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Crystal-Field Theory Validity Through Local (and Bulk) Compressibilities in CoF2 and KCoF3 J. Antonio Barreda-Argüeso,† Fernando Aguado,† Jesús González,† Rafael Valiente,‡ Lucie Nataf,§ Marta N. Sanz-Ortiz,†,∥ and Fernando Rodríguez*,† †

MALTA TEAM, DCITIMAC, Facultad de Ciencias, Universidad de Cantabria, Avenida de Los Castros s/n, 39005, Santander, Spain MALTA TEAM, Departamento Física Aplicada, Facultad de Ciencias, Universidad de Cantabria − IDIVAL, 39005, Santander, Spain § Synchrotron SOLEIL, L’Orme des Merisiers, St Aubin BP48, 91192 Gif-sur-Yvette cedex, France ‡

S Supporting Information *

ABSTRACT: Crystal field theory (CFT) predicts that crystal field acting on an transition-metal (TM) ion complex of cubic symmetry varies as R−5, where R is the TM-ligand distance. Yet simple and old-fashioned, CFT is used extensively since it provides excellent results in most TM ion-bearing systems, although no direct and thorough validation has been provided so far. Here we investigate the evolution of the electronic and crystal structures of two archetypal Co2+ compounds by optical absorption and X-ray diffraction under high pressure. Both the electronic excited states and crystal-field splitting, Δ = 10Dq, between 3d(eg + t2g) orbitals of Co2+ as a function of volume, V, and Co−F bond length, R, in 6-fold octahedral (oct) and 8-fold hexahedral (cub) coordination in compressed CoF2 have been analyzed. We demonstrated that Δ scales with R in both coordinations as R−n, with n close to 5 in agreement with CFT predictions. The pressure-induced rutile to fluorite structural phase transition at 15 GPa in CoF2 is associated with an increase of R due to the 6 → 8 coordination change. The experimental Δ(oct)/ Δ(cub) = −1.10 for the same R-values is close to −9/8, in agreement with CFT. A similar R-dependence is observed in KCoF3 in which the CoF6 Oh coordination is maintained in the 0− 80 GPa pressure range.

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R− (or V−) dependence of Δ as R−5 (or V−5/3) as given by crystal-field theory (CFT).10,16−21 The situation is even more challenging if different TM coordination geometries are involved, i.e., tetrahedral, octahedral, hexahedral, or dodecahedral coordinations.19 Our study solves out this problem as it provides precise Δ(R) data in two cobalt fluoride archetypes, enabling verification of CFT predictions in two different Co2+ coordinations. Experimental studies on Δ(R) have been usually performed at ambient pressure in TM series of compounds with different crystal structure.12−14,20 However, rest-of-lattice and compositional effects can significantly mask the actual bond-length dependence of the TM electronic structure.15,22−25 The application of high pressure continuously modifies the bond-length by tuning the electronic properties of TM and helping us to unravel R-dependences of Δ by combining visible absorption and X-ray diffraction/absorption measurements. It is important to point out that pioneering works dealt with that problem in a lot of TM oxides and halides.17 However, the correlations between Δ and V were performed mainly on Al2O3

INTRODUCTION The crystal-field splitting of d-orbitals is measured as the energy difference between eg and t2g energy levels. It is usually named as Δ, or 10Dq, in octahedral coordinated transition metal (TM) oxides and halides. Its volume, V, and TM-ligand bond length, R, dependences have attracted considerably a broad audience of multidisciplinary scientists. Δ plays a key role in relevant physical phenomena like color, magnetism, or conductivity. Examples of this behavior are spin crossover phenomena involving either excited states1,2 or the ground state,3−6 which affect the photoluminescence properties or the TM-ion magnetic moment, respectively, or metallization processes in TM oxides.7−9 The Δ(R) value results crucial to predict critical phenomena associated with the spin state of iron in magnesiowüstite (Mg,Fe)O, and other Fe2+/Fe3+ containing silicates, under the pressure and temperature conditions of the Earth’s interior,10,11 pressure-induced Mott-type insulator− metal transition in TM-oxides,7−9 or high-spin to low-spin transitions induced by pressure or temperature.3,4 In addition, Δ can be an efficient probe to determine impurity-ligand distance in diluted systems through optical spectroscopy, once the relation between Δ and R is established.12−15 Due to the lack of experimental studies, such models frequently assume a © XXXX American Chemical Society

