j, such that J ≫ j. In contrast, for T-shaped clusters we expect one pair of iron sites to interact strongly via J and these sites to interact only weakly with the remaining site via j. In other words, we anticipate the two spins at the base of an inverted T to be strongly coupled but only weakly interacting with the site at the peak of the inverted T; see Figure 1B. Although, for both types, the ground-spin state consists of an isolated total spin ST = 5/2, the difference in the exchange coupling constants leads to distinctly different properties. While the parameters describing the ground-state magnetic properties of the linear clusters can be expressed as a linear combination of local site parameters with coefficients that are of similar magnitudes, the properties of Tshaped clusters are essentially independent of the two strongly coupled sites and are, essentially, fully determined by those of the weakly interacting site, vide infra. Interestingly, the 57Fe Mössbauer spectroscopic investigation of 1, reported here, reveals the presence of a small, but nonzero unpaired spin density on the local iron sites of the dimer subunit. In turn, this observation indicates the presence of an effective mixing of one or more excited spin states into the ground-spin state. This mixing is rationalized by considering small, nontotally symmetric distortions of the trinuclear cluster structure. Ultimately, this manuscript demonstrates that the magnetic

Scheme 2. Synthesis of the mpmae-H Ligand

2.1. Synthesis. All manipulations were performed under aerobic conditions. All reagents and solvents were used as received. 2-(N-Methyl-N-((pyridine-2-yl)methyl)amino)ethanol (mpmaeH). To a solution of 2-(methylamino)ethanol (5 g, 66.57 mmol) in 50 mL of isopropanol was added 2-(chloromethyl)pyridine hydrochloride (7.8 g, 47.5 mmol) and sodium carbonate (5 g, 47.17 mmol); see Scheme 2. The solution was refluxed overnight. After evaporation

of the solvent, 100 mL of CH2Cl2 was added. The organic layer was washed with saturated brine and dried over MgSO4. The solvent was then removed, and the residue was dried under vacuum to give the ligand mpmae-H. Yield ≈ 65%. (1H NMR in CDCl3) δ 2.26 (s, 3H, NCH3), 2.60 (t, 2H, NCH2CH2), 3.61 (t, 2H, CH2OH), 3.67 (s, 2H, pyCH2N), 7.14, 7.28, 7.57, 8.47 (td, dd, td, dd, pyridine H). (13C NMR, 75 MHz) δ 42.5, 59.0, 63.3, 122.2, 123.1, 136.6, 149.0, 158.8. Selected IR data (attenuated total reflectance (ATR) IR, cm−1): 3290(w), 2945(w), 2842(w), 2796(w), 1592(m), 1570(w), 1475(w), 1435(m), 1363(vw), 1260(vw), 1149(vw), 1079(m), 1034(s), 1003(m), 938(vw), 875(w). Electron impact mass spectrometry (EIMS): 166.11 [M + H]. Anal. Calcd for (C9H14N2O): C, 65.03; H, 8.49; N, 16.85. Found: C, 65.030; H, 8.572; N, 16.813%. [Fe3O(mpmae)2(OAc)2Cl3]·2MeCN·H2O (1). FeCl3·6H2O (0.54 g, 2 mmol), NaOAc·3H2O (0.68 g, 5 mmol), and the mpmae-H ligand (0.17g, 1 mmol) were mixed in 30 mL of MeCN. The resulting solution was stirred at room temperature for 3 h. After filtration, slow diffusion of diethyl ether into the filtrate led to the formation, within 3 d, of X-ray quality brown crystals. Yield 26%. Selected IR data (ATRIR, cm−1): 1540 (vs), 1427 (vs), 1080 (s), 1025 (s), 968 (s). Anal. Calcd for (C22H34Cl3Fe3N4O8): C, 34.93; H, 4.53; N, 7.41. Found: C, 34.88; H, 4.67; N, 7.39%. 2.2. Physical Property Measurements. NMR spectra were recorded in a CDCl3 solution with a Bruker AV-300 spectrometer. Infrared spectra were recorded using KBr pellets on a PerkinElmer 1600 spectrometer in the 650−4000 cm−1 range. Direct-current (dc) magnetic susceptibility data were collected using a Quantum Design MPMS7 system. Samples were restrained with eicosane to prevent torquing. Magnetic data were corrected for the background caused by

Figure 1. (A) 50% ORTEP plot of 1. (B) Drawing of the first coordination spheres of the iron ions of 1. The dashed blue lines and the afferent labels of B highlight the exchange interactions considered in the analysis of the electronic structure, vide infra. When comparing the labels of the A and B plots the iron site at the peak of the inverted T corresponds to Fep = Fe1, and the two iron sites at the base of the triangle are denoted as Fe2 = Feb1, Fe3 = Feb2. Moreover, for A, the exchange coupling constants correspond to J = J23 and j = J12 = J131. Finally, the N atoms are shown in blue (Na and Npy label the N atoms of the amino and pyridine groups, respectively), Cl in green, O in red, and Fe in purple. B


Article

Inorganic Chemistry

[Fe3III] cluster, we also assessed the Jij values predicted for simpler [Fe2IIIGaIII] di-iron computational models. Thus, starting from the geometry-optimized structure of the [Fe3III] cluster in the F state we isolated the exchange pathways linking the FepFeb1,2 and Feb1Feb2 sites by substituting the ferric ion of the Feb1,2 or Fep sites with a Ga(III) ion. This substitution is justified by the nearly identical ionic radii, 0.61 Å for Ga3+ versus 0.63 Å for high-spin Fe3+, and by the known predilection of Ga3+ ions to substitute isomorphously with Fe3+.25,26 Charge and spin distributions were monitored on the basis of the Mulliken atomic spin densities and charges. The predicted ΔEQ and η values describing the electric field gradient and the predicted 57Fe hyperfine coupling constants were estimated using the standard prop keyword of the Gaussian code. The predicted isomer shift values were determined using the calibration given by Vrajmasu et al.27 The energy change as a function of a given structural parameterin particular, the internuclear distance between the Fep and Feb1(2) siteswas evaluated by performing a series of relaxed scans for which one internal coordinate was kept fixed and all others were optimized.

the gel cap and eicosane, and the correction of the intrinsic diamagnetism was estimated from Pascal’s constant. Elemental analyses (C, H, N) and dc magnetic susceptibility measurements were performed at the National Taiwan University Instrument Centre, College of Science. 2.3. X-ray Crystallography. Suitable crystals of complex 1 were selected for X-ray analysis, and the diffraction patterns were measured on a Bruker SMART CCD diffractometer using Mo Kα radiation (λ = 0.710 73 Å). The temperature of the crystal was controlled using an Oxford Cryosystems Cryostream Cooler. The detector was maintained at 5.00 cm from the crystal. The crystallographic data were collected over a hemisphere of reciprocal space, by a combination of four sets of exposures. Each set had a different φ angle for the crystal, and each exposure of 5 s covered 0.30° in ω. An empirical absorption was based on the symmetry-equivalent reflections, and the data were applied using the SADABS program.20 The SHELXTL program on a personal computer (PC) was used for the structure analysis. The structure was solved using the Shelxs-97 program21 and refined using the Shelxl-97 program22 by full-matrix least-squares fitting on F2. Non-hydrogen atoms were refined anisotropically. Hydrogen atoms were fixed at the calculated positions and refined using a riding method. 2.4. Single-Crystal HFEPR Spectroscopy. The High-Frequency Electron Paramagnetic Resonance (HFEPR) measurements of single crystals of 1 were performed employing cavity-perturbation techniques at the National High Magnetic Field Laboratory, in Tallahassee, FL. HFEPR spectra were recorded using a Quantum Design PPMS system equipped with a 7 T split-coil superconducting magnet and a cylindrical resonant cavity of a high quality (Q) factor. The sample temperature was controlled using a liquid helium flow cryostat and was monitored using a calibrated Cernox temperature sensor. The spectra were recorded in transmission mode using a millimeter-wave vector network analyzer (MVNA). The MVNA acts as a tunable microwave source as well as a phase-sensitive detector and allows for measurements over a wide range of frequencies from 50 to ∼1000 GHz. The single-crystal samples were mounted on a plate rotating in a plane perpendicular to the cavity base at the end of the EPR probe.23 In this geometry at least one of the crystallographic axes can be aligned almost parallel to the magnetic field. 2.5. 57Fe Mö ssbauer Spectroscopy. A series of variabletemperature (4.2−200 K), variable-field (0−8 T) 57Fe Nuclear Gamma Resonance (Mössbauer) spectra were recorded using a constant acceleration spectrometer equipped with a Janis Research Supervaritemp cryostat that was cooled with liquid helium and fitted with a superconducting magnet. The absorbers consisted of polycrystalline powders that were placed in 1.0 mL plastic holders and frozen in liquid nitrogen. Spectral simulations were performed using the WMOSS software package (See Co. formerly WEB Research Inc., Edina, MN). Isomer shifts are quoted relative to iron metal at room temperature. 2.6. Density Functional Theory Calculations. Density functional theory (DFT) calculations were performed using the Gaussian 2009 (revisions A02 and C01) quantum chemical software package (for the full reference see the Supporting Information), the spinunrestricted formalism, and the B3LYP/6-311G functional/basis set combination. Single-point self-consistent field (SCF) calculations and geometry optimizations were completed using standard convergence criteria. For each state, the ground-state character of the particular electronic configuration was assessed on the basis of time-dependent (TD) DFT calculations; for example, all one-electron excitations were found to be positive. A structural model of 1 was constructed from scratch and submitted to geometry optimization using the |S12, ST⟩ = |5, 15/2⟩ configuration, for which the individual spins of the three ferric ions are aligned ferromagnetically. The theoretical Jij values (Jij are exchange coupling constants between i and j iron spins) were estimated from the values of the predicted SCF energies of the ferromagnetic (F) and broken-symmetry (BS) states; see Supporting Information.24 The initial electronic guesses of the starting SCF calculations were obtained using the default guess option in the case of the F configuration and the f ragment option of the guess keyword for the BS states. In addition to scrutinizing the F and BS states of the

