Origin of the Zero-Field Splitting in Mononuclear Octahedral MnIV

Article pubs.acs.org/IC

Origin of the Zero-Field Splitting in Mononuclear Octahedral MnIV Complexes: A Combined Experimental and Theoretical Investigation Matija Zlatar,† Maja Gruden,‡ Olga Yu Vassilyeva,§ Elena A. Buvaylo,§ A. N. Ponomarev,∥ S. A. Zvyagin,∥ J. Wosnitza,∥,⊥ J. Krzystek,# Pablo Garcia-Fernandez,*,∇ and Carole Duboc*,○ †

Center for Chemistry, Institute of Chemistry, Technology and Metallurgy, University of Belgrade, Njegoševa 12, P.O. Box 815, 11001 Belgrade, Serbia ‡ Faculty of Chemistry, University of Belgrade, Studentski trg 12-16, 11001 Belgrade, Serbia § Department of Chemistry, Taras Shevchenko National University of Kyiv, 64/13 Volodymyrska str., Kyiv 01601, Ukraine ∥ Dresden High Magnetic Field Laboratory (HLD-EMFL), Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Saxony, Germany ⊥ Institut für Festkörperphysik, Technische Universität Dresden, D-01062 Dresden, Saxony, Germany # National High Magnetic Field Laboratory (NHMFL), Florida State University, Tallahassee, Florida 32310, United States ∇ Departamento de Ciencias de la Tierra y Física de la Materia Condensada, Universidad de Cantabria, Avenida de los Castros s/n, 39005 Santander, Cantabria, Spain ○ Département de Chimie Moléculaire, Université Grenoble Alpes/CNRS, UMR-5250, BP-53, 38041 Grenoble Cedex 9, France S Supporting Information *

ABSTRACT: The aim of this work was to determine and understand the origin of the electronic properties of MnIV complexes, especially the zero-field splitting (ZFS), through a combined experimental and theoretical investigation on five well-characterized mononuclear octahedral MnIV compounds, with various coordination spheres (N6, N3O3, N2O4 in both trans (trans-N2O4) and cis configurations (cis-N2O4) and O4S2). High-frequency and -field EPR (HFEPR) spectroscopy has been applied to determine the ZFS parameters of two of these compounds, MnLtrans‑N2O4 and MnLO4S2. While at X-band EPR, the axial-component of the ZFS tensor, D, was estimated to be +0.47 cm−1 for MnLO4S2, and a D-value of +2.289(5) cm−1 was determined by HFEPR, which is the largest D-magnitude ever measured for a MnIV complex. A moderate D value of −0.997(6) cm−1 has been found for MnLtrans‑N2O4. Quantum chemical calculations based on two theoretical frameworks (the Density Functional Theory based on a coupled perturbed approach (CP-DFT) and the hybrid Ligand-Field DFT (LF-DFT)) have been performed to define appropriate methodologies to calculate the ZFS tensor for MnIV centers, to predict the orientation of the magnetic axes with respect to the molecular ones, and to define and quantify the physical origin of the different contributions to the ZFS. Except in the case of MnLtrans‑N2O4, the experimental and calculated D values are in good agreement, and the sign of D is well predicted, LF-DFT being more satisfactory than CP-DFT. The calculations performed on MnLcis‑N2O4 are consistent with the orientation of the principal anisotropic axis determined by single-crystal EPR, validating the calculated ZFS tensor orientation. The different contributions to D were analyzed demonstrating that the d-d transitions mainly govern D in MnIV ion. However, a deep analysis evidences that many factors enter into the game, explaining why no obvious magnetostructural correlations can be drawn in this series of MnIV complexes.