Received: June 17, 2016 Revised: August 1, 2016

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DOI: 10.1021/acs.jpcc.6b06132 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Figure 1. (a) Room-temperature pressure evolution of the KCoF3 diffraction patterns in the 0−60 GPa range. (b) Variation of the volume per Co2+ with pressure, V(P). Continuous lines correspond to fittings to the Murnagahn equation of state of each phase. Drawings illustrate the CoF6 octahedron arrangement in the perovskite cubic (left) and orthorhombic (right) phases.

and MgO doped with TM ions (Ti, Cr, V) since the equation of state for such host materials was known at that time.17,26 The question is whether the TM-ligand bond length and its pressure dependence are the same as the host, e.g., the host (Al−O) and impurity (Cr−O) in ruby (Al2O3: Cr3+).21,25,27,28 More recently, the combination of high-pressure X-ray diffraction and optical spectroscopy provided such correlations in pure TM-ion compounds. High-pressure studies on NiO (ref 8) or BiFeO3 (ref 29) showed that Δ(V) behaved close to V−5/3 and thus Δ(R) as R−5 given that at least R(P) scales as V1/3(P) in the former compound. This result, which agrees with CFT predictions, is quite surprising since this simple theory does not take explicitly into account the TM-ligand bonding.18,19,30 Although efforts to justify the R−5 law have been carried out on the basis of ligand-field theory and through LCAO-type calculations,31,32 there is a lack of experimental studies aiming to definitively validate CFT. It is worth noting that although ab initio calculations are well suited to predict ground state properties (density functional theory),22−24 they can have serious limitations to predict electronic properties related to excited states. Due to this, accurate experimental studies dealing with the R and V dependences of the electronic energies constitute a benchmark test to validate ab initio methods aiming to predict excited state properties in TM ion systems, and eventually validate CFT predictions. Herein, we present results that addresses three CFT predictions on Δ(R) for 1) different TM coordinations in the same crystal, e.g,. 6-fold and 8-fold cubic coordinations in CoF2; (2) the same coordination in different crystals, e.g., 6fold in CoF2 and KCoF3; and (3) a coordination change, e.g. Δ(6-fold)/Δ(8-fold) for the same R. CFT provides analytical expressions for Δ as a function of R in tetrahedral, cubic, and octahedral coordinations:18,19 Δtet = 10Dq(tet) = −

20 2 ⟨r 4⟩ Ze 5 27 R

Δcub = 10Dq(cub) = −

Δoct = 10Dq(oct) = +

40 2 ⟨r 4⟩ Ze 5 27 R

45 2 ⟨r 4⟩ Ze 5 27 R

(2)

(3)

where Z is the ligand charge, ⟨r ⟩ is the mean value of 3delectron position to the fourth-power, and R is the TM-ligand distance (see Figure S1 in the Supporting Information). These equations establish that besides ⟨r4⟩, Δ depends on R as R−5. Interestingly, relative CF splittings between different coordinations can be easily obtained from eqs (1−3) and constitute a useful complementary R- and ⟨r4⟩-independent parameter to test the reliability of CFT, provided that we can measure Δ in different coordinations for the same R value. According to CFT, the relative CF splittings for the same metal-ligand distance are 4

Δoct /Δtet = − 9/4,

Δcub /Δtet = 2,

Δoct /Δcub = − 9/8

(4)

Here we combine optical absorption and X-ray diffraction measurements on CoF2 and KCoF3 under high-pressure conditions in the 0−80 GPa pressure range. Recent structural studies on CoF2 under pressure revealed that this compound undergoes a structural transformation associated with a change of Co2+ coordination from 6-fold (rutile type) to 8-fold (fluorite type) at 15 GPa.33 This transformation leads to an inversion of the eg and t2g 3d orbitals yielding change of the Co2+ ground state from t2g5eg2(4T1) electronic configuration to eg4t2g3(4A2), and thus allowing us to explore the Co2+ electronic structure, and hence Δ, as a function of R in 6-fold and 8-fold coordinations. Furthermore, we can compare these results with those obtained for 6-fold coordination in KCoF3, which perovskite structure is stable up to 24 GPa. At this pressure it undergoes a Cubic Pm3m to Orthorhombic Pnma secondorder phase transition (Figure 1) associated with rotations of the CoF6 octahedra. Their octahedral symmetry remains stable up to 80 GPa. The application of pressure up to 80 GPa in KCoF3 enables us to unravel the R-dependence of Δ in the widest R range ever before explored in octahedral TM ions ( R

(1)

R0

B

DOI: 10.1021/acs.jpcc.6b06132 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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V V0

high-pressure experiments were performed in parallel on the same CoF2 and KCoF3 single crystals employed in the optical absorption measurements.

