Article pubs.acs.org/IC
Double Magnetic Relaxation and Magnetocaloric Effect in the {Mn9[W(CN)8]6(4,4′-dpds)4} Cluster-Based Network Piotr Konieczny,*,† Szymon Chorazy,‡ Robert Pełka,† Klaudia Bednarek,‡ Tadeusz Wasiutyński,† Stanisław Baran,§ Barbara Sieklucka,‡ and Robert Podgajny*,‡ †
Institute of Nuclear Physics PAN, Radzikowskiego 152, 31-342 Kraków, Poland Faculty of Chemistry, Jagiellonian University, Ingardena 3, 30-060 Kraków, Poland § Department of Solid State Physics, Marian Smoluchowski Institute of Physics, Faculty of Physics, Astronomy and Applied Computer Science of the Jagiellonian University, Łojasiewicza 11, 30-348 Kraków, Poland ‡
S Supporting Information *
ABSTRACT: Cyanide-bridged {MnII9[WV(CN)8]6} clusters with the ground state spin SSG = 39/2 were connected by a 4,4′-dipyridyl disulfide (4,4′-dpds) linker into 2-D doubleconnected coordination layers of the I0O2 type, {MnII9(4,4′dpds)4(MeOH)16[WV(CN)8]6}·12MeOH (1). The intercluster contacts are controlled by the bridging MnII−(4,4′-dpds)−MnII coordination modes and direct hydrogen bonds W−CN··· HOMeOH−Mn in three crystallographic directions, with the vertex-to-vertex contact unprecedented in {Mn9W6}-based networks dominating over the typical edge-to-edge contacts. The resulting 3D supramolecular network of high-spin clusters was subjected to a thorough magnetic characterization in context of two critical issues. First, the intracluster WV−CN−MnII exchange coupling and intercluster interaction were successfully modeled through the combination of dc measurements, Quantum Monte Carlo simulations, and mean-field calculations, yielding a reasonable Jap = −8.0 cm−1, Jeq = −19.2 cm−1 (related to apical and equatorial CN bridges, depending on the angle they form with the S4 axis of dodecahedral [W(CN)8]3− units, respectively), and zJ′ = 0.014 cm−1 with the average gW = gMn = 2.0 parameter set. Continuing this approach, we simulated the magnetocaloric effect (MCE) and compared it to the experimental result of ΔSmax = 7.31 J kg−1 K−1 for fields >5.0 T. Second, two relaxation processes were induced by a relatively weak magnetic field, Hdc = 500 Oe, at an Hac field frequency range of up to 10 kHz, which are related to dipole−dipole interactions between high-spin (39/2) moieties. The observed relaxation times significantly differ from each other, the slow process with τslow at tenths of a second being temperature independent and the faster process being 3−5 orders of magnitude faster with the effective energy barrier Δeff = 17.6 K. These dynamic properties are surprising, since the compound is made up of isotropic high-spin molecules.
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MnIII,20,21 FeII,22,23 and others, to obtain a sufficiently large energy barrier for the reversal of magnetization. While the magnetic anisotropy of the metal sites was reported to be the most important condition for achieving high-efficiency SMMs,24 it was also pointed out that the coordination environment of metal ions25−28 and intermolecular dipolar interactions14 can also play an important role in slowing down the magnetic relaxation processes. Looking at the opposite side of the anisotropy “coordinate” axis, one sees that high-spin isotropic clusters with low-lying excited spin states, e.g. those based on Gd3+ ions (S = 7/2) supported by other paramagnetic 3d ions, bear a potential in magnetic cooling around liquid helium temperature, even more efficient than classical materials such as lanthanide alloys and magnetic nanoparticles.29−33
INTRODUCTION
Discrete coordination species, mononuclear complexes and polynuclear clusters, were particularly recognized among the broad range of magnetic molecular materials, as their functional potential originates from the opportunity of external control and manipulation of the magnetic state on a nanoscale.1−5 The potential is determined by several underlying key properties: nonzero spin in the ground state, magnetic anisotropy, and energy gap between the ground state and the excited states. These parameters can be tuned by chemical synthesis or postsynthetic treatment, leading to different schemes of magnetic exchange interactions, zero-field splitting, spin−orbit coupling, and, last but not least, weak intermolecular magnetic interactions. Along this line, the single-ion magnets (SIM) and single-molecule magnets (SMM) have been widely studied in the context of slow magnetic relaxation.6−13 To observe these phenomena, one in most cases searches for compounds with anisotropic metal ions, e.g. DyIII,14,15 ReIV,16 OsIII,11 CoII,17−19 © 2017 American Chemical Society
