Octahedral–Tetrahedral Systems [Co(dppmO,O)3 ... - ACS Publications

Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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Octahedral−Tetrahedral Systems [Co(dppmO,O)3]2+[CoX4]2− Showing Slow Magnetic Relaxation with Two Relaxation Modes Cyril Rajnák,*,† Filip Varga,† Ján Titiš,† Ján Moncol,‡ and Roman Boča*,† †

Department of Chemistry, Faculty of Natural Sciences, University of SS. Cyril and Methodius, 917 01 Trnava, Slovakia Institute of Inorganic Chemistry, Slovak University of Technology, 812 38 Bratislava, Slovakia

‡

S Supporting Information *

ABSTRACT: Three compounds with octahedral−tetrahedral Co(II) moieties of [Co(dppmO,O)3][CoX4] type, where X = SCN (1), Cl (2), or I (4) have been synthesized and characterized by the X-ray structure analysis (1 and 4), and spectroscopic methods. The dc magnetic measurements show high magnetic anisotropy for octahedral centers whereas tetrahedral sites possess moderate D values. These results are confirmed by the ab initio calculations. The ac susceptibility data reveals a slow magnetic relaxation for 2 and 4, similar to that of the X = Br analogue (3), whereas 1 displays no ac-absorption signal. There are two relaxation channels; the slower for 2 (4) possesses a relaxation time as long as τLF= 178 (588) ms at T = 1.9 K and Bdc = 0.7 T. Also, the half-Zn analogue, [Co(dppmO,O)3][ZnI4], shows slow magnetic relaxation with two relaxation channels conditioned by the cationic unit [Co(dppmO,O)3]2+.

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INTRODUCTION

In continuing our investigation of bimetallic, ionic complexes with the general formula [Co(dppmO,O)3][CoX4] with X = Br (3),10 three other members of this series with X = NCS (1), Cl (2), and I (4) have been synthesized and analyzed. Free dppm ligand, bis(diphenylphosphan)methane, was used in the synthesis; however its oxidized form dppm O,O , bis(diphenylphosphanoxido)methane, resulted (for details see Supporting Information − SI). The magnetic response under the direct current (dc) and the alternating current (ac) magnetic fields is addressed, and the SIM behavior is probed.

Cobalt(II) complexes are known as systems with considerable magnetic anisotropy manifesting itself in a moderate (for tetrahedral complexes) or large (for octahedral systems) zerofield splitting (zfs) parameter (D) that enters the spin Hamiltonian formalism. The ground crystal field term for the tetrahedral system is orbitally nondegenerate 4A1, and the D parameter can adopt positive as well as negative values. This was well documented by the parallel studies using highfrequency/high-field electron magnetic resonance, magnetometry (susceptibility and magnetization), and ab initio calculations.1,2 For octahedral systems, the situation is more complex. Theoretical modeling confirms that for a compressed tetragonal bipyramid D > 0 holds true. For an elongated bipyramid the ground term (4T1g) is orbitally degenerate and the spin-Hamiltonian formalism cannot be applied. In such a case, 12 magnetic energy levels are grouped into 6 Kramers doublets that might be thermally accessible.3,4 Earlier studies on single-molecule (ion) magnetism, SMM or SIM, were conducted online such that the negative sign and a large value of the D parameter will result in a high barrier to spin reversal U = |D|(S2 − 1/4). This enters the relaxation time via the Orbach mechanism, τ = τ0 exp(U/kBT).5−7 Recent studies, however, argue that with large values of D/hc ≈ 100 cm−1 the Orbach process becomes discriminated in favor of the Raman, direct, and quantum tunneling processes.8 Moreover, experimentally found Ueff is approximately half of the predicted value, which also has been theoretically explained.9 © XXXX American Chemical Society