= 0.70). Therefore, it constitutes an archetype to

validate whether the R−5-dependence of Δ still holds for wider R ranges. It must be noted that although optical absorption studies were performed in NiO up to 240 GPa,34 Δ(R) could only be measured up to 90 GPa, with a relative change of V (and Ni−O distance) of 0.78 (and 0.92),35 which is significantly lower than those attained in KCoF3 at 80 GPa.

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RESULTS AND DISCUSION Figure 1a shows the ADXRD pressure dependence of KCoF3 in the 0−60 pressure GPa range. According to ADXRD patterns, the crystal structure corresponds to the cubic Pm3m perovskite phase in the 0−24 GPa range, whereas it transforms to an Orthorhombic Pnma phase above this pressure up to 80 GPa. The phase transition is associated with rotations of the CoF6 octahedra (Figure 1b). The variation of the volume per Co2+ with pressure, V(P), for each phase can be described by a Murnaghan equations of state. The fitting parameters are V0 = 67.37 ± 0.06 Å3; a bulk modulus, K = 114 ± 3 GPa; and a bulk modulus pressure derivative, K′ = 2.2 ± 0.2 in the 0−24 GPa range (cubic phase), and V0 = 63 ± 2 Å3; K = 130 ± 30 GPa; K′ = 6 (fixed) in the 24−80 GPa range (orthorhombic phase). Note that in the cubic phase the Co−F distance is directly obtained from the cubic lattice parameter by R = a/2 (regular perovskite Figure 1b). In the orthorhombic phase, the average Co−F distance can be obtained with an accuracy better than 5% from V(P) by the expression R = 1/2 V1/3. Figure 2 shows the visible absorption spectra of CoF2 and KCoF3 at ambient pressure, and of CoF2 at 22 GPa. The

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EXPERIMENTAL SECTION Crystal Structure: X-ray Diffraction. Single crystals of CoF2 and KCoF3 were grown by the Bridgman method according to methods described elsewhere.33 At ambient conditions CoF2 crystallizes in the tetragonal space group P42/mnm (rutile phase)33,36 and KCoF3 in the cubic Pm3̅m (perovskite phase).37 The evolution of the crystal structure of KCoF3 with pressure was studied by angle dispersive X-ray diffraction (ADXRD) on powdered samples using the 12.2.2 beamline at the Advance Light Source (ALS). Pressure was applied by means of a symmetric piston-cylinder Diamond Anvil Cell (DAC). High pressure experiments on polycrystalline CoF2 were performed in the Materials Science and Powder Diffraction beamline (BL04) at ALBA synchrotron using a Boehler-Almax DAC. In all experiments, samples were loaded with several ruby microspheres (typically 10 μm diameter) as pressure gauge,38 using methanol−ethanol−water and silicone oil as pressure transmitting media. Optical Absorption and Raman Spectroscopy. Optical absorption and Raman experiments were performed on singlecrystal plates of CoF2 (90 × 80 × 14 μm3) and KCoF3 (100 × 80 × 20 μm3) for high-pressure experiments. The optical spectroscopy experiments were carried out in membrane and Boehler-Almax DACs. 200-μm-thick Inconel gaskets were preindented to 40 μm. 200-μm-diameter holes were drilled with a BETSA motorized electrical discharge machine. The DAC was loaded with a single-crystal plate of CoF2 or KCoF3 and ruby microspheres as pressure probes38 using silicon oil as pressure-transmitting medium. Optical absorption under high-pressure conditions was performed on a prototype fiber-optics microscope equipped with two 25× reflecting objectives mounted on two independent xyz translation stages for the microfocus beam and the collector objective, and a third independent xyz translation stage for DAC micropositioning. Optical absorption data and images were obtained simultaneously with the same device.39 Spectra in the UV−vis and NIR were recorded with an Ocean Optics USB 2000 and a NIRQUEST 512 monochromators using Si- and InGaAs-CCD detectors, respectively. Unpolarized micro-Raman scattering measurements were performed with a triple monochromator Horiba-Jobin-Yvon T64000 spectrometer in subtractive mode and backscattering configuration, equipped with a Horiba Symphony liquidnitrogen-cooled CCD detector. The 514.5 and 647 nm lines of a Coherent Innova 70 Ar+-Kr+ laser were focused on the sample with a 20× objective and the laser power was kept below 4 mW in order to avoid heating effects. The laser spot was 20 μm in diameter and the spectral resolution was better than 1 cm−1. The Raman technique was used complementary to X-ray diffraction to check the sample structure through the characteristic first-order modes in CoF2 (ref 33) and the absence of first-order modes in KCoF3 (ref 37) as well as to determine structural phase-transition pressures. The Raman