Received: March 20, 2017 Published: June 8, 2017 7089
DOI: 10.1021/acs.inorgchem.7b00733 Inorg. Chem. 2017, 56, 7089−7098
Article
Inorganic Chemistry
mg. Anal. Calcd for C89H86Mn9N56O26S8W6: C, 25.4; H, 2.1; N, 18.6; S, 6.1. Found: C, 25.0; H, 2.0; N, 18.4; S, 6.14. IR (in cm−1): ν(C N), 2170 m, 2132 w cm−1; ν(CC) and ν(CN), 1589 s, 1544 w, 1484 w, 1415 ms, 1320 vw; ring deformation γ(C−H), 1222 vw, 1099 vw, 1062 w, 812 w; ν(C−S), 712 m; ν(S−S), 465 m. Crystal Structure Solution and Refinement. The single-crystal X-ray diffraction data for 1 were collected using a Bruker D8 Quest Eco Photon50 CMOS diffractometer equipped with Mo Kα radiation and a graphite monochromator. The selected single crystal was taken from the mother liquor, covered with ApiezonN grease, and measured at the low temperature of 120(2) K (see Table S1 in the Supporting Information for details). Data reduction and cell refinements were executed using the SAINT and SADABS programs. The reflection intensities were corrected for the sample absorption by a multiscan method. The structure was solved by an intrinsic phasing method using SHELXT and refined anisotropically by a weighted full-matrix least-squares technique on F2 using SHELXL-2014/7.56,57 All further calculations were performed using a WinGX (ver. 1.80.05) integrated system.58 Except for the disordered solvent molecules, all of the nonhydrogen atoms were refined anisotropically. The positions of hydrogen atoms were calculated for the ideal positions, and a riding model of the refinement was applied. Due to the significant structural disorder, the C−O distances of crystallization methanol molecules were restrained. The restraints were also applied on the C−O distances (DFIX) and thermal ellipsoids (ISOR, DELU) of selected coordinated methanol molecules, and the strongly disordered −S−S− part of the 4,4′-dpds ligand bridging between Mn4 and Mn5 centers. All of the restraints were necessary in order to maintain the proper geometries of the 4,4′-dpds ligand and methanol molecules and to ensure the convergence of the refinement process. Structural diagrams were prepared using Mercury 3.5.1 software. The CCDC reference number for the crystal structure of 1 is 1535542. Physical Measurements. Infrared spectra (IR) were measured for tiny crystalline or powder samples of 1 protected in mother liquor or Apiezon grease in the 3500−675 cm−1 range using a Nicolet iN10 MX FTIR microscope and for powder 1hyd in KBr pellets in the range 4000−400 cm−1 using a Bruker EQUINOX 55 FT-IR spectrometer, both in transmission mode. Elemental analyses were performed on an Elementar Vario Micro Cube CHNS analyzer. Magnetic measurements were obtained with the use of a Quantum Design SQUID MPMS-XL magnetometer. For this purpose the sample was immersed in a minimal amount of MeOH to prevent the drying and closed in a glass tube. The isothermal magnetization was collected at T = 2.0 K in the field range of ±70 kOe. The static magnetic susceptibility χdc was measured in a temperature range of 2.0−300 K and in an applied field of 500 Oe. The data were corrected for the diamagnetic contribution from the solid sample and the solution. ZFC/FC types of measurements were performed in the dc field Hdc = 50 Oe. The ac susceptibility (χac) measurements were performed with both in-phase χ′ and out-of-phase χ″ components recorded simultaneously. The χac signals were collected as a function of temperature, dc field, and frequency with the oscillating field strength Hac = 1.0 Oe. The applied dc field dependence was measured with 120 Hz in magnetic field from 0 to 70 kOe. The temperature dependence without and with 500 Oe applied field were collected with frequencies of 0.1, 1.0, 10.0, and 997.3 Hz. The frequency dependence of χac was measured with the use of a SQUID MPMS-XL instrument (in the frequency range 0.1−1000 Hz) and a Physical Property Measurement System PPMS (in the frequency range 0.1−10 kHz).