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RESULTS The compound (1) crystallizes in the triclinic crystal system (space group P1̅), 4 is monoclinic (P21/c), and previously reported 3 is monoclinic as well (P21/c); the ionic entities are drawn in Figure 1.11 These compounds are formed from two ionic moieties: nearly octahedral [Co(dppmO,O)3]2+ and a nearly tetrahedral [CoX4]2−. The bond lengths in the octahedral units vary between Co−O = 2.04−2.12 Å with no significant deviations in bond angles from octahedral vertices; these are listed in SI. An average of the bond lengths situated in trans positions indicates that the coordination polyhedron refers to a compressed tetragonal bipyramid with some orthorhombic component (Table S3). Within the tetrahedral unit of 1, two bond angles are below and the remaining four are above the tetrahedral value (109.5 Received: December 19, 2017

A

DOI: 10.1021/acs.inorgchem.7b03193 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

magnetization per formula unit is M1 = Mmol/NAμB = 5.17 at T = 1.9 K and B = 7.0 T. This value is much lower than the spinonly estimate M1 = 2gavS = 7.43, again owing to the zfs. For the analysis of magnetic data, the spin Hamiltonian consisting of two merged zfs models has been considered ̂ 2 z − SO⃗ 2/3)ℏ−2 + μ Bg SO, ̂ aℏ−1 Hâ = DO(SO, B O, z ̂ 2 z − ST⃗ 2/3)ℏ−2 + μ Bg ST, ̂ aℏ−1 + DT(ST, B T, z

(1)

where subscript O (T) refers to the octahedral (tetrahedral) center; a = x and z. A simultaneous fitting of the susceptibility and magnetization data led to the optimum set of magnetic parameters listed in Table 1. Nonlinear optimization of

Figure 1. Molecular structures of 1 and 4.

deg); this is consistent with the geometry of an elongated (prolate) bisphenoid. On the contrary, in 4, four angles lie below and the two remaining are above the tetrahedral value, which describes the compressed (oblate) bisphenoid. The electronic spectra of 1−4 are essentially analogous (Figure 2), with a clear shift of the intense third d−d band of the tetrahedral chromophore E3(4A2 → 4T1(P)) ≈ 15B + 12Dq(Td) from 16 000 (X = NCS) to 12 500 cm−1 (X = I).

Table 1. Fitted and Calculated Magnetic Parameters parametera

1

2

gO,x gT,z gT,x DO/hc [cm−1] DT/hc [cm−1] ρ(DO,DT)b ab initio data DO/hc [cm−1] DT/hc [cm−1]

2.76(1) 2.14(2) 2.20(1) 91(2) −5.0(3) −0.18

2.55 2.286 2.29 77 4.6 −0.30

2.68 2.10 2.39 122 15.0 −0.92

2.70 2.28 2.56 99 19.3 −0.55

102 −3.5

157c −1.89

129 −2.53, + 6.57

107 14.9

3

4

gO,z = 2.0 was fixed. bPair correlation coefficient. cBased upon the Xray structure of a solvent-rich species published elsewhere.17 a

magnetic data (both dc and ac) was conducted by the MIF&FIT program that utilizes modern genetic algorithms along with other advanced methods.12−16 The spin Hamiltonian formalism is legitimate to use in the present case of the compressed tetragonal bipyramid for the cationic unit since the daughter ground term is orbitally nondegenerate 4A1g. As expected, axial zero-field splitting parameter DO for the octahedral site is very high, whereas tetrahedral center DT adopts a moderate value. Negative DT in 1 is consistent with its geometry of an elongated (prolate) bisphenoid and positive in 4 with its geometry of a compressed (oblate) form. The dc susceptibility data for 1 displays an analogous course when compared to 2 and 4; however, the magnetization data is different (Figure S9 in ESI) and a little dependent between T = 2.0 and 4.6 K. It is likely due to an extensive system of hydrogen bonds mediated by the sulfur atoms of the [Co(NCS)4]2− moiety. For this reason, only the fitting of the susceptibility data was successful. Ab initio calculations (CASSCF/NEVPT2)18 for 1 and 4 confirm the results based upon magnetometry (for details see SI): high positive D > 100 cm−1 for the octahedral sites that arise from the quasi-degeneracy of the daughter terms of 4T1g on symmetry lowering from the octahedral geometry. For isolated units [Co(NCS)4]2− and [CoI4]2− in their experimental geometry, the calculated D values are moderate: D/hc = −3.5 and +14.9 cm−1, respectively. The ac susceptibility measurements for 1, 2, and 4 reveal that there is not an out-of-phase susceptibility response at zero field. This component also stays silent at the applied field for 1. For 2 and 4, however, it rises and culminates between Bdc = 0.1 and 0.5(0.7) T depending upon the frequency of the oscillating field (Figure 4). These data confirm that 2 and 4 exhibit a fieldinduced slow magnetic relaxation.