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INTRODUCTION

their electronic structure and reactivity would be of great importance. In this context, the development of pertinent, complementary methods to assist in the definition of the geometric and electronic structure of such centers is crucial. The zero-field splitting (ZFS), which represents the leading term in the spin Hamiltonian for transition-metal complexes

Manganese(IV) is largely involved in the design of a large variety of single-molecular magnets, the most famous being the [Mn12O12(CH3CO2)16(H2O)4] cluster composed by eight MnIII and four MnIV ions.1 High-valent MnIV centers are also implicated in a number of biological2−7 and synthetic processes8−14 as key intermediates, in either heme or nonheme environments. However, the exact structure of such active species is still under debate, and finding correlation between © XXXX American Chemical Society

Received: October 14, 2015

A

DOI: 10.1021/acs.inorgchem.5b02368 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Chart 1

magnitude of D, but the ZFS magnitude in MnII and MnIII complexes is regularly underestimated compared to the experimental data.36,38,40,41 Other methods, in particular multiconfigurational wave function approaches, generally give more satisfactory predictions of D. Methods like the complete active space self-consistent field (CASSCF), DDCI, and Nelectron valence second-order perturbation theory (NEVPT2) lead to calculated D values in good agreement with the experimental data38,42−47 but are computationally much more expensive than DFT, significantly hampering their ability to be applied to medium and large transition-metal complexes. More recently, a hybrid methodology (LF-DFT), which combines a multideterminant DFT-based method with ligand-field theory has been successfully employed to investigate the ZFS of different transition-metal ions.48−51 Regarding MnIV, only one theoretical investigation has been reported so far, on a Ni, Mn codoped LiCoO2 material with the aim of defining the structure of the MnIV ion inside the material.35 Using a DFT framework, the authors predicted the ZFS parameters in various calculated geometries for the MnIV and compared the calculated D-values with those determined experimentally by HFEPR. However, there has been no benchmark study to validate the choice and the accuracy of their methodology. Systematic studies have shown that the performance of different methods on various metal ions in different oxidation states varies significantly and that a benchmark investigation is required to validate the most appropriate approach. The lack of such systematic studies could be related to the fact that the calculation of the ZFS for MnIV is a very delicate task. Octahedral MnIV complexes display a spatially nondegenerate 4A2g ground term that is not split in first order by spin−orbit coupling or covalency, leading to a quite isotropic metallic center even when coordinated to strong ligands that can break perfect octahedral symmetry. As a result, the computation of ZFS values in these complexes is difficult and the predictions are usually sensitive to several factors including the geometry or the level of calculation employed in the simulations. In this context, we report here a combined experimental and theoretical investigation of five octahedral MnIV complexes,

with S > 1/2, is the most widely used and usually best-suited to describe the magnetostructural properties of such systems.15 The ZFS tensor is defined by the D and E parameters, which represent its axial and rhombic contributions, respectively. Several experimental techniques have been developed to determine the ZFS parameters including indirect methods such as magnetometry15 and variable-temperature, variable-field magnetic circular dichroism16 or direct methods such as inelastic neutron scattering17,18 and frequency domain magnetic resonance spectroscopy.19,20 However, the most widely used and powerful technique to accurately define the ZFS parameters remains the electronic paramagnetic resonance (EPR) spectroscopy for a large range of ZFS. A precise determination of D generally necessitates high frequency/field limit conditions, i.e. when the quantum energy provided by the EPR spectrometer (hν, 0.3 cm−1/9.4 GHz and 1.2 cm−1/34 GHz at X- and Q-band frequencies, respectively) is much larger than the magnitude of D. Therefore, for systems with |D| > ∼0.2 cm−1, high-frequency and -field EPR (HFEPR) is required (from 3 cm−1/95 GHz up to 33 cm−1/1 THz).21−23 In the special case of MnIV (d3; S = 3/2), numerous X-band EPR studies have been reported, but only rarely D-values were determined as they are frequently too large for the X-band energy quantum.24−30 More recently, a combined X- and Qband EPR investigation,31 as well as a few HFEPR ones,32−35 have shown that the expected range of D values in MnIV is moderate, from 0.2 cm−1 up to 1.65 cm−1. However, unlike for MnIII and MnII,36−39 no systematic investigation of MnIV in complexes involving different types of coordination sphere (nature of the ligands, coordination number) has been reported so far, avoiding definition of magnetostructural correlation. In parallel, important theoretical efforts have been carried out to develop suitable methodologies to predict the ZFS parameters and to rationalize the experimental observations. For such investigations, both contributions to D, i.e. the spin− orbit coupling (SOC) and the electron−electron spin−spin interaction coupling (SSC), should be accurately calculated. In line with this approach, density functional theory (DFT) calculations have been applied to predict both sign and B