Aiming to contribute to molecular cluster magnetochemistry, we have taken a strong interest in an amazing family of pentadecanuclear cyanido-bridged clusters {M9M′6(CN)48L24} (M = MnII−CuII; M′ = WV, MoV, ReV; L = ROH, MeCN, chelating or bridging ligands).34−40 Simply by setting the molar ratio in solution, a variety of such bimetallic or even trimetallic clusters can be attained, to grow crystalline phases revealing geometrical isomerism,39,41 high-spin molecular character,40−45 SMM-like behavior,36,38,39,46−50 and an electron transfer induced phase transition or spin crossover.35,37 Currently, we wish to exploit further the properties of the highest spin congeners {Mn9W6} (SGS = 39/2) to consider the nonintuitive hypothesis of the occurrence of field-induced magnetic relaxation in a molecular network composed of isotropic highspin species. This issue was not considered in the previous research dedicated to {Mn9W6}-based phases. Nevertheless, some literature reports indicated that, by a very weak internal cluster anisotropy, slow magnetic relaxation below 2 K could be observed due to the anisotropy of intercluster (i.e., intermolecular) interactions: e.g., in the case of a {Mn19} cluster of giant spin SGS = 83/2 in [MnIII12MnII7(μ4-O)8(μ3,η1N3)8(HL)12(MeCN)6]Cl2·10MeOH·MeCN.51,52 It is worth noting that intercluster separation, overall supramolecular self-organization, and thus also the anisotropy of intercluster interactions in {M9M′6}-based phases can be tuned by a set of externally coordinated ligands,38,39,41 which make this family even more attractive for the studies of magnetic relaxation. In this report we present the novel layered cluster-based coordination polymer {Mn II 9 (4,4′-dpds) 4 (MeOH) 16 [WV(CN)8]6}·12MeOH (1; 4,4′-dpds = 4,4′-dipyridyl disulfide linker) with I0O2 dimensionality of connectivity53 exploiting MnII−(4,4′-dpds)−MnII linkages. 1 reveals an alternative manner of hydrogen-bonded supramolecular organization of the {Mn9W6} clusters, in comparison to those observed previously.42,43,45,54 Field-induced double magnetic relaxation, involving a slow T-independent process and a fast T-dependent process, was evidenced for the first time in this group of molecular materials using ac measurements over a broad frequency range (up to 10 kHz, PPMS). This unusual behavior, in our opinion, is related to collective degrees of freedom due to intercluster interactions which have dipole−dipole, superexchange, mediation by the 4,4′-dpds linker, and through hydrogen bond character. Moreover, the intracluster JMnW exchange interactions and resultant magnetocaloric effects were described using a Monte Carlo simulation procedure.
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EXPERIMENTAL SECTION
Materials and Syntheses. 4,4′-Dipyridyl disulfide (4,4′-dpds, known also as Aldrithiol-4) was purchased from a commercial source (Sigma-Aldrich) and used as obtained. Potassium octacyanotungstate(IV) dihydrate, K4[W(CN)8]·2H2O,55 and sodium octacyanotungstate(V) tetrahydrate, Na3[W(CN)8]·4H2O,39 were prepared according to the synthetic procedures described previously. {MnII9(4,4′-dpds)4(MeOH)16[WV(CN)8]6}·12MeOH (1). A 10.7 mg portion (0.054 mmol) of MnCl2·4H2O and 19.2 mg (0.036 mmol) of sodium octacyanotungstate were dissolved in 10 mL of MeOH and mixed with a solution of 59.5 mg (0,27 mmol) of 4,4′dpds in 15 mL of MeOH. The solution was left for slow evaporation until dark brown plates appeared after 2 weeks. The formula of the resulting {MnII9(4,4′-dpds)4(MeOH)16[WV(CN)8]6}·12MeOH (1) was determined by crystal structure solution and refinement. The crystals are unstable in air and exchange solvent for water. The formula of the hydrated form {MnII9[WV(CN)8]6(4,4′-dpds)4·MeOH·25H2O} (1hyd) was derived from CHNS elemental analysis. Yield for 1hyd: 20
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RESULTS AND DISCUSSION Crystal Structure. Compound 1 crystallizes in the monoclinic P21/n crystallographic space group. The details of crystal data, structure refinement, and structure parameters are presented in Tables S1 and S2 in the Supporting Information. The crystal structure of 1 is composed of coordination layers of pentadecanuclear cyanido-bridged {Mn9W6} clusters bridged by double sets of 4,4′-dpds spacers, oriented parallel to the ab 7090