Figure 2. Electronic spectra of 1−4.

The dc magnetic data for 1−4 are available (see SI), and they are essentially analogous (with the exception of magnetization for 1). An illustrative case is presented in Figure 3 for 2.

Figure 3. Magnetic functions for 2; temperature dependence of the effective magnetic moment (left) and field dependence of the magnetization per formula unit (center); inset, molar magnetic susceptibility; lines, fitted by the merged zfs model.

The effective magnetic moment for 2 at room temperature adopts a value of μeff = 6.78 μB, and it gradually decreases upon cooling (more rapidly below 20 K); at T = 1.9 K its value is μeff = 5.28 μB. Two uncoupled S = 3/2 systems imply μeff/μB = gav[2S(S + 1)]1/2 and then gav = 2.48. The decrease in the effective magnetic moment is due to the zero-field splitting (zfs) of both the octahedral and tetrahedral Co(II) centers. The B

DOI: 10.1021/acs.inorgchem.7b03193 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 4. ac susceptibility components for 2 and 4 as a function of the external magnetic field for a set of frequencies. Lines act as guides for the eye. Figure 5. The ac susceptibility components for 2 and 4 as a function of the frequency at a fixed external field. Lines are fitted by the two-set Debye model.

The ac response is a complex function of three factors: temperature, the applied dc field, and the frequency of ac field f. A more detailed mapping of the ac susceptibility data for a set of frequencies ranging between f = 0.06−1500 Hz is presented in Figure 5. It can be seen that two peaks coexist at the out-ofphase susceptibility; a low-frequency (LF) peak around or below f ≈ 1 Hz and a high-frequency (HF) peak whose maximum lies outside the hardware limit (1500 Hz). In fitting the magnetic data by the generalized Debye model χk − χk − 1 χ (ω) = χS + ∑ 1 + (iωτk)1 − αk (2) k

A representative diagram of χ″ vsf for a set of temperatures at fixed field Bdc = 0.5 T for 4 is shown in Figure 6. The extrapolation/interpolation lines for the optimum parameters enter the Argand diagram as displayed in Figure 7.

adiabatic susceptibility χS (the high-frequency limit), relaxation times τk, distribution parameters αk, and isothermal susceptibilities χk for the k th relaxation channel were calculated (details in the SI). It is seen that the external dc field causes a shift of the LF peak to lower frequencies that implies a prolongation of the relaxation time. For 4, the relaxation time derived from frequency f ″, when the out-of-phase susceptibility adopts a maximum value τ = 1/(2πf ″), is as slow as τ = 0.14(1) s at T = 1.9 K and Bdc = 0.3 T. An increase in the external magnetic field to Bdc = 0.5 and 0.7 T causes a shift of χ″ to lower frequencies; consequently, the relaxation time is prolonged to τ = 0.33(1) and 0.59(3) s, respectively. There is interplay between the LF and HF relaxation channels; an increase in the height of the LF peak (χLF) (proportional to the mole fraction of LF species xLF) with the magnetic field is associated with the decrease in the height of the HF peak (χHF) so that x LF = (χLF − χS )/(χHF − χS )

Figure 6. The ac susceptibility components for 4 as a function of the ac frequency. The solid lines are fitted.