DOI: 10.1021/acs.inorgchem.5b02368 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry which display different coordination spheres [N6,52 N3O3,32 N2O4 in both trans (trans-N2O4) and cis configurations (cisN2O4)33 and O4S253], as shown in Chart 1. Well-characterized MnIV complexes being rare, systems for which structural and electronic data were available were chosen, and additional experiments on two other complexes have been carried out. The X-ray diffraction structures of these complexes have been previously reported, while the ZFS parameters have been determined by HFEPR for MnLN3O3 and MnLcis‑N2O4 and by Xband EPR for MnLN6. In addition, the magnetization principal axes of MnLcis‑N2O4 have been defined through a single-crystal HFEPR investigation.33 In the present work, we carried out extra HFEPR measurements on MnLtrans‑N2O4 and MnLO4S2, the latter displaying a record D-magnitude for MnIV of 2.29 cm−1. In parallel, the ZFS parameters were predicted based on two theoretical frameworks, DFT and LF-DFT, in order to define appropriate methodologies to calculate the ZFS for octahedral MnIV centers. Besides, these calculations allow us to define the orientation of the principal magnetization axes with respect to the molecular frame as well as to provide a deeper insight into the physical origin of the different contributions to D.

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DFT energy of all the Slater determinants arising from the dn configuration of the transition-metal ion in the environment of coordinating ligands using Kohn−Sham orbitals. This set of energies is then analyzed within a ligand-field model to obtain variationally the energy and multideterminant wave function of the ground and excited states. In doing so, both dynamical correlation (via the DFT exchangecorrelation energy) and nondynamical correlation (via CI) are considered. With this procedure we were able to calculate all customary molecular properties, aware that its validity decreases with increasing metal−ligand covalency. Details about the LF-DFT procedure can be found elsewhere.68 These calculations were carried out using the Amsterdam Density Functional (ADF) code69−71 employing the OPBE functional72−74 that had produced excellent results in many previous studies,50,68 in combination with all-electron triple-ζ quality basis set with polarization (TZP). The scalar relativistic effects were treated at the ZORA level, and the ZFS parameters were deduced using an effective Hamiltonian approach from the lowest eigenvalues and corresponding eigenvectors from LF-DFT multiplet calculations, in the basis of ±1/2 and ±3/2 MS wave functions.

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RESULTS AND DISCUSSION HFEPR Measurements. X- and Q-band EPR experiments (Figure S1) were carried out at liquid helium temperature on MnLtrans‑N2O4, displaying spectra with only two dominant transitions at very low field compared to g = 2, demonstrating that high frequency/field limit conditions were not met at these frequencies. Based on the absence of a signal at g = 2, the presence of MnII impurity can be excluded. HFEPR spectra were recorded at different frequencies (Figure 1), also at liquid