3. RESULTS 3.1. Development of the mpmae-H Ligand and the Synthesis of 1. Metal-oxide clusters are often stabilized by chelating polydentate ligands that incorporate either a NNO, NOO, or NNOO structural motif. For example, we have successfully used N-(2-pyridylmethyl)-iminodiethanol (H2pmide), a NNOO-type ligand, to bind Mn2+/3+ ions and to obtain an octanuclear cluster.28 Moreover, a quick literature survey revealed that 2-{[2-(dimethylamino)ethyl]methylamino}ethanol (dmem-H), a ligand that incorporates the NNO motif, has been used to stabilize a whole series of iron-based clusters.16 These examples convinced us that a ligand obtained by combining an amino alcohol with pyridine will exhibit an increased propensity for supporting iron-oxo clusters. Therefore, we explored the reactivity of a new ligand, 2-(N-methyl-N-((pyridine-2-yl)methyl)amino)ethanol (mpmae-H), obtained in a high yield, by replacing the base used to synthesize H2pmide with Na2CO3. The mixing of mpmae-H with hexahydrated ferric chloride in the presence of acetate yields 1 (see Section 2.1). For this reaction the Fe:mpmae = 2:1 ratio is rather close to the anticipated 3:2 (1.5:1) stoichiometric value. The small excess of iron(III) is used to mitigate the precipitation of ferric oxide/ hydroxides favored by the alkaline reaction environment, which is caused by the large amount of sodium acetate.29 This reaction uses a five-fold excess of acetate: Fe:OAc = 2:5 and mpmae:OAc=1:5 vs the ratios required by the reaction stoichiometry: Fe:OAc = 1.5:1 and mpmae:OAc=1:1. The excess is required by the dual role of the acetate anion, which functions both as a ligand and as a base. Thus, the [Fe3O(mpmae)2(OAc)2Cl3] formula shows that the formation of each molecule of 1 necessitates the removal of four protons, two from a water molecule to yield an oxo bridging ligand and two from the mpmae-H ligands. We found that minor changes in the initial reaction conditions lead to different products. This behavior highlights the versatile chemical behavior of both the iron(III) ions and of the mpmae− ligands. To ensure the purity of the samples used for the spectroscopic investigations in this study, we used the same synthetic procedure, and we only harvested the resulting single crystals. In turn, this methodology led to a rather low reported yield. 3.2. Structure Description. Complex 1 crystallizes in the P1̅ space group. The refinement parameters of the crystallographic investigation are listed in Table 1. Figure 1A illustrates the ORTEP plot of 1. This cluster encloses three Fe(III) C


Article

Inorganic Chemistry Table 1. Crystallographic Data for 1 empirical formula formula weight temperature wavelength crystal system space group unit cell dimensions

volume Z density (calculated) absorption coefficient F(000) crystal size θ range for data collection index ranges reflections collected independent reflections completeness to θ = 27.50° absorption correction max and min transmission refinement method data/restraints/parameters goodness-of-fit on F2 final R indices [I > 2σ(I)] R indices (all data)

Table 2. Selected Bond Lengths [Å] and Bond Angles [deg] of 1

C26H40Cl3Fe3N6O8 838.54 150(2) K 0.710 73 Å triclinic P1̅ a = 11.1614(2) Å α = 68.7062(8)° b = 11.8108(2) Å β = 85.8127(12)° c = 15.6510(3) Å γ = 68.1357(10)° 1779.44(6) Å3 2 1.565 Mg/m3 1.484 mm−1 862 0.30 × 0.28 × 0.26 mm3 1.40 to 27.50° −14 ≤ h ≤ 14, −15 ≤ k ≤ 15, −20 ≤ l ≤ 20 33 210 8139 [R(int) = 0.0319] 99.30% semiempirical from equivalents 0.644 and 0.576 full-matrix least-squares on F2 8139/0/421 1.134 R1 = 0.0300, wR2 = 0.0879 R1 = 0.0353, wR2 = 0.0908

Fe(1)−O(2) Fe(1)−O(3) Fe(1)−O(1) Fe(1)−O(6) Fe(1)−O(4) Fe(1)−Cl(1) Fe(2)−O(1) Fe(2)−O(2) Fe(2)−O(5) O(2)−Fe(1)−O(3) O(2)−Fe(1)−O(1) O(3)−Fe(1)−O(1) O(2)−Fe(1)−O(6) O(3)−Fe(1)−O(6) O(1)−Fe(1)−O(6) O(2)−Fe(1)−O(4) O(3)−Fe(1)−O(4) O(1)−Fe(1)−O(4) O(6)−Fe(1)−O(4) O(2)−Fe(1)−Cl(1) O(3)−Fe(1)−Cl(1) O(1)−Fe(1)−Cl(1) O(6)−Fe(1)−Cl(1) O(4)−Fe(1)−Cl(1) O(1)−Fe(2)−O(2) O(1)−Fe(2)−O(5) O(2)−Fe(2)−O(5) O(1)−Fe(2)−N(1) O(2)−Fe(2)−N(1) O(5)−Fe(2)−N(1) O(1)−Fe(2)−N(2)

cations that are bridged by a μ3-oxo anion. The dissimilar highspin ferric ion is bridged to the other two Fe(III) ions by two deprotonated mpmae− ligands and two η1:η1:μ2-bridging acetate ligands. The coordination sphere of the three iron sites is completed by a chloride that functions as an apical ligand and leads for each of the iron ions to a distorted octahedral geometry. The charges of the three iron ions were further corroborated using the bond-valence sum (BVS) method (see Table S1), which reveals that indeed, all iron ions adopt a “+3” oxidation state. Table 2 lists a series of selected metal−ligand bond lengths and angles. Additional information is presented in Tables 3 and S2−S4. The structure of the [Fe3(μ3-O)]7+ framework is illustrated in Figure 1B. This cluster encloses two short iron-oxo bonds d(Fe−O) = 1.861(2) and 1.856(2) Å formed by the μ3-O bridging ligand with the two iron sites at the base of the inverted T-shaped cluster Feb1,b2. The bond formed by the μ3-O anion with the Fep ion, d(Fe−O) = 2.068(2) Å, is considerably longer than those supported by the bridging alkoxo groups of the mpmae− ligand; that is, d(Fe−O)average = 1.928 Å. As expected from the topology of the cluster, the bond angle ∠(Feb1-(μ3-O)-Feb2) = 161.48(8)° is considerably larger than those involving the apical iron site, ∠(Fep-(μ3-O)-Feb2,b1)average = 99.24°. The [FeIII3] cluster of 1 takes the form of an isosceles triangle with a T-shaped geometric arrangement. There are five other known examples of T-shaped [FeIII3] clusters, vide infra. For 2−4 and 6 all Fe(III) ions have a distorted octahedral geometry. In contrast, for 5, the middle iron(III) site is fivecoordinate and exhibits a distorted trigonal-bipyramidal geometry.18 In spite of having different binding ligands and geometries, compound 1 shares many common features with the previously characterized compounds; some selected metric parameters are listed in Table 3. For all complexes, the Fe(1)−