The high-temperature mode of the relaxation behaves in accordance with previous investigations; it involves Orbach and/or Raman processes completed by the direct and quantum tunneling terms19,20 τ −1 = τ0−1 exp( −U /kBT ) + CT n + ATBm + D1/(1 + D2B2 )

(4)

The starting set of parameters for a full nonlinear fit in eq 4 has been estimated; (a) from the linear fit ln τ = ln τ0 + (U/kB) T−1 for the four high-temperature data points and (b) from the

(3)

holds true. C

DOI: 10.1021/acs.inorgchem.7b03193 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Cobalt nuclei possess nuclear spin I = 7/2 so that, in addition to the electronic spin states, there is a hyperfine interaction leading to the splitting of each MS level into eight hyperfine levels. This situation also can influence the slow magnetic relaxation in Co(II)-based SIMs.8 Finally, the SMR has been observed for a number of S = 1/2 spin systems such as low-spin Mn(IV), V(IV), Ni(I), and Cu(II).20,32−35 The D parameter for these systems stays undefined, though there exists a magnetic anisotropy, at least well documented by different g factors for Cu(II). The Orbach mechanism will be discriminated for D largely enough, since then energy gap Δ = 2|D| is not thermally accessible, and the system behaves like an S* = 1/2 pseudospin system.8 In the low-temperature region, the Raman, the direct, and eventually the quantum tunneling processes adopt their significance via eq 4. Individual regimes dominate in different temperature regions. In the high-temperature limit, the Orbach process is consistent with linear fit ln τ = ln τ0 + (U/kB)T−1. In the intermediate-temperature region, linear fit ln τ = −ln C − m(ln T) recovers the Raman process. In the low-temperature region, linear equation τ−1 = (ABn)T + D1 maps the direct and quantum tunneling processes. Having good representative data, all of these contributions can be reliably fixed. This statement hold true for the single-channel relaxation mode as often seen in high frequency region f = 10−10 000 Hz. Observation of the low-frequency channel of relaxation (f = 0.05−10 Hz) in Cu(II), Ni(II), Co(II), and some Dy(III) complexes represent an unexplored field.36−38 The presence of the slowly relaxing moieties on cooling resembles a nucleation of mononuclear entities to oligomers in the solid state (finite chains, plates, and blocks). The mole fraction of the LF mode, xLF, is determined by the heights of the respective peaks at χ″ (isothermal susceptibilities) via eq 3. This quantity decreases upon heating in favor of xHF; it increases with the applied external field. The magnetic field supports an exchange coupling among paramagnetic centers mediated, for instance, by a set of hydrogen bonds or other intermolecular (interion) contacts. With increasing temperature, the strength of these interactions escapes so that eventual oligomers in the solid state disintegrate to monomers; these single ions obey a faster relaxation via the HF mode. This explanation is supported by the experiments examining doping into a diamagnetic Zn matrix.8,36,38 The systems of the present study for 2 and 4 (in accordance with previously reported 3) are unique in the feature that the LF mode is a dominating relaxation path in monitored frequency window f = 0.05−1500 Hz. This process is as slow as τLF = 33, 63, and 120 ms for 2, 3, and 4 at Bdc = 0.1 T and T = 2.0 or 1.9 K, respectively. It is prolonged at higher field Bdc = 0.7, 0.8, and 0.7 T to τLF = 178, 295, 588 ms so that a “magic limit” of one second is closely being approached. Notice that the estimate for the mole fraction of the low-frequency phase under these conditions amounts to xLF = 0.67, 0.63, and 0.72. Though the dc susceptibility data for 1 is analogous to that for 2, 3, and 4, the absence of the slow magnetic relaxation in 1 is surprising. The hydrogen bonds identified in the solid state probably mediate an exchange coupling of the antiferromagnetic nature that holds the structure together and prevents the slow magnetic relaxation. Also, a weak influence of the magnetic field to the magnetization curves of 1 supports the idea that in this case a chainlike magnetic behavior occurs. However, if we look at the crystal packing of complex 4 the hydrogen bond system is also visible (with a little bit greater