EXPERIMENTAL METHODS

Synthesis. The synthesis of MnLtrans‑N2O4 and MnLO4S2 followed the method previously reported.53,54 HFEPR Spectroscopy. HFEPR spectra were recorded in HLD in a transmission spectrometer using Virginia Diodes Inc. (VDI, Charlottesville, VA) sub-THz sources in conjunction with a 16-T cold-bore superconducting (SC) magnet. Some experiments were also conducted at NHMFL using similar VDI sources and a 15/17-T warm-bore SC magnet.55 In both cases an InSb bolometer (QMC, Cardiff, Wales) was used as a detector. The necessary modulation was obtained through modulating the magnetic field. The signal was converted from ac to dc by a lock-in amplifier (Stanford SR-830). The powder of MnLO4S2 was ground and pressed into a pellet with neicosane because a strong torquing effect was observed on neat powder. The electrostatic powder of MnLtrans‑N2O4 was immobilized in an n-eicosane mull. The HFEPR spectra were analyzed by simultaneously fitting the parameters of the standard spin Hamiltonian (eq 1) to the complete two-dimensional (field vs frequency) map of turning points, following the principles of tunable-frequency EPR.22 The sign of ZFS was obtained by simulating single-frequency spectra using software (program SPIN) available from A. Ozarowski.

⎛ 2 1 2⎞ 2 2 H = μB B̂· g · S ̂ + D⎜Sẑ − S ̂ ⎟ + E(Sx̂ − Sŷ ) ⎝ 3 ⎠

(1)

Computational Details. Since the predicted ZFS values are highly sensitive to the geometry of the complexes, the calculations reported here were performed on the experimentally determined X-ray structures. Two approaches rooted in very different physical foundations were used. The first one is based on the coupled perturbed SOC method (CP)56 as implemented in ORCA (version 3.0.3)57 and closely related to the work of Pederson and Khanna.58 In this case we used the BP8659−61 functional along with the ZORATZVP basis set for all the atoms. The BP86 functional was chosen with respect to much more expensive hybrid functionals as it was previously shown that BP86 is a reasonable choice for calculating ZFS in the case of several transition-metal ions, including MnII and MnIII complexes.37,38,62 Scalar relativistic effects were taken into account at the Zero-Order-Regular-Approximation (ZORA)63 level, while spin−orbit coupling was included using the coupled-perturbed method.64 The spin−spin contribution was calculated using a restricted spin-density obtained from singly occupied unrestricted natural orbitals.65 The second method is the ligand-field DFT approach by C. Daul et al.,66,67 based on a multideterminant description of the transition metal’s multiplet fine structure, that is able to tackle many difficult problems including orbital degeneracy.50 It works by evaluating the

Figure 1. Experimental powder HFEPR spectra of MnLtrans‑N2O4 recorded at about 60, 101, and 151 GHz as indicated on the plot and at 4.5−7 K. The spectra are approximately normalized to the amplitude of the strongest line.

helium temperature, in order to obtain interpretable spectra. Interestingly, a near zero-field transition was directly observed at 60 GHz that could be assigned to the energy gap between the two Kramers doublets of the quartet state (MS = ±1/2 and ±3/2), and which (for axial ZFS) corresponds to 2|D|, giving an estimate of the magnitude of |D| of about 1 cm−1. Consistently with this estimate, the EPR line located at 3.35 T at 151 GHz can be attributed to the |S, MS> = |3/2; − 3/2> → |3/2; − 1/2> transition with the B0 along the z-axis for a negative D. The 1.05 T field difference between this line and the g = 2 point (5.4 C

DOI: 10.1021/acs.inorgchem.5b02368 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry T), is expected to be equal to |D|, which yields D = −0.98 cm−1. The resonances at around 6.3 and 6.7 T at 151 GHz are perpendicular (B0||x and B0||y, respectively) turnings points of the same |3/2; − 3/2> → |3/2; − 1/2> transition, and their splitting is consistent with a moderate rhombicity factor E/D of the ZFS tensor. Using these estimates as seeds for computer fits, the accurate values of the ZFS parameters (D = −0.997(6) cm−1, E = −0.054(3) cm−1, E/D = 0.054) were obtained not from singlefrequency spectra but from a two-dimensional field/frequency map (Figure 2) and the confirmation of the negative sign of D from a comparison of experimental and calculated spectra at the highest frequencies (Figure 3).