DOI: 10.1021/acs.inorgchem.7b00733 Inorg. Chem. 2017, 56, 7089−7098
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Inorganic Chemistry
Information). Additionally, a large number of crystallization methanol molecules were used to complete the modeling of the structure. The structural identity and uniformity were confirmed by PXRD diffraction (Figure S3 in the Supporting Information). The two-dimensional double-coordination topology in 1 is accompanied by a dense closely packed 3D supramolecular architecture realized mainly by the direct W−CN···HOMeOH− Mn synthons (Figure 2). Two types of such close contacts can be distinguished. Along the directions [111] and [1−11] the clusters are contacted by single vertex-to-vertex hydrogen bonds W3−C21−N21···O6−Mn4, with an N21···O6 distance of 2.68 Å, an W3···Mn4 separation of 7.19 Å, and an Mn1···Mn1 distance of 18.3 Å, forming a kind of square grid supramolecular layer. Further, along the [100] direction the double edge-to-edge W2−C14−N14···O6−Mn5 mode occurs with an N14···O6 distance of 2.67 Å, a slightly larger W2···Mn5 separation of 7.43 Å, and a slightly shorter Mn1···Mn1 distance of 17.9 Å, in comparison to the former contact. Larger intercluster separation with intermetallic distance between 9.5 and 10.0 Å is observed along the [−1−11] direction realized by the indirect W−CN···OMeOH···O−Mn contact as well as along the [11−1] and [010] directions. The double edge-to-edge M−CN···HOsolv−Mn (M = Mo, W) contacts typically dominate in the known supramolecular architectures based on {Mn9M6} clusters,42,43,45 with intermetallic distances Mn···M of between 7 and 9 Å using different blocking or bridging ligands. The same tendency is observed for {Co9W6}38,39,48 and {Ni9W6}41 based crystals, where double edge-to-edge contacts wins the competition with a variety of vertex-to-vertex, vertex-to-edge, and face-to-face contacts, according to a careful inspection of the available structural data. In contrast to that, in the crystal structure of 1 we observe the domination of the alternative vertex-to-vertex short contacts spread in two dimensions, accompanied by the traditional short edge-to-edge contact realized in the linear manner in the third dimension (Figure 2). We believe this arrangement together with the accompanying sets of longer contacts determines the specific scheme of intermolecular contacts underlying the magnetic properties of 1 described below. Magnetic Properties. dc Measurements. Figure 3 presents the χT versus T plot for 1, where the χT values increase on decreasing temperature from 300 K to 2.0 K. The room-temperature χT value was determined as 35.6 emu K mol−1. The obtained value is smaller than the value of 41.7 emu K mol−1 expected for nine uncoupled MnII ions with SMn = 5/2 (Landé factor gMn = 2.0) and six WV ions with SW = 1/2 (gW = 2). This suggests the presence of appreciable antiferromagnetic intramolecular interactions even at room temperature, typically for {Mn9W6} based compounds as well as for cyanide-bridged MnIIWV compounds.59 The maximum χT value of 313.6 emu K mol−1 recorded at 2.0 K is much higher than the lowtemperature limit of χT = 200 emu K mol−1 expected for an isolated ground state spin of 39/2 (antiparallel arrangement of MnII and WV magnetic moments inside the cluster). This excess indicates the presence of effective intermolecular ferromagnetic interactions, which are weak superexchange (via a 4,4′-dpds linker), through hydrogen bond and dipole−dipole interactions. The inset of Figure 3 presents the experimental M−H data at 2.0 K. In a field of 70 kOe the magnetization curve reaches a value of 38.9 NμB which corresponds well to the expected value of 39 NμB for an antiparallel spin alignment of MnII and WV ions. The ZFC/FC (Figure S4 in the Supporting
crystallographic plane (Figure 1). The layers are further connected by hydrogen bonds involving the terminal cyanide
Figure 1. Crystal structure of 1: (a) one cluster unit; (b) 2D layer of doubly connected clusters; (c) 3D packing of layers.