Figure 7. Argand diagram (left) and the Arrhenius-like plot for 4. The line connecting LF points serves as a guide for the eye; for the HF mode they are fitted. Dashed lines are linear fits for the pure Orbach and/or Raman process.

linear fit ln τ = −ln C − m(lnT) for the three points in the intermediate temperature region. Then the temperature dependence for Bdc = 0.5 T was fitted with parameters τ0 = 1.4 × 10−15 s, U/kB = 69(6) K, C = 108(31) K−7 s−1, and D1 = 1.1 × 105 s−1. The field dependence at the lowest temperature was recovered by (AT) = 3.2 × 106 T−4 s−1, D1 = 2.6 × 104 s−1, and D2 = 41 T−2 (see SI). Temperature evolution of the relaxation time for the lowfrequency channel in the double frequency relaxation case is different from the HF behavior; upon heating, the relaxation time starts to decrease, but upon further heating, it increases. This behavior has not yet been modeled.

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DISCUSSION The properties of the single molecule (ion) magnets assembled from Co(II) centers are very versatile. Some of these systems exhibit slow magnetic relaxation (SMR) even in the absence of the magnetic field.21−29 A majority of them, however, require some external magnetic field to prevent fast magnetic tunneling. It was believed that a small field Bdc ≈ 0.1 T is sufficient for creating this effect. More detailed studies show that until Bdc = 0.5 T and higher, the maximum of the out-of-phase susceptibility depends upon the temperature, field, and frequency of the ac field f, χ″max = F(T, Bdc, f), so a determination of the small optimum field is rather problematic. For a long period, the relaxation time was associated with the “rule” based upon the Orbach mechanism, i.e., τ = τ0 exp(U/ kBT), where the barrier to spin reversal relates to axial zero-field splitting parameter D via U = |(S2 − 1/4) → 2|D| for S = 3/2 spin systems. There is a serious obstacle for Co(II) systems when the ground term is orbitally (quasi)degenerate such as 4 T1g in the nearly octahedral geometry. In this case, the spin Hamiltonian formalism cannot be applied since the perturbation theory diverges. In other words, the magnetic anisotropy is substantial, owing to the spin−orbit coupling but is not described by the D and E parameters. Negative values of D associated with the easy axis of magnetization is also no longer an ultimate demand for SIMs behavior; there is mounting evidence for SMR in the case of D > 0 combined by some ortho-rhombic component E.30,31 Another aspect is represented by the fact that the values of Ueff retrieved from the experimental data are about half of those predicted by the above formula, Ueff ≈ |D|. This effect has been recently modeled through the role of anharmonic phonons.9 D

DOI: 10.1021/acs.inorgchem.7b03193 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry distance but larger electronegativity for the I− ion than for the sulfur ion), so maybe there is not only one reason for this situation. The effect of the exchange coupling has already been observed in the series of small [Co(2L)X2] complexes where 2L = biquinoline (biq), 4,7-diphenyl-2,9-dimethyl-1,10-phenanthroline = batocuproine (bcp), and 2,9-dimethyl-1,10-phenanthroline = neocuproine (dmphen).39−41 In [Co(bcp)Cl2] SMR exists, but in [Co(bcp)Br2] and [Co(bcp)I2] it is absent. In [Co(dmphen)Cl2] it is absent, but in [Co(dmphen)Br2] and [Co(dmphen)I2] it is present. All members of the [Co(biq)X2] series exhibit SMR with two or three relaxation modes. This versatility points to a complex concurrence of the magnetic anisotropy and the exchange interaction in tuning the SIM behavior. In order to bring more light into the relaxation processes, doping experiments have been conducted. The mixture of Co/ Zn salt precursors resulted in the single crystals of [Co(dppmO,O)3][ZnI4] (hereafter 5), whose X-ray structure analysis confirmed that Zn(II) enters only the [ZnI4]2− moiety (for details see the SI). The electronic spectra confirm the disappearance of the d−d transitions for the tetrahedral units when compared to the case of [CoI4]2−. The ac susceptibility data confirms the presence of two relaxation modes, of which the low-frequency mode is visibly supported by the external dc magnetic field (Figure 8).