Figure 3. Experimental (black trace) and simulated (colored traces) HFEPR spectra of MnLtrans‑N2O4 recorded at 151.2 GHz and 4.5 K. The following spin Hamiltonian parameters were used in the simulations: |D| = 0.98 cm−1, |E| = 0.056 cm−1, giso = 1.98 with D > 0 for the red trace and D < 0 for the blue trace. The spectra are approximately normalized to the amplitude of the two central, strongest resonances.

Figure 2. Field vs frequency map of resonances observed in MnLtrans‑N2O4 at 4.5−7 K. The squares are experimental HFEPR resonances, while the curves were simulated using the following bestfit spin Hamiltonian parameters: S = 3/2, D = −0.997(6) cm−1, E = −0.054(3) cm−1, gx = 1.994(4), gy = 1.988(4), gz = 1.954(13). Color caption: red for B0∥x, blue for B0∥y; black for B0∥z, and green for offaxis turning points. The dashed vertical bars represent the three frequencies at which spectra shown in Figure 1 were recorded.

Regarding the complex MnLO4S2, previous X-band EPR experiments found ZFS to be of moderate magnitude (D = +0.47 cm−1, E/D = 0.09).53 Since a D value of this magnitude is comparable to the quantum energy, which makes X-band EPR less than a perfect technique to measure ZFS, we carried out HFEPR experiments on the same complex at liquid helium temperatures at different frequencies (Figure 4). The first observation was that the polycrystalline sample undergoes strong torquing in magnetic field, similar to the phenomenon found in many MnIII complexes.75 The resulting quasi-single crystal spectra could be successfully interpreted (Figure S4) but only after the spin Hamiltonian parameters were obtained from an n-eicosane constrained sample. Second, at the onset we observed in MnLO4S2 that much higher frequencies than in MnLtrans‑N2O4 were required to record EPR spectra in high frequency/field limit conditions, which suggested significantly larger ZFS in the former. Consistently with this observation, a |D| value of about 2.38 cm−1 (in the case of an axial ZFS tensor) can be estimated based on the transition recorded near zero field at 143 GHz in Figure 4. Also, in contrast to MnLtrans‑N2O4, a transition at high field is observed

Figure 4. Experimental powder HFEPR spectra of MnLO4S2 recorded at three frequencies as indicated on the plot, and at 4−4.5 K.

(at 13.7 T at 246 GHz) that can be assigned to the |3/2; − 3/ 2> → |3/2; − 1/2> transition along the z-axis in the case of a positive D. This attribution is confirmed from the intensity dependence of this transition as a function of temperature (Figure S5). Its intensity drastically decreases from 4.5 to 15 K, and it cannot even be observed at higher temperatures. From the position of this transition, |D| can be estimated to be about 2.4 cm−1. Using the above estimates as seeds in computer fits, accurate ZFS parameters were determined from a twodimensional field/frequency map (Figure 5): D = +2.289(5) cm−1, E = +0.323(4) cm−1 (E/D = 0.141). Remarkably, this magnitude of D is the largest ever measured for a MnIV complex. The positive sign of D was confirmed by comparing D

DOI: 10.1021/acs.inorgchem.5b02368 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