1.965(2) 1.975 (2) 2.068(2) 2.075(2) 2.075 (2) 2.272(1) 1.861(2) 2.044(2) 2.048(2) 156.64(6) 78.08(5) 78.57(5) 90.97(6) 88.07(6) 89.34(5) 89.50(6) 90.26(6) 87.69(5) 176.84(6) 102.17(4) 101.19(4) 178.43(4) 92.20(4) 90.75(4) 81.06(6) 94.00(6) 88.12(6) 99.13(6) 90.45(6) 166.41(6) 158.76(6)

Fe(2)−N(1) Fe(2)−N(2) Fe(2)−Cl(2) Fe(3)−O(1) Fe(3)−O(7) Fe(3)−O(3) Fe(3)−N(3) Fe(3)−N(4) Fe(3)−Cl(3) O(2)−Fe(2)−N(2) N(1)−Fe(2)−N(2) O(1)−Fe(2)−Cl(2) O(2)−Fe(2)−Cl(2) O(5)−Fe(2)−Cl(2) N(1)−Fe(2)−Cl(2) N(2)−Fe(2)−Cl(2) O(1)−Fe(3)−O(7) O(1)−Fe(3)−O(3) O(7)−Fe(3)−O(3) O(1)−Fe(3)−N(3) O(7)−Fe(3)−N(3) O(3)−Fe(3)−N(3) O(1)−Fe(3)−N(4) O(7)−Fe(3)−N(4) O(3)−Fe(3)−N(4) N(3)−Fe(3)−N(4) O(1)−Fe(3)−Cl(3) O(7)−Fe(3)−Cl(3) O(3)−Fe(3)−Cl(3) N(3)−Fe(3)−Cl(3) N(4)−Fe(3)−Cl(3)

2.144(2) 2.242 (2) 2.320(1) 1.856(2) 2.026(2) 2.046(2) 2.142 (2) 2.252 (2) 2.321 (1) 78.32(6) 76.07(6) 105.13(4) 173.43(4) 89.23(4) 90.71(5) 95.69(5) 95.56(6) 81.87(6) 88.07(6) 99.02(6) 165.28(6) 92.01(6) 159.29(6) 89.11(6) 78.13(6) 76.52(6) 104.51(4) 90.98(4) 173.61(4) 87.30(5) 95.54(4)

O(1) distance is considerably longer than the Fe(2)−O(1) and Fe(3)−O(1) distances. Comparison of all iron−iron distances shows that, while those between Fe(1)···Fe(2) and Fe(1)··· Fe(3) are quite close to one another, they are much shorter than the Fe(2)···Fe(3) separation. Inspection of the bond angles reveal an Fe(2)−O(1)−Fe(3) value close to 160°, with Fe(1)−O(1)−Fe(2) and Fe(1)−O(1)−Fe(3) angles of ∼99°. 3.3. Magnetic Susceptibility and Magnetization Studies of 1. The magnetic susceptibility of 1 was recorded for a polycrystalline sample under a dc magnetic field of 1000 G, for temperatures from 5 to 300 K (Figure 2). The χMT value observed at 300 K, 5.65 cm3 mol−1 K, is significantly lower than that expected for three noninteracting Fe(III) ions, that is, 13.12 cm3 mol−1 K. This observation reveals that, even at room temperature, large anti-ferromagnetic interactions dominate the magnetic behavior of 1. Lowering the temperature leads, initially, to a decrease of the χMT product to a plateau of ∼4.32 cm3 mol−1 K at 40 K followed by a smaller decrease to 4.01 cm3 mol−1 K at 5 K. The magnetic susceptibility data of 1 were analyzed using the Kambe approach in the framework of an isotropic Heisenberg, Dirac, van Vleck (HDvV) spin-Hamiltonian that takes into account the approximate C2 point-group symmetry of the cluster.30 The topology of the spin sites of 1 is best approximated as an isosceles triangle and is incorporated in the HDvV spin-Hamiltonian employed here, eq 1, where Sb1, Sb2 label the spin sites at the base of an inverted T, and Sp accounts for the site at the top of the tail; see Figure 1B.31 Furthermore, eq 1 allows for the determination of the energies D


Article

Inorganic Chemistry Table 3. Selected Bond Lengths [Å] and Angles [deg] in the Crystal Structure of Complexes 1, 2, 3, 4, 5, and 6 Fe(1)−O(2) Fe(1)−O(3) Fe(1)−O(1) Fe(2)−O(1) Fe(2)−O(2) Fe(3)−O(1) Fe(3)−O(3) Fe(1)−Fe(2) Fe(1)−Fe(3) Fe(2)−Fe(3) Fe(2)−O(1)−Fe(1) Fe(3)−O(1)−Fe(1) Fe(3)−O(1)−Fe(2)

1a

2b

3c

4d

5e

1.965(2) 1.975(2) 2.068(2) 1.861(2) 2.044(2) 1.856(2) 2.046(2) 3.002(1) 2.986(1) 3.669(1) 99.52(6) 98.95(6) 161.48(8)

1.979(2) 1.983(2) 2.070(2) 1.872(2) 2.029(2) 1.865(2) 2.025(2) 2.997(1) 2.980(1) 3.694(2) 98.85(8) 98.34(8) 162.82(11)

1.988(2) 1.988(2) 1.985(3) 1.902(1) 1.975(2) 1.902(1) 1.975(2) 2.936 2.936 3.767 98.06(8) 98.06(8) 163.89(15)

1.991(6) 1.994(6) 2.067(6) 1.867(7) 2.074(6) 1.8762(7) 2.074(6) 3.027(2) 3.018(2) 3.6867(1) 100.3(3) 100.5(3) 159.1(5)

1.975(2) 2.007(2) 1.992(2) 1.884(2) 2.0412) 1.865(2) 1.971(2) 3.056(1) 3.017(1) 3.646(1) 104.03(10) 102.83(10) 152.99(12)

6f

2.016(6) 1.853(6) 1.866(6)

103.8(3) 103.3(3) 152.8(4)

a

1: [Fe3O(mpmae)2(OAc)2Cl3]·2MeCN·H2O (mpmae-H = 2-(N-methyl-N-((pyridin-2-yl)methyl)amino)ethanol) current work. b2: [Fe3O(O2CBut)2(N3)3(dmem)2] (dmemH = 2-{[2-(dimethylamino)ethyl]methylamino}-ethanol), ref 16. c3: [Fe3O(CH3O)2(CH3COO)2(phen)2Cl3] (phen = 1,10-phenanthroline monohydrate), ref 17. d4: [Fe3O(TIEO)2(O2CPh)2C13] (TIEO− = 1,1,2-tris(L-methylimidazol-2-y1)ethoxide), ref 14. e 5: [Fe3Cl5O(OMe)2(L1)2(MeOH)] (HL1 = 3-(pyrid-2-yl)-5-(tert-butyl)-1-H-pyrazole), ref 18. f6: [{Fe(L2)(3,5-dcba)}2OFe(OCH3)] (H2L2 = N,N-bis(2-hydroxybenzyl)-N,N-dimethylethylenediamine), ref 15.

allowed us to assess the magnitude of the ground-spin state zero-field splitting (ZFS). Thus, the reduced magnetization data of Figure 3, M versus H/T, was measured for dc magnetic

Figure 2. Plot of χMT vs T measured for complex 1. The red solid line is a theoretical curve obtained using eq 2.

of the individual spin levels; that is, its eigenvalues can be easily ̂ + Sb2 ̂ and ST̂ = Sp̂ + S12 ̂ . calculated using eq 2, where Ŝ12 = Sb1 Ĥ exch = J Ŝ b1·Ŝ b2 + j(Ŝp ·Ŝ b2 + Ŝp ·Ŝ b1)

Figure 3. Plot of reduced magnetization (M/Nβ) vs H/T for complex 1. The solid lines are simulations obtained using eqs 3 and S1; see text.