[CoI4]2− to [ZnI4]2− causes a visible shortening of the lowfrequency relaxation time by an order of magnitude (102 vs 14 ms at T = 1.9 K and Bdc = 0.1 T). The opposite is true for the high-frequency relaxation time (prolongation from 53 to 259 μs).

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CONCLUSIONS Compounds [Co(dppmO,O)3][CoX4] formed from octahedral and tetrahedral Co(II) complexes, where X = NCS, Cl, Br, or I, behave in the dc magnetic field as paramagnets with large magnetic anisotropy referring to octahedral entity DO/hc ≈ 100 cm−1 and minor magnetic anisotropy referring to tetrahedral units [CoX4]2−. In the ac magnetic field, a slow magnetic relaxation is identified for X = Cl, Br, and I as opposed to for NCS− containing anion complex 1. The [Co(NCS)4]2−containing compound has an extensive hydrogen-bond network that probably prevents the single-molecule behavior. There are two slow relaxation channels for 2−4: the low-frequency mode possesses the relaxation time as long as τLF = 178, 295 and 588 ms at T = 1.9 K and Bdc = 0.7 T for X = Cl, Br, and I. In complex [Co(dppmO,O)3][ZnI4], isostructural with 4, only the cationic entity is responsible for the presence of the two relaxation channels. This leads to the conclusion that the [CoX4]2− units act as spacers, not determining the slow magnetic relaxation.

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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.7b03193. Details about the synthesis, crystal and molecular structure (CCDC 1526142, 1526143, 1825175, 1825176), ab initio calculations, and dc and ac magnetic data and their analysis (PDF) Accession Codes

CCDC 1526142−1526143 and 1825175−1825176 contain 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 [email protected]. uk, or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

Figure 8. ac susceptibility components for 5 as a function of the frequency at fixed external field. Lines are fitted by the two-set Debye model.

A comparison of the relaxation time for complex 4 with its partial Zn analogue 5 shows that the two relaxation modes belong to octahedral entity [Co(dppmO,O)3]2+ since the tetrahedral unit in 5 is magnetically silent. The data analysis based upon the two-set Debye model results in the relaxation parameters as listed in Table 2. In both cases, the magnetic field lifts the low-frequency relaxation time toward a higher value, whereas the opposite is true for the high-frequency relaxation time. However, the alteration of the counteranion from

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Corresponding Authors

*E-mail: [email protected], *E-mail: [email protected] ORCID

Roman Boča: 0000-0003-0222-9434 Notes

Table 2. Relaxation Time for 4 and 5 at T = 1.9 K [Co(dppmO,O)3][CoI4] (4)

AUTHOR INFORMATION

The authors declare no competing financial interest.

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[Co(dppmO,O)3][ZnI4] (5)

Bdc/T

τLF/10−3 s

τHF/10−6 s

xLF

τLF/10−3 s

τHF/10−6 s

xLF

0.1 0.3 0.5 0.7

102(2) 148(4) 334(13) 588(31)

53.1(9) 30.3(7) 9.9(25) 0.68

0.06 0.41 0.64 0.72

14.0(37) 37.5(15) 42.9(37) 72.4(59)

259(4) 91(8) 45(5) 20(7)

0.10 0.49 0.68 0.71

ACKNOWLEDGMENTS Slovak grant agencies (APVV-14-0078 and VEGA 1/0534/16) and the Research and Development Operational Program (University Science Park of STU Bratislava, ITMS 26240220084), cofunded by the European Regional Development Fund, are acknowledged for financial support. E

DOI: 10.1021/acs.inorgchem.7b03193 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

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DOI: 10.1021/acs.inorgchem.7b03193 Inorg. Chem. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.inorgchem.7b03193 Inorg. Chem. XXXX, XXX, XXX−XXX