low-frequency studies should thus be taken with caution, but the problem is of more general nature and concerns a larger number of high-spin (S > 1/2) Kramers (half-integer spin number) metal ions (non-Kramers ions are typically “EPRsilent” in the same conditions). In general, if the hypothesis regarding the relative intensity between D and the energy provided by the EPR spectrometer is incorrect, the analysis of the data can lead to a set of parameters, which well-simulates a low frequency EPR spectrum but which is erroneous. A double check with at least two frequencies (X- and Q-band) is therefore required for the analysis of such Kramers systems. Quantum Chemical Calculations. The ZFS parameters of the five complexes displaying in Chart 1 were calculated in two different theoretical frameworks, i.e. CP-DFT (based on the coupled-perturbed DFT approach) and LF-DFT (based on the ligand-field DFT approach). Axial D Parameter. Except in the case of MnLtrans‑N2O4, the experimental and calculated D values (Table 1) are in a Table 1. Experimental and Calculated ZFS Parameters for the MnIV Complexes Figure 5. Field vs frequency map of resonances observed in MnLO4S2 at 4−4.5 K. The squares are experimental HFEPR turning points, while the curves were simulated using the following best-fit spin Hamiltonian parameters: S = 3/2, D = +2.289(5) cm−1, E = +0.323(4) cm−1, gx = 1.987(4), gy = 1.978(5), gz = 1.992(3). Color caption: red for B0∥x, blue for B0∥y, black for B0∥z, and green for off-axis turning points. The dashed vertical bars represent the three frequencies at which spectra shown in Figure 4 were recorded.

method MnL

N3O3

MnLtrans‑N2O4

MnLcis‑N2O4

spectra simulated with both signs of D and an experimental one at 221 GHz (Figure 6). The current determination of the ZFS parameters of MnLO4S2 by HFEPR demonstrates that estimating these parameters in absence of high frequency/field limit is risky at best: D = +2.289(5) cm−1 by HFEPR vs D = +0.47 cm−1 by Xband EPR.53 Specifically, ZFS values for MnIV resulting from

MnLO4S2

MnLN6

a

32

HFEPR LF-DFT CP-DFT HFEPR LF-DFT CP-DFT HFEPR33 LF-DFT CP-DFT X-band EPR53 HFEPR LF-DFT CP-DFT X-band EPR52 LF-DFT CP-DFT

D (cm−1)

E (cm−1)

E/D

+0.245 +0.294 +0.163 −0.997 +0.569 −0.695 +1.650 +1.671 +1.341 +0.47 +2.289 +2.443 +1.377 1.335a +1.72 +1.19

+0.000 +0.091 +0.028 −0.054 +0.034 −0.117 +0.000 +0.111 +0.075 + 0.04 +0.323 +0.009 +0.177 0.360a +0.26 +0.12

0.00 0.30 0.17 0.054 0.061 0.168 0.000 0.067 0.056 0.09 0.141 0.004 0.128 0.225 0.15 0.10

Sign not determined.

reasonably good agreement, and the sign of D is also well predicted. This is remarkable since the prediction of the D sign is not straightforward because it becomes ambiguous when E/D approaches the rhombic limit (E/D ≈ 1/3) as in the case of MnLN6. The largest disagreement in the data occurs for MnLtrans‑N2O4 where LF-DFT predicts a positive D value that contrasts with both EPR data and CP-DFT (D < 0). Apart from this discrepancy, whose origin will be rationalized below, the numerical agreement is more than adequate for calculations to provide an insight on the origin of the magnetic anisotropy of these systems. Based on the quality of the D prediction with respect to both theoretical approaches, judged by comparing the experimental and calculated values (Figure 7), several conclusions can be drawn (the case of MnLtrans‑N2O4 is excluded from this discussion). (i) LF-DFT is more satisfactory (with a relative error ∼13%) than CP-DFT (with a relative error ∼30%). (ii) While LF-DFT steadily overestimates the value of D, the opposite trend is observed with CP-DFT with a systematic underestimation of D. The slight overestimation in LF-DFT could be due to a systematic underestimation of the electronic transitions, which is a well-known problem of DFT-based

Figure 6. Experimental (black trace) and simulated (colored traces) HFEPR spectra of MnLO4S2 at 220.8 GHz and 4.5 K. The following spin Hamiltonian parameters were used in the simulations: |D| = 2.29 cm−1, |E| = 0.33 cm−1, giso = 1.99 with the case of D > 0 represented by the red trace and D < 0−blue trace. The spectra are approximately normalized to the amplitude of the strongest resonance. E