(1)

fields between 0.3 and 6 T in the 2−4 K temperature range. The complete data set was analyzed in the framework of a single-site spin-Hamiltonian, S = 5/2, described by eq 3, that accounts for the Zeeman and ZFS interactions. For the latter term we only considered the axial contribution D and neglected the influence of the rhombic component E.

1 1 ε(S12 , ST) = (J − j)S12(S12 + 1) + jST(ST + 1) (2) 2 2 The solid red line of Figure 2 shows our best fit of the experimental data. This curve was obtained from the leastsquares fitting of the magnetic susceptibility using eq 2, which yielded fit parameters of J = 114.5 cm−1 and j = 7 cm−1. Ultimately, through a subsequent series of simulations, we determined that the exchange interactions of 1 are best described using J = 115(5) cm−1 and j = 7(1) cm−1. As expected, this analysis led to positive (AF) exchange coupling constants. However, we find that J ≫ j, which indicates that the two spins at the base of the inverted T exhibit a strong antiferromagnetic interaction that ultimately leads to a sextet, |S12, ST⟩ = |0,5/2⟩, ground-spin state. The strong superexchange coupling of the two spin sites at the base of the triangle, Sb1,b2, leads to a subcluster with an S = 0 ground state for which, at low temperature, we anticipate an effective diamagnetic behavior. Moreover, under these conditions we expect the magnetic properties of 1 to be, in effect determined by those of the site at the top of the inverted T-shaped cluster, Sp, see below. The spin value of the ground state was further corroborated by the analysis of the magnetization data. This analysis also

⎤ ⎡ 2 1 Ĥ = gμB B⃗ ·Ŝ + D⎢Sẑ − S(S + 1)⎥ ⎦ ⎣ 3

(3)

The theoretical values of the magnetization were obtained by substituting the eigenvalues obtained from the diagonalization of eq 3 into equation S1, which subsequently was used to calculate the powder-averaged value of the magnetization. This analysis demonstrates a molecular spin of S = 5/2 and suggests an axial zero-field splitting |D| = 0.5(2) cm−1, and g = 1.98(4). Figure 3 shows the experimental reduced magnetization together with the theoretical curves obtained using eqs 3 and S1. The theoretical curves presented here were obtained using D = −0.49 cm−1 and g = 2.00, values derived from the analysis of the HFEPR data; see below. 3.4. Single-Crystal HFEPR Spectroscopy. Analysis of the magnetic susceptibility data strongly supports the presence for 1 of a sextet, S = 5/2, ground-spin state characterized by a relatively small ZFS parameter |D| ≈ 0.5 cm−1. To further refine E


Article

Inorganic Chemistry

to establish the crystal orientations for which the applied field is most closely aligned to the z-axis and the xy plane of the sextet ground-state ZFS tensor. Inspection of Figure 4 shows that, for an orientation of the applied magnetic field parallel to the easy axis at 2 K, the 92.6 GHz spectrum is dominated by an intense resonance, labeled a, occurring at a resonant field of ∼1.2 T. As the temperature is increased, the relative intensity of this resonance decreases, while, at the same time, four additional resonances, b−e, are observed. Interestingly, at ∼20 K all five resonances exhibit comparable intensities and are equally displaced from one another by ∼1 T. In the absence of a ZFS we expect the spectra to be dominated by a single resonance centered at an effective gaverage ≈ 2.00. In contrast, for an S = 5/2 spin state characterized by a finite but small ZFS, consistent with the experimental observations, we anticipate up to five distinct, evenly separated resonances. These resonances correspond to Δms = ±1 transitions, and the spacing between two consecutive lines is expected to be frequency-independent. Furthermore, the observed splitting should be proportional the ZFS parameter D; that is, to a good approximation, the peak-topeak separation is given by 2D/gzμB. Consequently, assessment of the observed spacing affords a quick estimate of |D| ≈ 0.5 cm−1, which is in good agreement with the value obtained from the magnetic susceptibility data. The investigation of the temperature-dependent behavior of the observed resonances also allows for the determination of the sign of D. Thus, at low temperature due to the increased Boltzmann populations of the lowest spin sublevels, one anticipates the resonance involving the ground-spin sublevel to be dominant. Moreover, for D < 0, it should occur at field values lower than the g = 2.00 position, that is, below 3.3 T for a frequency ν = 92.6 GHz. In contrast, for a positive D value, one expects the Δms = ±1 ground-state resonance to be observed at fields above the g = 2.00 position. Consequently, the 2−10 K spectra of Figure 4 clearly demonstrate that 1 exhibits a sextet ground state characterized by a negative ZFS parameter D. Finally, inspection of Figure 5 shows that, as expected for a regime where the Zeeman interaction is dominant, the frequency and field dependence of the observed resonances is linear for virtually the entire range of microwave frequencies available to us.

the ZFS parameters of the ground-spin state we recorded a series of frequency- and temperature-dependent single-crystal EPR spectra. Although currently, there have been five examples of T-shaped [FeIII3] clusters reported in the literature, none of these compounds has been characterized by EPR. Figures 4, S1, and S2 show a series of single-crystal, temperature- and frequency-dependent EPR spectra recorded

Figure 4. (left) Temperature-dependent EPR spectra recorded at 92.6 GHz for a single crystal of 1. The experimental traces are color-coded such that the spectrum recorded at the lowest temperature is shown in deep blue and that at that highest temperature in bright red. (right) Frequency-dependent spectra recorded at 10 K for a single crystal of 1. The spectra shown in both panels were recorded for an orientation of the single crystal such that the z-axis of the ZFS tensor was essentially parallel to the applied magnetic field. The dips in transmission correspond to EPR.

for 1. The spectra of Figure 4 were obtained for a single crystal oriented such that the z-axis of the ground-state ZFS tensor, that is, the easy axis of the magnetic anisotropy, was essentially aligned with the applied magnetic field. In contrast, those of Figure S2 were obtained for an orientation of the single crystal such that the applied field was parallel to the xy plane of the ZFS tensor, that is, the hard plane of the magnetic anisotropy. These orientations were determined after performing a series of angle-dependent measurements on a single crystal of suitable quality. Thus, a rectangular single crystal was mounted flat on one of its elongated faces on a rotating plate that is perpendicular to the base of the EPR cavity. The rotation of this plate together with that of the entire probe allowed for a full set of rotations about two orthogonal axes. The careful consideration of an extended set of angle-dependent spectra recorded using a step size of 2°, some of which are shown in Figure S1, in conjunction with spectral simulations, allowed us

⎡ 2 1 2 ⎤ E 2 Ĥ e = μB B⃗ · g̃· Ŝ + D⎢Sẑ − S(S + 1) + (Sx̂ − Sŷ )⎥ ⎦ ⎣ 3 D

(4)

Figure 5. (left) Frequency and field dependence of the resonances (blue □) observed for a single crystal of 1 oriented such that the z-axis of the ground-state ZFS tensor is nearly parallel to the applied magnetic field. The solid black lines account for the theoretical dependencies. (right) Relative energies of the spin sublevels of the sextet ground-spin state calculated for a magnetic field applied along the z-axis. The vertical lines indicate the positions of resonances expected for a microwave frequency of 92.6 GHz and a magnetic field applied parallel to the z-axis of the ZFS tensor, see text. F