Figure 2. (a) Optical absorption spectra of CoF2 and KCoF3 at ambient pressure and 290 K and low temperature (13 and 18 K, respectively). Spectra are normalized to their absorption coefficient. Peak energies are compared with those predicted by the Tanabe− Sugano diagram for octahedral Co2+ (3d7): Racah B and crystal-field Δ parameters obtained by fitting are indicated (C/B = 4.6). (b) Room temperature optical absorption spectrum of CoF2 at 22 GPa in the fluorite phase (Co2+ cubic coordination).33 Peak energies are compared with the calculated ones in the Tanabe−Sugano diagram for Co2+ 3d3-like hole structure (see text for explanation).

spectra at ambient pressure are very similar and consist of three main bands corresponding to d−d transitions of octahedral Co2+: 4T1(F) → 4T2(F), 4A2(F), and 4T1(P). These transitions are located at 0.90, 1.72, and 2.35 eV, respectively, in CoF2; and 0.89, 1.74, and 2.35 eV in KCoF3. In terms of the TanabeSugano diagram for d7 ions,40 it corresponds to Δ = 0.96 eV (CoF2) and 0.95 eV (KCoF3) and Racah parameter of B = 0.110 eV and Δ/B = 9 (Figure 2a).41 The similarity between both spectra reinforces the relevance of the CoF6 octahedron to account for the Co2+ electronic structure beyond other atomic C

DOI: 10.1021/acs.jpcc.6b06132 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C shell contributions to the crystal-field splitting, the influence of which seems to be much weaker than the first F− shell, despite their distinct crystal structure: rutile (CoF2) and perovskite (KCoF3). The slightly larger Δ value for CoF2 than for KCoF3 contrasts with the shorter Co−F distance in KCoF3: R = 2.042 Å (average of 4 × 2.055 and 2 × 2.015 Å) in CoF2,38 and R = 2.035 Å (a = 4.0694 Å) in KCoF3.39 As indicated later on, this effect must be ascribed to crystal-field contributions of the restof-the-lattice beyond CoF6, which is estimated to be less than 4% of Δ. The evolution of the absorption spectra with pressure is quite different for the two compounds (Figure 3). KCoF3 displays

Figure 4. Variations of the Co2+ crystal-field splitting energy between eg and t2g d-orbitals with pressure in CoF2 (a) and KCoF3 (b). The coordination of Co2+ and the Δ(P) pressure shift are indicated for each crystal phase. Anomalies in Δ(P) observed at 6, 15, and 44 GPa in CoF2, and at 24 GPa in KCoF3, correspond to structural phases transitions P42/mnm (rutile) ↔ Pnma ↔ Fm3m (fluorite) ↔ Pnma (cotunnite) in CoF2,33 and Pm3m ↔ Pnma (perovskite) in KCoF3 (Figure 1), respectively. Note the different Δ scales in panels a and b.