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as possible to the first-neighboring atoms to match the MnL6 pseudo-octahedron. When possible the z-axis was chosen as the “special” direction. For example in MnLtrans‑N2O4, the z-axis lies close to the N−Mn−N axis (Figure 8). For the MnLO4S2/ MnLcis‑N2O4 complexes that display a cis- O4S2/N2 octahedral geometry, the reference structure has all cis angles of 90° and metal−ligand bond lengths corresponding to the particular complex. The xy plane contains the two O−Mn−S/N axes with the x- and y-axis along these equatorial bonds, and the z-axis is oriented along the O−Mn−O axis. The entire complex ion is then translated and rotated in such a way that the best superposition of its MnO4S2/N2 fragment and the reference structure is achieved. The superposition is obtained by making the least-squares deviation of the distances between the equivalent nuclei of the reference structure and the structure that is being oriented as small as possible. The main axes of the ZFS tensor with respect to the frame of the molecule are displayed in Figure 8 for each complex. Experimental data are available only for MnLcis‑N2O4, for which single-crystal EPR experiments have been reported.33 In this system it has been shown that the experimental principal anisotropy axis lies within the N−Mn−N plane, in perfect agreement with our calculations that show that it runs through the dividing line of the N−Mn−N angle, validating our theoretical approach. Our calculations evidence that MnLtrans‑N2O4 displays an easy magnetic axis corresponding to D < 0, while the other complexes exhibit an easy-magnetic plane related to D > 0. Looking at Figure 8, we see that the magnetic axes run relatively close to special directions of our reference frame, i.e. they are either near one of Mn-L bonds (e.g., axial direction in MnLtrans‑N2O4), bisect them (e.g., equatorial directions in MnLtrans‑N2O4), or are in the vicinity of one of the main symmetry directions of the complex (e.g., the pseudo C3 axis in MnLN3O3 or the pseudo C2 axis in MnLO4S2/ MnLcis‑N2O4). Contributions to D. As it has been well established in the literature, the main factor driving the magnetic anisotropy in such systems is the spin−orbit coupling (SOC). We can corroborate this trend by decomposing D into its SOC (DSOC) and SSC (DSSC) terms using CP-DFT (Table 2). As expected, DSOC dominates over DSSC corresponding to, approximately, 75−90% of the total D-values. This is further substantiated by the LF-DFT results, which rely exclusively on the SOC contribution to predict the ZFS. Consequently, we will focus solely on this mechanism to discuss the origin of the magnetic anisotropy in these systems. Both LF-DFT and CP-DFT frameworks provide mechanisms to further decompose the SOC terms in order to gain chemical insight. The CP-DFT method, when expressed in the Pedersen and Khanna spin-unrestricted formalism,58 can be divided according to the single-electron excitations from singly occupied α and β molecular orbitals into unoccupied α and β molecular orbitals (α and β orbitals for spin-up and spin-down electron, respectively):76

Figure 7. Comparison of LF-DFT (blue squares) and CP-DFT (red circles) calculated D values with experimental data. A black line shows as an eye-guide representing the exact match with experimental results. The point corresponding to the LF-DFT calculated D value of MnLtrans‑N2O4 is highlighted with a blue empty circle.

methods with LDA or GGA functionals. (iii) LF-DFT does not include spin−spin contributions, which would lead to a larger overestimation of D in all cases (see Table 2 and below the discussion on the SSC contribution). Table 2. Decomposition of the D Parameter Obtained through CP-DFT into Its Spin-Orbit-Coupling (SOC) and Spin−Spin (SSC) Contributions N3O3

MnL MnLtrans‑N2O4 MnLcis‑N2O4 MnLO4S2 MnLN6

DSOC (cm−1)

DSSC (cm−1)

D (cm−1)