Article

Inorganic Chemistry The spectra were analyzed in the framework of a standard S = 5/2 spin Hamiltonian described by eq 4. Our best simulations of the experimental data are shown in Figures 5 and S3 and were obtained using gx,y,z = 2.00, D = −0.49 cm−1, and E/D ≈ 0.055. The finite E parameter is needed to obtain the best agreement with the xy-plane spectra (Figure S2). However, since the orientation of the field within the xy-plane was not exactly known, the E parameter is only approximate. Note, however, that its value has no discernible influence on the z-axis spectrum. Additionally, Figure 5 also shows the predicted energy-level diagram obtained for these parameters and an orientation of the magnetic field parallel to the z-axis of the g and D tensors. The red vertical lines correspond to the Δms = ±1 transitions associated with the observed resonances. When the magnetic field is strictly parallel to the z-axis, only the Δm = ±1 resonances display a nonzero transition probability. Interestingly, even a minute angle between the applied field and the z-axis can lead to a considerable increase in the transition probabilities of formerly forbidden resonances such as those indicated by dotted blue lines. Inspection of Figure 4 shows that under some experimental conditions the b−d resonances exhibit an apparent shoulder. This observation suggests that either the alignment of the easy axis of magnetization with the applied field is less than ideal or that the single crystal used for these measurements is contaminated by smaller, microscopic-sized single-crystal shards that are not quite aligned with the dominant fragment. Finally, these fine structure parameters are typical of mononuclear, high-spin iron(III) sites. Such species have been extensively characterized by EPR, most often at X-band (∼9 GHz), but also at higher frequencies.32 To facilitate the comparison of these results with our study we have recorded, for a neat powder sample of 1, several low-temperature X-band EPR spectra; see Figure S4. Moreover, we also present some representative theoretical spectra predicted for 1, see Figure S5, and their rationalization, see Figures S6 and S7. Unfortunately, the experimental X-band spectra of 1 are severely broadened mainly by spin−spin interactions (not included in our simulations), and thus they are rather uninformative. Since at higher microwave frequencies the EPR spectra are less sensitive to spin−spin interactions, these X-band spectra clearly highlight the utility of using HFEPR to investigate solid samples of molecular complexes. 3.5. 57Fe Mö ssbauer Spectroscopy. Mössbauer Quadrupole Splittings and Isomer Shifts. The zero-field Mössbauer spectra of polycrystalline 1 recorded at 4.2 and 70 K are shown in Figure 6. At 4.2 K the observed spectrum consists of a broad, asymmetric doublet that can be described using an isomer shift δ = 0.48(2) mm/s, quadrupole splitting ΔEQ = 0.82(4) mm/s, and line widths Γ ≈ 0.6−0.7 mm/s. Whereas ΔEQ was found to be essentially temperature-independent, the isomer shift decreases in magnitude with increasing temperature such that at 293 K the apparent δ = 0.38 mm/s. The observed temperature dependence of the isomer shift is consistent with the expected influence of the second-order Doppler effect.33 Furthermore, increasing the temperature leads to considerably narrower line widths, Γ ≈ 0.4 mm/s at 70 K, which indicates that the broadness observed at lower temperatures is due to the onset of an intermediate relaxation regime. The equivalence of the two Feb1,b2 sites suggests that, in a fast relaxation regime corresponding to an electron spin flip rate faster than 1 × 107 s−1, the zero-field Mössbauer spectrum of 1 should exhibit two distinct quadrupole doublets with a 2:1 relative area. Furthermore, analysis of the magnetic suscepti-

Figure 6. Zero-field Mössbauer spectra of polycrystalline 1 recorded at 4.2 K (top), 70 K (middle), and their difference (bottom). The later spectrum accounts for the p-site contribution to the 70 K data, which, in turn, allows us to delineate the b-sites spectral component.

bility and HFEPR data, as well as our theoretical analysis (vide infra), indicates that 1 adopts an ST = 5/2 ground state that arises from strong anti-ferromagnetic coupling of the local spins at the base of the inverted T-shaped cluster; that is, |S12, ST⟩ = |0, 5/2⟩. Consequently, in a slow relaxation regime (spin flip rate slower than 1 × 105 s−1) at low temperature, the zero-field spectra should exhibit two spectral components, namely a spectrum that exhibits a magnetic hyperfine splitting and a quadrupole doublet, accounting for the contributions of the iron sites at the peak (p-site) and the base (b-sites) of the inverted T-shaped cluster, respectively. At 70 K, we have a fast relaxation regime for which we expect both sites to exhibit quadrupole doublets without relaxational broadening. Analysis of individual zero-field spectra did not allow for unambiguous deconvolution into individual spectral components. However, the considerations listed above suggest that only the spectral component associated with the p-site is affected by relaxational broadening, while, at the same time, the b-site component should be virtually temperature-independent. By taking the difference between the spectra recorded at 4.2 and 70 K we can cancel out the spectrum of the two b-sites and thus isolate the p-site subspectrum of the 70 K data. This procedure allows us to also delineate the spectral contribution of the b-sites (Figure 6).34 The quadrupole doublet of the difference spectrum is characterized by δp = 0.52(2) mm/s and ΔEQp = 0.94(2) mm/s. These values have been subsequently used to deconvolute the 70 K spectrum into two Gaussian-shaped quadrupole doublets with a 2:1 relative area. The dominant spectral component associated with the two b-sites is shown in blue and exhibits δb1,2 = 0.48(2) mm/s and ΔEQb1,2 = 0.82(1) mm/s. These parameters are well within the range observed for high-spin ferric ions occupying octahedral sites with a mixed nitrogen/oxygen first coordination sphere. Magnetically Perturbed Mö ssbauer Spectra. Figure 7 shows a series of field-dependent Mössbauer spectra recorded at 4.2 K in fields up to 8 T applied parallel to the propagation direction of the γ-rays used to detect the Mössbauer effect. G


Article

Inorganic Chemistry and Iî ·Pĩ ·Iî =

eQVZZ , i 12

2 2 2 ̂ , i − I(I + 1) + η (IXX ̂ , i − IYY ̂ , i)} {3IZZ i

(6b)

The terms of 6a, from left to right, account for the electric monopole (isomer shift), electric quadrupole, nuclear Zeeman and magnetic hyperfine interactions of the local iron sites labeled i = p, b1, and b2. The second term reveals the size and asymmetry of the electric field gradient (EFG) tensor P̃ , which is usually described in terms of VZZ and the asymmetry parameter η, such that η = (VXX − VYY)/VZZ. The quadrupole splitting is expressed as ΔEQ = (1/2)eQVZZ 1 + η2 /3 . We found that the EFG tensors of the local iron sites are rotated from (x, y, z), the reference frame of the zero-field splitting tensor of the ground-spin state. For eq 6b each one of the EFG tensors is expressed in its standard, principal axis frame (X, Y, Z). The relative orientation of these tensors with respect to the (x, y, z) reference frame is described by a standard set of Euler angles, that is Rz(α) → Ry′(β) → Rz″(γ). Inspection of the 8 T spectra (Figure 7D,E) revealed the presence of a spectral component with a large, field-induced magnetic hyperfine splitting that is easily identifiable by two intense absorptions at −6.6 and +7.6 mm/s. The observed hyperfine splitting of this component corresponds to an internal field, B⃗ int = −⟨Ŝ⟩th·Ã /gnβn, of ∼52 T, a value that is well within the range of those observed for high-spin Fe(III) ions. Analysis of the magnetic and HFEPR data revealed the presence for 1 of a ground-spin state that is best described as |S12, ST⟩ = |0, 5/2⟩. Consequently, the two b-sites are expected to form a subcluster with an effective S12 = 0 ground-spin state. However, simulations performed considering two diamagnetic sites |B⃗ int(b1)| = |B⃗ int(b2)| = 0 T, which would account for a putatively diamagnetic major spectral component, are unable to reproduce the observed hyperfine splitting pattern of the central portion of the spectrum (Figure 7E). Furthermore, inspection of the central spectral region in all the spectra revealed the presence of two distinct hyperfine splitting patterns: one that is slightly larger and the other that is slightly smaller than that induced by the nuclear Zeeman interaction alone. Consequently, the field-dependent spectra recorded at 4.2 K can be understood only by considering three magnetically distinct iron sites: one with a large negative hyperfine coupling constant and two others that have small, but nonzero, hyperfine coupling constants with opposite signs. At high temperature the Boltzmann populations of the individual magnetic sublevels of an isolated spin multiplet become nearly equal. Under these conditions ⟨Ŝ⟩th ≈ 1/T, and, thus, the magnetic hyperfine interactions have a limited effect on the spectra. In turn, they are dominated by the nuclear Zeeman and quadrupolar interactions. Accordingly, by investigating the high-field, high-temperature Mö ssbauer spectra, it is typically possible to establish the sign of the largest component of the EFG tensors (VZZ, and consequently of ΔEQ) as well as the asymmetry parameters (η). Our best simulation of the 150 K, 8 T spectrum suggests that, while the p-site exhibits a positive ΔEQ and an axial EFG tensor (η ≈ 0), the two b-sites have negative ΔEQ values and η ≈ 0.4(4); see Figures S8 and S9. Although the ZFS of the S = 5/2 ground state is relatively small and axial (D = −0.49 cm−1, E/D ≈ 0.055), at low

Figure 7. Field-dependent 57Fe Mössbauer spectra recorded at 4.2 K for polycrystalline 1 in 1.0 T (A), 2.0 T (B), 4.0 T (C), and 8.0 T (D, E). The magnetic field is applied parallel to the observed γ-radiation beam. The theoretical traces shown in gray and overlaid over the experimental data (A−D) are simulations obtained using the S = 5/2 spin-Hamiltonian of eq 7 and the parameters listed in Table 4. The red, blue, and green traces drawn above the experimental data are theoretical spectra calculated for the individual iron sites: p-site and, respectively, b1,2 sites. The theoretical trace overlaid over the 8 T experimental spectrum of (E) accounts for the predicted spectrum of a b-site in the absence of magnetic hyperfine coupling (A/gnβn = 0 T).