ligands and coordinated MeOH molecules. Typical of this family of clusters,34 the central Mn(μ-NC)6 ion site coordinates six octahedrally arranged [W(CN)8]3− metalloligands. The [W(CN)8]3− ions coordinate eight further six-coordinated Mn units located in the corners of the cube, giving four fac-[Mn(μNC)3(μ-4,4′-dpds)(MeOH)2] moieties (Mn2, Mn2′, Mn5, Mn5′), two fac-[Mn(μ-NC)3(MeOH)3] moieties (Mn3, Mn3′), and two fac-[Mn(μ-NC)3(μ-4,4′-dpds)2(MeOH)] moieties (Mn4, Mn4′) (Figure S1 in the Supporting Information). The distribution of Mn units and the overall bridging coordination scheme are similar to those found by us recently in the layered {Mn II 9 (4,4′-bpy) 4 [W V (CN) 8 ] 6 (EtOH)12(H2O)4}·10EtOH coordination polymer.45 The octacyanidometalates adopt a shape close to the ideal triangular dodecahedron DD-8 (W1 and W2) or to the mixed square antiprism (SAPR-8) and bicapped trigonal prism (BTP-8) (W3) (Table S3 in the Supporting Information). The superpolyhedra {Mn8} and {W6} composed of the corresponding peripheral metallic centers are only slightly distorted from an ideal cube and octahedron, respectively (Figure S2 in the Supporting 7091
DOI: 10.1021/acs.inorgchem.7b00733 Inorg. Chem. 2017, 56, 7089−7098
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Figure 2. Intercluster contacts in 1: short vertex-to-vertex contacts along the directions [111] and [1−11] (yellow) (a) and edge-to-edge contacts along the direction [100] (purple) (b); long contacts along the directions [1−1−1] (c) and [11−1] and [010] (green). (d, e) More general projections of the crystal structure. Selected hydrogen bonds and intermetallic distances (in Å) are included in each case.
Quantum Monte Carlo Simulations. In order to describe experimental magnetic results, we use a spin-only Hamiltonian within the cluster: 12
Ĥ = −Jap
18
∑
̂ (i)·SMn ̂ (j) − J SW eq
(ij) = 1 6
̂ z (i ) + + g μ B (∑ S W i=1
∑
̂ (i)·SMn ̂ (j) SW
(ij) = 1 9
̂ z(j))H ∑ SMn j=1
(1)
where the first two terms account for the superexchange interactions and the last term corresponds to the Zeeman coupling with the external field H. The superexchange interaction is mediated by the CN− bridges between W and Mn ions, with two distinct magnetic exchange coupling pathways and two related constants Jap and Jeq. We adopt here the arguments of Ruiz et al.60 that 30 CN− bridges can be divided into two groups, 12 apical and 18 equatorial, as shown in the diagram of Figure 4. The above division can be done assuming the reasonable approximation of ideal dodecahedral geometry of octacyanidometalate moieties in {Mn9W6} in 1 (see Table S3 in the Supporting Information).The apical (ap) and equatorial (eq) bridges are distinguised by the angle θ that the W−C bonds form with the S4 axis of the dodecahedron, and these are 36.85 and 69.46°, respectively. Every tungsten ion is thus bridged by the apical CN− ligands to the central
Figure 3. Temperature dependence of χT for 1 as measured at H = 500 Oe. The green solid line marks the 200 emu K−1 mol−1 limit for an isolated spin of 39/2. Inset: isothermal magnetization at T = 2.0 K, whereas the dotted line shows the 39 NμB value for an antiparallel spin alignment of MnII and WV ions. In both cases (χT(T) and M(H) plots), the red solid line shows the results of the quantum Monte Carlo calculations.
Information) and the χac vs T (Figure S10, top, in the Supporting Information) curves do not reveal any signatures of long-range magnetic order. Moreover, the reduced magnetization M(H/T) test shows rather small overall magnetic anisotropy, indicating the internal isotropic character of the {Mn9W6} clusters (Figure S5a in the Supporting Information). 7092
DOI: 10.1021/acs.inorgchem.7b00733 Inorg. Chem. 2017, 56, 7089−7098
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Inorganic Chemistry
parameter values are comparable with the DFT calculations for MeOH solvated clusters.60,61 Moreover, the positive value of zJ′ confirms the intercluster ferromagnetic interactions, which were pointed out in the χT(T) description. This observation is in contradiction to the previously described Mn9W6 based phases with a domination of antiferromagnetic intercluster interactions. This difference can be tentatively correlated with different types of dominating intercluster contacts in 1 and previous solids. It is worth noting that, using the Hamiltonian with the anisotropy term (DŜ2) included, we did not achieve a significant nonzero value of parameter D, which is in agreement with the expected isotropic character of the {Mn9W6} clusters, also evidenced by the M(H/T) curves (Figure S5a). Magnetocaloric Effect. The magnetocaloric effect (MCE) has been estimated by an indirect method from the isothermal measurements of magnetization. The magnetic entropy change ΔS was calculated with the use of the integrated Maxwell relation: ΔS(T ) =
Figure 4. Exchange interaction diagram. Peripheral manganese ions are marked with green pentagons, the red hexagon shows the central Mn ion, and blue octagons are ascribed to W ions. Dashed lines indicate interactions described by apical Jap and dotted lines interactions described by equatorial Jeq.