+0.119 −0.596 +1.085 +1.114 +0.941

+0.044 −0.099 +0.256 +0.263 +0.245

+0.163 −0.695 +1.341 +1.377 +1.185

E/D Ratio. The E/D ratio is related to geometric distortion around the metal center and ranges from 0 for a perfectly axial system to 0.33 for a highly distorted one. Interestingly, the experimental E/D values of the test set range between these two limits. It has been generally reported that DFT approaches present considerable problems in the prediction of E/ D.38,39,41,76,77 In the present case of MnIV both CP-DFT and LF-DFT display a significant deviation with respect to the experimental values. This can be rationalized taking into account that E is usually a very small quantity ( 0 = Cζ *2⎜ P ⎝ P(P + δt )(P − δt ) ⎠

(4)

IV

This comes to show that many Mn complexes naturally tend toward having an easy magnetization plane (D > 0) when d(t2g)-d(t2g) excitations dominate the magnetic anisotropy, as consistent with the LF-DFT calculations. Regarding MnLN6, even if the d-d excitations represent the dominant contribution to D, it displays the smallest Δ value (by a margin of at least 20%) consistently with the presence of weak field ligands, as well as the largest relative α → α contribution with respect to α → β. Under such conditions, eqs 3 and 4 are not applicable. In fact, inclusion of t2g* → eg* excitations introduces several terms, among which a linear term with tetragonality into eq 3 that would compete with eq 2 and could lead to negative D with the right sign of δt and strong enough. This is probably the reason why CrIII impurities in Al2O3 display a negative D value.78 However, this is not enough to explain why D < 0 in MnLtrans‑N2O4 as clearly captured by CPDFT but not by LF-DFT that includes these excitations. A tentative explanation is that there are two low-lying empty ligand orbitals (approximately 0.5 eV below the eg* levels) that H

DOI: 10.1021/acs.inorgchem.5b02368 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

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DSOC. Consistently, the LF-DFT shows that the doublet excited states related to d-d transitions mainly contribute to D. The electronic structure of the investigated complexes also reveals that many MnIV complexes naturally tend toward having an easy magnetization plane (D > 0) when d(t2g)-d(t2g) excitations dominate the magnetic anisotropy. This is consistent with our experimental data, for which only one compound displays a negative D value, MnLtrans‑N2O4. In this particular case, the negative D value is rationalized by the presence of several lowlying empty ligand orbitals that contribute to D. Our investigation demonstrates that both CP-DFT and LFDFT are acceptable frameworks to predict D. The number of well-characterized MnIV complexes being limited, a systematic theoretical study using simplified theoretical models will be required to go further with the objective of defining clear magnetostructural correlations, which can be used for the design of new MnIV complexes with targeted electronic properties.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.5b02368. Additional EPR spectra and computational details (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by Deutsche Forschungsgemeinschaft (DFG, Germany) and Serbian Ministry of Science (Grant no. 172035). We acknowledge the support of the HLD at HZDR, member of the European Magnetic Field Laboratory (EMFL). JK thanks the HLD for financial support of his sabbatical stay in Dresden. Part of this work was conducted at the NHMFL, which is funded by the NSF through a Cooperative Agreement DMR 1157490, the State of Florida and the US Department of Energy. We are grateful to Dr. Andrew Ozarowski, NHMFL, for the EPR simulation and fitting software SPIN. We thank Dr. Joshua Telser, Roosevelt University for many critical remarks of importance. CD gratefully acknowledges the French National Agency for Research n° ANR-09-JCJC-0087, Labex arcane (ANR-11-LABX-003) and IR-RPE CNRS 3443. PGF was financially supported by the Ramon and Cajal fellowship RYC2013-12515. The authors also acknowledge COST Action CM1305 ECOSTBio (Explicit Control Over Spin-States in Technology and Biochemistry) including a STSM grant (COST-STSM-CM1305-25068).

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DOI: 10.1021/acs.inorgchem.5b02368 Inorg. Chem. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.inorgchem.5b02368 Inorg. Chem. XXXX, XXX, XXX−XXX