Inspection of these spectra reveals a gradual development of a magnetic hyperfine splitting pattern from a broad quadrupole doublet observed in zero and small fields, to a splitting spanning nearly 15 mm/s for the 8 T spectrum. Although the increased broadness of the low-field spectra is ascribable to the onset of an intermediate relaxation regime, the internal field inducing the observed hyperfine splitting does not reach its saturation value even at 8 T. To circumvent a tedious analysis of relaxational line broadenings in our discussion below, we assumed a fast relaxation regime. Although this assumption leads to somewhat less-than-satisfactory simulations of the lowfield spectra (B < 2 T), the high-field spectra are wellreproduced. These spectra were analyzed in the framework of an S = 5/2 spin-Hamiltonian obtained by amending eq 4 that was used in the analysis of the HFEPR spectra by adding terms that account for 57Fe hyperfine interactions: Ĥ = Ĥ e + Ĥ hf

(5)

where 3

Ĥ hf =

∑ (δi + Iî ·Pĩ ·Iî − gnβn B⃗ ·Iî + Ŝ ·Ã i ·Iî ) i=1

(6a) H


Article

Inorganic Chemistry Table 4. Hyperfine Parametersa of 1 site

D [cm−1]

E/D

g

p b1 b2

−0.49c

0.055c

2.00c

δ [mm/s]

ΔEQ [mm/s]

η

0.52(2)

0.94(2)d

0.0(2)d

0.48(2)

−0.82(1)

e

0.4(4)

αEFG [deg]

e

βEFG [deg]

γEFG [deg]

90

90

0

0

55(10)

0

Ax/gnβn [T]

Ay/gnβn [T]

Az/gnβn [T]

Aiso/gnβnb [T]

−20.9(4) +2.1(4) −1.0(2)

−21.3(2) +1.3(4) −1.0(2)

−21.6(2) +2.3(2) −2.6(2)

−21.3 +1.9 −1.5

a

Obtained from the analysis of the 4.2 K spectra, quoted for the S = 5/2 multiplet as described by eqs 4−6. bThese values account for the effective hyperfine coupling constants, Aeffective. Moreover, A/gnβn = 1 T corresponds to A = 1.371 MHz. cValues determined from single-crystal HFEPR measurements. dIn the reference frame (defined by the ZFS tensor) these values are ΔEQ = −0.94 mm/s and η = 3. eFor these values an alternative solution has been found, namely, ΔEQ = −0.82 mm/s and η = −9. When these values are expressed in their proper reference frame, that is, in the standard frame, they yield ΔEQ = 0.82 mm/s, η = 0.6, and αEFG = 0°, βEFG = 90°, γEFG = 0°. However, this solution was discarded on the basis of the 8 T spectrum recorded at 150 K.

temperature, it induces a sizable anisotropy in the magnetic behavior of 1. This anisotropy is due to the difference in the thermally averaged spin expectation values along the principal directions of the ZFS tensor, Δ⟨Ŝ⟩th = ⟨Ŝz⟩th − ⟨Ŝx/y⟩th. At 4.2 K, as a function of the applied field, Δ⟨Ŝ⟩th reaches its maximum value, Δ⟨Ŝ⟩th ≈ 0.5 at ∼2 T. The largest component of ⟨Ŝ⟩th is found along z (see Figure S10). Typically, the presence of broad outer features in the high-field, lowtemperature spectra of mononuclear high-spin ferric sites is indicative of the presence of an anisotropic hyperfine coupling tensor A. However, for the p-site spectral component of 1, we found that the breadth of the outer features of the variable-field spectra recorded at 4.2 K closely matches the predicted changes in the Δ⟨ŜT⟩th values, and thus, for this site we obtain an effective A tensor that is essentially isotropic. To avoid introducing unnecessary complications into our analysis, we attempted to restrict our simulations to solutions that did not involve rotations of the EFG tensors. However, close inspection of the 4−8 T spectra recorded at 4.2 K suggests that the magnetic hyperfine splitting patterns associated with both the p and b1,2 sites exhibit vanishing quadrupole perturbations. Therefore, to reconcile the apparently small quadrupole perturbations of the variable field, 4.2 K spectra with the relatively large ΔEQ values, we rotated the axial-EFG tensor at the p-site such that the large positive EFG component is aligned with the largest positive component of the ZFS tensor. For the b-sites we introduced a rotation of the EFG tensor around the y-direction of the ZFS tensor; see Table 4.

Table 5. Predicted and Experimental Exchange Coupling Constants model

J (Feb1Feb2) [cm−1]

j (Fep Feb1,2) [cm−1]

[FeIII2GaIII] Gorun−Lippard relation experimental

+135.36 +134.28a +124.26 +112.16 +115(5)

+6.24 +6.12a −1.58 +29.95b +7(1)

III

[Fe 3]

a

Values calculated using SCF energies including zero-point corrections. bAverage value.

symmetry (BS) DFT calculations at the B3LYP/6-311G level of theory. For these calculations we considered two distinct structural models, that is, a structurally unabridged [Fe3III] cluster and a series of computationally simpler [Fe2IIIGaIIII] diiron clusters for which a selected S = 5/2 Fe(III) ion was replaced by a diamagnetic Ga(III). Inspection of Table 5 reveals a good agreement between the DFT-predicted, experimentally determined, and empirical exchange coupling constants. The validity of the DFT-predicted electronic structures was further assessed on the basis of the predicted zero-field Mössbauer parameters and hyperfine coupling tensors. Thus, inspection of Tables S5 and S8 reveals a strong similitude among the DFTpredicted and experimentally observed hyperfine splitting parameters. Nature of the Ground-Spin State. The salient features of the field-dependent Mössbauer spectra of 1 are determined by the thermally averaged expectation values of the total spin ̂ . Figure S10 shows a plot of ⟨ŜT,ξ⟩th operator, ST̂ = Ŝp + Ŝb1 + Sb2 (ξ = x, y, z), along the principal axes of the ZFS tensor. For this plot, as well as for our investigation of the magnetic hyperfine splitting, we used DT = −0.49 cm−1 and ET/DT = 0.055, values obtained from the analysis of the single-crystal HFEPR spectra. Thus, the hyperfine splitting at the ith site is dominated by the internal field B⃗ int(i) = −⟨ST̂ ⟩th·A(i)gn βn, where the effective hyperfine coupling tensors A(i) are related to the intrinsic tensors, a(i), by the relation A(i) = cia(i). Furthermore, both the ZFS and g tensors of the ST = 5/2 ground state are related to the intrinsic tensors by D T = ∑i =3 1 di D(i) and gT = ∑i =3 1ci g(i), where the coefficients di and ci are the standard spin projection factors.37 Analysis of the magnetic susceptibility data, as well as theoretical predictions, indicate that the ST = 5/2 ground state of 1 arises from the strong anti-ferromagnetic coupling, J ≅ 120 cm−1, of the Sb1 = Sb2 = 5/2 iron spins of the b-sites. Furthermore, the Sp = 5/2 of the p-site is weakly coupled to the two b-site spins such that J ≫ j ≅ 10 cm−1. In the strong coupling limit, |J| ≫ |Di|, for the case where jb2,p = jb1,p = j, the ZFS and magnetic properties of the sextet ground state, |S12 ST⟩