H max
⎛ ∂M(T , H ) ⎞ ⎜ ⎟ dH ⎝ ⎠H ∂T
(3)
where the M(T,H) data were obtained from an array of isothermal magnetization curves for fields 0−70 kOe and temperatures 2−80 K, as shown in Figure S6 in the Supporting Information. The resultant temperature dependence of −ΔS for μ0ΔH = 0.1, 0.2, 0.5, 1.0, 2.0 3.0, 4.0, 5.0, 7.0 T is presented in Figure 5. The values of magnetic entropy change for 1 increase
manganese ion and one peripheral manganese ion, while the remaining three CN− equatorial bridges provide a linkage to three further peripheral manganese ions. In that way eight peripheral manganese ions are divided into three groups, with 0, 1, or 2 apical CN− connections. A similar description was presented in the work by Zhang et al.;61 however, they considered 14 apical and 16 equatorial CN bridges. Using the Hamiltonian defined above, the magnetic susceptibility χ0 and magnetization M0 of an isolated cluster were evaluated by quantum Monte Carlo method implemented in the ALPS package.62 In the next step an effective interaction between the clusters was included within the mean field approximation: χ=
∫0
χ0 1 − zJ ′χ0 /NAμB2 g 2
(2)
Figure 5. Magnetic entropy change as a function of temperature for μ0ΔH = 0.1, 0.2, 0.5, 1.0, 2.0, 3.0, 4.0, 5.0 T.
where zJ′ denotes the averaged coupling constant between the neighboring clusters, μB is the Bohr magneton, and NA is Avogadro’s number. The fitting procedure was performed for χT (Figure 3) measured over a wide temperature range (2.0− 300.0 K). The resulting best fit parameters Jap, Jeq, and zJ′ were used for the magnetization calculation (inset in Figure 3 and Figure S5b in the Supporting Information). The results are presented in Table 1. Let us note that the obtained Jap and Jeq
with decreasing temperature down to the lowest measured temperature. They also rise with increasing change of the magnetic field but only up to μ0ΔH ≈ 5 T (Figures S8 and S9 in the Supporting Information), at which −ΔS saturates, reaching the value −ΔSmax ≈ 7.31 J kg−1 K−1. This value corresponds well to the full change of the total magnetic entropy ΔSGS = R ln(2S + 1) = 7.25 J kg−1 K−1 for the ground spin state of 1, S = 39/2. The obtained value is distinctly higher than 3.36 J kg−1 K−1 found for the recently reported material based on {Ni9W6} clusters.63 However, it must be noted that the value of ΔSGS does not include the degrees of freedom from other spin states64 and intercluster ferromagnetic interactions, which both can give additional contributions. We have also used the quantum Monte Carlo methods with the best fit parameters to simulate the magnetic entropy change and compare it with the experimental data (Figure S7 in the Supporting Information). As can be observed, the values agree
Table 1. Calculated Exchange-Coupling Constants Jap and Jeq for 1, {Mn9W6(MeOH)24}61 (Mn9W6), and {Mn9Mo6(MeOH)24}60 (Mn9Mo6) 1 {Mn9W6(MeOH)24}61 {Mn9Mo6(MeOH)24}60
Jap (cm−1)
Jeq (cm−1)
zJ′ (cm‑1)
−8.0 −12.4a −9.0
−19.2 −25.0a −23.8
0.014
a Due to the difference in the definition of model Hamiltonians, the J values given for Mn9W6 are twice a large as those in the original paper61 to easily compare them with 1 and Mn9Mo6 cases.
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DOI: 10.1021/acs.inorgchem.7b00733 Inorg. Chem. 2017, 56, 7089−7098
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Inorganic Chemistry well for smaller μ0ΔH (