structural phase transition sequence: P42/mmm (rutile) ↔ Pnma ↔ Fm3m (fluorite) ↔ Pnma (cotunnite), respectively.33 The Co2+ coordination changes from CoF6 (P42/mmm and Pnma) to CoF8 (Fm3m) and CoF11 (Pnma), giving rise to important variations of Δ(P) (Figure 4). Besides discontinuities in the slope of Δ(P) at 8 and 44 GPa, pressure induces a regular increase of Δ from 0.96 to 1.07 eV in the 0−8 GPa range, being almost constant between 8 and 15 GPa (CoF6). At 15 GPa, Δ sharply falls down −0.27 eV with the 6 to 8 coordination change. Between 15 and 44 GPa, Δ(P) increases linearly at a rate of 9.0 meV/GPa (CoF8) and above 44 GPa its slope decreases to 4.4 meV/GPa (CoF11). The estimation of R(P) for the two compounds from X-ray diffraction and X-ray absorption data33 allows us to get Δ(R) from the corresponding Δ(P) as shown in Figure 5. The regular increase of Δ(R) in CoF6 and CoF8 with decreasing R is noteworthy. It means that the anomalies in Δ(P) observed in octahedral Co2+ in both CoF2 and KCoF3 (Figure 4) are concurrent with similar anomalies in R(P), not exhibited by V(P), thus highlighting the suitability of R to describe variations of Δ with pressure. Furthermore, Δ(R) obeys a potential law behavior as R−n with n close to 5 in both compounds. In particular, we get an exponent n = 5.1 ± 0.3 in KCoF3 in an R range with a 12% variation, whereas in CoF2 the exponents obtained are n = 5.0 ± 0.1 (rutile phase) and n = 6.0 ± 0.2 (fluorite phase). The reliability of CFT to account for the Rdependence of Δ is also confirmed through the experimental relative value of Δ obtained for CoF6 and CoF8 at the same Co−F distance, e.g., R = 2.045 Å, as Δ(oct)/Δ(cub) = −1.10, very close to the CFT predicted value of −9/8 (Figure 5 and eq 4). It must be noted that Δ(R) varies similarly in KCoF3 and CoF2 (rutile phase) although the absolute value of Δ(R) is slightly different in each crystal, i.e., Δ = 0.92 and 0.95 eV, respectively, at R = 2.050 Å. It means that Δ(R) in CoF2 is about 4% higher than in KCoF3 in the explored R range. This difference must be associated with rest-of-the-lattice effects beyond the main contribution due to CoF6. The contribution to Δ(R) from the second and third cation shells is significantly higher in CoF2 mainly due to the stronger contribution from neighboring Co2+ point charges (Z = +2) than in KCoF3 due to K+ (Z = +1; first shell) and Co2+ (Z = +2; second shell), with its total contribution being less than 4% for both crystals. This

Figure 3. Room-temperature pressure dependence of the optical absorption spectra of CoF2 (a) and KCoF3 (b). Spectra of CoF2 are arranged according to its crystal structure: rutile (blue), fluorite (red), and cotunnite (green) in order of increasing pressure. Spectra of KCoF3 correspond to the cubic (0 and 11 GPa) and orthorhombic (25 and 62 GPa) perovskite phases. The four images were taken with the crystals inside the DAC at different pressures. Ruby microspheres were used for pressure calibration.

the characteristic band structure of an octahedral Co2+ in the whole pressure range, whereas CoF2 exhibits two different band structures with pressure: one characteristic of CoF6 (3d7 electron structure) in the 0−15 GPa pressure range and the other one associated with CoF8 coordination (3d3 hole structure) above 15 GPa (Figure 2b), in accordance with the phase-transition sequence induced by pressure.33 The 6 to 8 coordination change reverses the sign and magnitude of the Co2+ d-orbital splitting yielding ground state configurations t2g5eg2 for P < 15 GPa and eg4t2g3 for P > 15 GPa. The excited state energies involved in the absorption spectrum in the two phases can thus be described by d7 and d3 configurations, respectively (Figure 2). Detailed information on the pressure dependence of the peak energies can be seen in Figures S2−S5 in the Supporting Information. The experimental Δ(P) data of KCoF3 and CoF2 show several anomalies at the phase-transition pressures (Figure 4). In KCoF3 we observe an anomaly associated with a change of slope at 24 GPa that is related to the Pm3m ↔ Pnma secondorder phase transition (Figure 1). In CoF2, Δ(P) shows three anomalies at 8, 15, and 44 GPa, which are also related to the D