4. DISCUSSION Magneto-Structural Correlations and DFT-Predicted Exchange Coupling Constants. Over the years, the study of numerous oxo-bridged metal clusters, particularly dinuclear compounds, has led to the formulation of several empirical magneto-structural correlations.35 Thus, for oxo-bridged iron(III) clusters it has been found that larger bond angles promote stronger anti-ferromagnetic interactions. Furthermore, Gorun and Lippard have formulated a quantitative relationship between the strength of the anti-ferromagnetic exchange coupling constant J and a structural parameter P defined as the shortest superexchange pathway involving the two iron(III) sites; that is, J = A·exp(BP), where A = 4.381 × 1011 cm−1 and B = −12.663 Å−1.36 Consequently, both the larger FeOFe bond angle and the shorter Fe−O distances involving the two iron sites at the base of the inverted T suggest that, for 1, these sites should exhibit a considerably stronger anti-ferromagnetic interaction than those involving the site at the peak position of the cluster; see Table 5. To further corroborate these empirical correlations with the exchange coupling constants, we performed a series of brokenI


Article

Inorganic Chemistry ̂ = Sb1 ̂ + Sb2 ̂ , are independent of the Sb1 and = |0, 5/2⟩, where S12 Sb2 local sites, and are determined entirely by the parameters of the Sp site; that is, the spin projection factors are db1 = db2 = 0, dp = 1 and cb1 = cb2 = 0, cp = 1. Consequently, under these conditions, the field-dependent Mössbauer spectra should exhibit two distinct spectral components with a 1:2 relative ratio, namely, a minor component with a magnetic hyperfine splitting characteristic of high-spin ferric ions, Bint,ξ(p) = −⟨ŜT,ξ⟩thaξ(p)/gn βn, and a major component with a splitting identical to that of diamagnetic sites, Bint,ξ(b1) = Bint,ξ(b2) = 0, where ξ = x,y,z. Interestingly, this is indeed the case observed for 4, the only other T-shaped [Fe3(μ3-O)]7+ cluster that was characterized using field-dependent 57Fe Mössbauer spectroscopy (see ref 38). Typically, high-spin ferric ions that occupy octahedral sites exhibit a tensors that are nearly isotropic and such that aiso ≅ −22 T. At 4.2 K, for large applied field values (B > 6 T), |⟨ST̂ ⟩th| approaches 5/2, and consequently, for the magnetic component, we expect |B⃗ int(p)| ≈ 55 T. However, inspection of the dominant spectral component revealed that | B⃗ int(b1, b2)| ≠ 0 T, which demonstrates that, for 1, cp < 1 and cb1 ≠ cb2 ≠ 0. Consequently, the ST = 5/2 ground state of 1 exhibits an appreciable mixing of one or more excited states into the lowest sextet, that is, the |S12, ST⟩ = |0, 5/2⟩ state. Effect of Antisymmetric Exchange Interactions. The most prominent class of synthetic [FeIII3] complexes is represented by basic iron carboxylates and their pyrazolate analogues, [Fe(μ3-O)(2μLL)6 L′3], where LL are bridging carboxylate (R−CO2−, R is an aryl or alkyl group) or pyrazolate ligands, and L′ is a terminal ligand such as pyridine or H2O.13 These clusters incorporate [FeIII3(μ3-O)]7+ cores that exhibit threefold symmetry, a structure for which the three iron ions are equivalent and form an equilateral triangle; see Scheme 1A. This symmetry implies that all exchange interactions between iron spins are equal and that the magnetic properties of these clusters are describable using a single coupling constant Jij. For virtually all known cases the exchange interactions between high-spin iron(III) ions are anti-ferromagnetic, Jij > 0. In the case of an equilateral triangle topology they lead to spin frustration and the stabilization of a fourfold degenerate ground-spin state consisting of two degenerate ST = 1/2 doublets. This electronic structure is exquisitely sensitive to structural distortions, and any minor conformational change removes the degeneracy of the two lowest ST = 1/2 states. The effect of such distortions on the magnetic properties can be easily modeled considering an isotropic HDvV spin Hamiltonian and inequivalent exchange coupling constants between the local SFe = 5/2 spins, that is, by assuming an effective scalene or isosceles triangle topology.39,40 While most of these clusters exhibit EPR signals centered on g = 2.01, some exhibit values that are as low as g ≈ 1.85.41 This behavior is also shared by some biological, sulfide-supported, [Fe3S4]+ clusters.42 Considering that the local iron(III) sites have an isolated 6A singlet orbital ground state, the observation of a sizable magnetic anisotropy reflected by the latter g values is unexpected. Furthermore, this anisotropy cannot be accounted for by the isotropic HDvV Hamiltonian and requires the inclusion in the spin Hamiltonian of anisotropic terms, in particular, an antisymmetric exchange (AE), that is, a Dzialoshinski−Moriya term.43,44 AE terms originate from higher-order spin−orbit interactions, and, in the case of a trinuclear cluster, they can lead to lower g-values by mixing the two ST = 1/2 states of the coupled system.45 Interestingly, detailed Mössbauer spectroscopic investigations of the anti-

ferromagnetically coupled di-iron(III) cluster of soluble methane monooxygenase (sMMO),46 and of a sMMO synthetic model, demonstrated that sizable AE terms can be observed even for diferric clusters that have an ST = 0 ground state.47 Considering the striking influence that AE interactions have on the magnetic properties of some spin-frustrated highspin Fe(III) clusters we assessed the extent to which they modulate the properties of 1; see Section 6 of the Supporting Information. Ultimately, we found that AE cannot account for the nonzero magnetic hyperfine splitting of Feb1,2 sites. Thus, while the AE interaction between the two b-sites leads to effective Aeffective(b1,b2) values that are 2 orders of magnitude smaller than those observed experimentally (Figure S11), the combined contributions of the b- and p-site interactions is null (the two individual contributions to the effective A tensor cancel out; see Figure S13). Effects of Structural Distortions. Exchange coupling constants are strongly modulated by weak perturbations of structural parameters, in particular, of bond angles involving bridging ligands and of intermetallic distances.48 Consequently, even a minor structural distortion can have a dramatic effect on the magnetic properties of a polynuclear cluster. A structural distortion can be analyzed in terms of the normal modes of the respective molecule.49 For a moiety with an isosceles triangle topology, such as the [Fe3] cluster of 1, we find three normal modes from which only one is nontotally symmetric (B1); see Figure S14. While the two totally symmetric A1 modes leave the composition of the ground state unchanged, they only modulate the energies of the excited states, a distortion along B1 leads to the mixing of excited spin states into the ground states. Following the arguments presented in Section 7 of the Supporting Information the effects of a Q(B1) distortion on the magnetic properties of 1 are best modeled by the last term of eq 7, that is, ΔjŜb1·Sp̂ .50 Ĥ = J Ŝ b1·Ŝ b2 + j(Ŝ b1·Sp̂ + Ŝ b2 ·Sp̂ ) + ΔjŜ b1·Sp̂

(7)

This term connects the |S12, ST⟩ = |0, 5/2⟩ sextet ground state with excited states that have the same multiplicity. Among these, the lowest S = 5/2 excited state, |S12, ST⟩ = |0, 5/2⟩, lies at ΔE = J − j ≈ 100 cm−1 above the ground state. This excited state exhibits the strongest influence on the ground state and is ̂ ·Sp̂ with the second-lowest excited sextet further mixed by ΔjSb1 state |S12, ST⟩ = |0, 5/2⟩. The latter state has an energy of ΔE = 3(J − j) ≈ 300 cm−1. In the presence of an applied magnetic field a finite Δj leads to nonzero spin expectation values of the local Ŝb1,2 spin operators. Furthermore, we find that, while for one of the local b-sites ΔjŜb1·Ŝp leads to a positive spin expectation value, for the other site we predict a negative spin expectation value, such as ⟨0,5/2|Ŝ b 1 , ξ |0,5/2⟩ ≅ ̂ |0,5/2⟩ > 0 (ξ = x, y, z). In turn, knowledge of −⟨0,5/2|Sb2,ξ the spin expectation values allows us to assess the magnitude of the effective hyperfine coupling constants, Ã effective(b1,2). 35 Δj Ã effective (b1,2 ) ≅ ±ã 6 ( J − j)

(8)

Thus, Figure 8 shows the calculated effective hyperfine coupling constants obtained considering J = 115 cm−1, j = 7 cm−1, g = 2.00, Bapp = 8 T, and aiso/gnβn = −22 T. Moreover, this behavior is well-reproduced by a simple expression such as eq 8, which was derived using perturbation theory (|J| ≫ |j|). Interestingly, this analysis shows that a relatively small Δj leads to sizable effective hyperfine coupling constants for the two b-sites: the J