DOI: 10.1021/acs.jpcc.6b06132 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Figure 5. (a) Co−F bond length, R, dependence of the crystal-field splitting energy, Δ(R), in CoF2 (top) and KCoF3 (bottom). Δ(R) was derived from Δ(P) through the corresponding EOS and XRD data (ref 33 and Figure 1). The absence of discontinuities in Δ(R) in both crystals is noteworthy. Lines correspond to the fit of data to a power law. The corresponding fitting parameters are R0 = 2.035 ± 0.002 Å, Δ0 = 0.96 ± 0.02 eV; n = 5.1 ± 0.3 for KCoF3, and R0 = 2.045 ± 0.003 Å, Δ0 = 0.96 ± 0.01 eV; n = 5.0 ± 0.1 (rutile phase), and R0 = 2.091 ± 0.003 Å, Δ0 = 0.77 ± 0.01 eV; n = 6.0 ± 0.2 (fluorite phase) in CoF2. The relative crystal-field splitting at R = 2.045 Å is Δ(rutile) = −1.10. (b) Variation of Δ(R) for KCoF3 Δ(fluorite)

and CoF2 in logarithmic scale. The fits of Δ(R) to the nth-power law correspond to straight lines with slopes close to 5 within experimental uncertainty. Note that Δ(R) for octahedral Co2+ in CoF2 is 5% larger than Δ(R) in KCoF3.

effect accounts for the slightly different Δ(R) values measured in CoF2 and KCoF3 (Figure 5).

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CONCLUSIONS Here we demonstrate that the CF splitting Δ(eg−t2g) in octahedral Co2+ increases with pressure, Δ(P), showing anomalies at the structural phase transition pressures in CoF2 and KCoF3. However, no anomaly is observed, and Δ shows a regular variation by scaling Δ with the Co−F distance, R. In both compounds, Δ(R) behaves as (R0/R)n with n close to CFT predictions, n = 5. In KCoF3 this behavior is obeyed in the widest R range explored ever, from 2.045 to 1.833 Å, yielding variations of Δ from 0.96 to 1.67 eV. In CoF2 the sharp decrease of Δ from 1.03 to 0.76 (−26%) at 15 GPa is due to the increase of R from 2.00 to 2.09 Å along with the 6 → 8 coordination change. Δ(R) in hexahedral Co2+ follows a similar R-dependence as R−6, close to the CFT prediction. However, this behavior cannot be compared with other compounds since no data on Δ(R) in hexahedral TM ions have been reported so far. This study provides suitable experimental data to test ab initio methods aiming to calculate electronic structure (excited states) in TM ions, and also provides a full consistency for semiempirical methods based on R−5 (or V−5/3) dependences of Δ as predicted by CFT.

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tronic structure derived from the absorption spectra of CoF2 and KCoF3 as a function of pressure (Figures S2− S6) (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; Tel.: +34 942 201514. Present Address ∥

M.S.: Bionanoplasmonic Laboratory, CIC biomaGUNE, 2009 Donostia-San Sebastián, Spain. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from Projects MAT2015-69508-P (MINECO/FEDER) and MAT2015-71070-REDC (MALTA TEAM/ MINECO), and a Technical Grant (ref. No. PTA2011-5461-I) is acknowledged. X-ray diffraction experiments under pressure in KCoF3 were performed in the 12.2.2 beamline at the Advance Light Source (ALS), and in the Materials Science and Powder Diffraction beamline (BL04) at ALBA for CoF2.

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REFERENCES

(1) Hernández, I.; Rodríguez, F.; Tressaud, A. Optical Properties of the (CrF6)3− Complex in A2BMF6:Cr3+ Elpasolite Crystals: Variation with M−F Bond Distance and Hydrostatic Pressure. Inorg. Chem. 2008, 47, 10288−10298. (2) Sanz-Ortiz, M. N.; Rodíguez, F.; Hernández, I.; Valiente, R.; Kück, S. Origin of the 2E↔4T2 Fano Resonance in Cr3+-Doped LiCaAlF6: Pressure-Induced Excited-State Crossover. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81, 045114.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b06132. Predictions of crystal-field theory for different transitionmetal coordination geometries (Figure S1), and elecE

DOI: 10.1021/acs.jpcc.6b06132 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.jpcc.6b06132 J. Phys. Chem. C XXXX, XXX, XXX−XXX