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Inorganic Chemistry

energies of eq 9 are given by the expression Ea = 25(−J − j + j′)/4, Eb = 25(−J + j − j′)/4, Ec = 25(J − j − j′)/4, and Ed = 25(J + j + j′)/4. These equations can be solved to obtain both the coupling constants J = (Ed + Ec − Eb − Ea)/25, j = (Ed − Ec + Eb − Ea)/25, j′ = (Ed − Ec − Eb + Ea)/25, as well as Δj = j − j′ = 2(Eb + Ea)/25. Ĥ = J Ŝ b1·Ŝ b2 + jŜ b1·Sp̂ + j′Ŝ b2 ·Sp̂

(9)

The substitution of the Ea‑b values into these expressions yielded the j, j′, and Δj values plotted in Figure 9 (black traces). The analogous dependence obtained for J is shown in Figure S16. Inspection of Figure 9 and S18 shows that near the equilibrium, that is, d0(FebFep) = 3.064 and 3.047 Å for the two lowest configurations, a and b, the predicted SCF energies exhibit a quadratic dependence on the FedFep distance. As expected, this behavior is analogous to that of a harmonic oscillator. Although, the predicted values of equilibrium Fep− Fed distances are 0.04−0.08 Å larger than the experimental values, they are well within the error margin associated with this method. Moreover, Figure S18 shows that the energy minima of the a and b configurations are separated by a Fep−Fed distance of ∼0.017 Å and an energy barrier of ∼2 cm−1. The DFT-predicted j and j′ values allow us to assess the dependence of the Δj parameter on the scanned FepFeb internuclear distance. Analysis of Figures S17 and S19 shows that, at the equilibrium position d0(FebFep), we find that the derivative of the exchange coupling constants with respect to the internuclear distance between the Fep and Fed sites are dj/ d(FepFed) = −26.5 cm−1/Å, dj′/d(FepFeb) = 41.1 cm−1/Å, and dJ/d(FepFeb) = 50.4 cm−1/Å. These values lead to dΔj/ d(FepFeb) = 67.5 cm−1/Å. The later number indicates that Δj ≈ 1.5 cm−1 requires a distortion of 1 along the FepFeb distance of ∼0.022 Å. The geometry optimizations of the FepFeb relaxed scan leave the other optimized FepFeb distance virtually unchanged. Consequently, the dΔj/d(FepFeb) highlighted above can be also related to the difference of the two FepFeb internuclear distances, that is, between the scanned FepFeb distance and the geometry optimized FepFeb distance. Inspection of the experimentally determined crystal structure reveals that, while one of the FepFed distances of 1 is equal to 2.986 Å, the other is equal to 3.001 Å. This difference in the experimental FepFed distances of ∼0.015 Å is only slightly smaller than that theoretically required to yield a Δj ≈ 1.5 cm−1 and leads to theoretical effective hyperfine splitting constants, Aeffective(b1,2), for the b-sites that are equal to those observed experimentally. Consequently, this theoretical analysis strongly supports the idea that the nonzero internal fields of the b-sites originate with a minute symmetry-breaking distortion of the [FeIII3(μ3-O)]7+ core that leads to the mixing of the lowest excited S = 5/2 state in the ground state. Origin of Structural Distortions. The relaxed scans of Figure 9 also allow us to estimate the energy required to distort 1 from its predicted stationary state. Thus, we find that changing the internuclear FepFed distance of 1 by 0.022 Å from its equilibrium value requires 12.2(2) cm−1 (0.034 kcal/mol). This value is well within the range expected for weak intermolecular interactions. In contrast to 1, the spectroscopic characterization of 4, [FeIII3(μ3-O)(TIEO)2(O2CPh)2Cl3]· 2C6H6 (see ref 38), the only other [FeIII3] T-shaped cluster characterized by 57Fe Mössbauer spectroscopy, showed that the internal fields at the strongly (AF) exchange-coupled b-sites are strictly zero. This observation suggests that a spontaneous

Figure 8. Dependence of the effective hyperfine coupling constants, Aeffective(Feb1,b2,p), of the three iron sites of 1 as a function of Δj. The vertical red arrow highlights the Δj value required to reproduce the experimentally determined values.

observed experimental values of the effective hyperfine splitting constants are reproduced by assuming Δj ≈ 1.5 cm−1, the value highlighted by the red vertical arrow of Figure 8. To evaluate the effect of Q(B1)-like distortions on the Δj parameter we performed a series of (DFT) relaxed scans along one of the FepFed distances using the unabridged structural model of 1 for the a−b configurations (shown at the top of the Figure 9), at the B3LYP/6-311G level of theory. Although near

Figure 9. DFT-predicted dependence of exchange coupling constants on the FepFeb distance. Spin configurations (top) with magnetic quantum numbers Ms = 5/2 (a−c) and 15/2 (d) whose energies Ea‑b were used to calculate the j, j′, and Δj exchange coupling constants as a function of the FepFeb internuclear distance of 1 (bottom). The dotted vertical line marks the FepFed distance, where the energies of the a and b configurations intersect, that is, 3.055 Å.

equilibrium all geometry-optimized structures have an approximate C2 point group symmetry, as the scan of the selected FepFed distance proceeds the symmetry element embodied by the twofold C2 rotation axis is lost. Consequently Δj was estimated by considering the three independent exchange coupling constants of eq 9. The J, j, and j′ constants were obtained by equating the predicted SCF energies, shown in red and blue in Figure 9, with the expectation values of the HDvV spin Hamiltonian of eq 9 for the a−b configurations. Thus, the individual expectation values, that is, the Eγ=a,b,c,d = ⟨γ|Ĥ |γ⟩ K


Article

Inorganic Chemistry distortion of the [FeIII3(μ3-O)]7+ core of T-shaped clusters along a Q(B1) coordinate is not an intrinsic property of these clusters. Consequently, the observed distortion of 1 is induced, most likely, by weak van der Waals interactions, that is, crystal packing forces.

support from the NHMFL Jack E. Crow Postdoctoral Fellowship. S.H. and C.B. also acknowledge the support of NSF (Grant Nos. DMR-1309463 and DMR-1610226). C.B. also acknowledges funding from the Florida State University Schuler Postdoctoral Fellowship. This research was also supported in part by the NSF through TeraGrid resources provided by TACC under Grant No. TG-CHE150036 to S.A.S. We thank Professor Boi Hanh (Vincent) Huynh at Emory University for the equipment he donated to the EMR group.

5. CONCLUSIONS We have successfully prepared and characterized a rare, Tshaped, trinuclear iron cluster. This complex exhibits an S = 5/2 ground state and was fully characterized using a suite of advanced spectroscopic techniques such as magnetic susceptibility, single-crystal high-frequency EPR, and field-dependent 57 Fe Mössbauer spectroscopy. The observed ground state originates from the strong AF interaction of the two spins at the base of the inverted T that, in turn, are only weakly coupled to the spin of the site at the peak of the cluster. Owing to these interactions, the magnetic properties of the ground state are determined, essentially, only by the weakly coupled site. However, the field-dependent Mössbauer spectra revealed that, while one iron site is characterized by a large, negative hyperfine coupling constant, typical of Fe(III) ions, the other two are characterized by small negative and positive internal fields. The later, nonzero hyperfine coupling constants were rationalized through a theoretical analysis. Thus, they originate from the mixing of the lowest S = 5/2 excited states into the ground state, which, in turn, is induced by a minute structural distortion.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b00455. Additional HFEPR spectra, Mossbauer spectral simulations, summary of computational data (PDF) Accession Codes

CCDC 1550256 contains the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing data_ [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

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REFERENCES

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. (S.A.S) *E-mail: [email protected]. (S.H.) *E-mail: [email protected]. (E.C.Y) ORCID

Sebastian A. Stoian: 0000-0003-3362-7697 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Ministry of Science and Technology of Taiwan (No. NSC-100-2113-M-030-005). Work performed at the NHMFL is supported by the U.S. National Science Foundation (Award No. DMR-1157490) and by the State of Florida. The Mössbauer instrument was purchased using the NHMFL User Collaboration Grant Program (UCGP5064) awarded to Dr. A. Ozarowski. S.A.S. acknowledges partial L


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