HFEPR and Computational Studies on the Electronic Structure of a

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HFEPR and Computational Studies on the Electronic Structure of a High-Spin Oxidoiron(IV) Complex in Solution Lukas Bucinsky,† Gregory T. Rohde,‡ Lawrence Que, Jr.,*,‡ Andrew Ozarowski,§ J. Krzystek,§ Martin Breza,† and Joshua Telser*,⊥ †

Institute of Physical Chemistry and Chemical Physics, Faculty of Chemical and Food Technology, Slovak University of Technology, Radlinského 9, SK-81237 Bratislava, Slovakia ‡ Department of Chemistry and Center for Metals in Biocatalysis, University of Minnesota, Minneapolis, Minnesota 55455, United States § National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310, United States ⊥ Department of Biological, Chemical and Physical Sciences, Roosevelt University, Chicago, Illinois 60605, United States S Supporting Information *

ABSTRACT: Nonheme iron enzymes perform diverse and important functions in biochemistry. The active form of these enzymes comprises the ferryl, oxidoiron(IV), [FeO]2+ unit. In enzymes, this unit is in the high-spin, quintet, S = 2, ground state, while many synthetic model compounds exist in the spin triplet, S = 1, ground state. Recently, however, Que and coworkers reported an oxidoiron(IV) complex with a quintet ground state, [FeO(TMG3tren)](OTf)2, where TMG3tren = 1,1,1-tris{2-[N2-(1,1,3,3-tetramethylguanidino)]ethyl}amine and OTf = CF3SO3−. The trigonal geometry imposed by this ligand, as opposed to the tetragonal geometry of earlier model complexes, favors the high-spin ground state. Although [FeO(TMG3tren)]2+ has been earlier probed by magnetic circular dichroism (MCD) and Mössbauer spectroscopies, the technique of high-frequency and -field electron paramagnetic resonance (HFEPR) is superior for describing the electronic structure of the iron(IV) center because of its ability to establish directly the spin-Hamiltonian parameters of high-spin metal centers with high precision. Herein we describe HFEPR studies on [FeO(TMG3tren)](OTf)2 generated in situ and confirm the S = 2 ground state with the following parameters: D = +4.940(5) cm−1, E = 0.000(5), B40 = −14(1) × 10−4 cm−1, g⊥ = 2.006(2), and g∥ = 2.03(2). Extraction of a fourth-order spin-Hamiltonian parameter is unusual for HFEPR and impossible by other techniques. These experimental results are combined with state-of-the-art computational studies along with previous structural and spectroscopic results to provide a complete picture of the electronic structure of this biomimetic complex. Specifically, the calculations reproduce well the spin-Hamiltonian parameters of the complex, provide a satisfying geometrical picture of the S = 2 oxidoiron(IV) moiety, and demonstrate that the TMG3tren is an “innocent” ligand.

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in energy than the paramagnetic states.17 The S = 2 state is of the greatest interest because it is that observed for the reactive ferryl intermediate in nonheme iron enzymes.1,3−9 That the enzymes exhibit spin quintet, rather than triplet, ground states is not merely a spectroscopic curiosity. The observed quintet spin state may be a consequence of the weak ligand field exerted by the ligands to the iron(IV) center, namely, two histidines and two carboxylates.18 It may also reflect evolutionary pressure on the enzymes to be kinetically competent because current theoretical considerations on the spin state of the oxoiron(IV) unit favor the quintet state over the triplet state as more reactive toward C−H bond cleavage.4,19−21 The structural basis for the preference for spin quintet or triplet ground states can be easily seen qualitatively in Scheme 1,

INTRODUCTION Nonheme iron enzymes are widely found in biology and perform a broad range of functions, particularly in the activation of dioxygen and subsequent oxidative chemistry.1−9 Considerable effort has been devoted to their spectroscopic characterization, by a variety of techniques including magnetic circular dichroism (MCD) and Mössbauer spectroscopies, as well as conventional electron paramagnetic resonance (EPR). In parallel, synthetic efforts have led to the isolation and characterization of model complexes for high-valent intermediates in nonheme enzymes.1−3,10−16 The currently accepted model for the action of nonheme iron oxygenases is via an oxidoiron(IV) (“ferryl”, [FeIVO]2+, 3d4) intermediate.3,4 The electronic spin ground state of an oxidoiron(IV) species can be high spin (the quintet, S = 2), intermediate spin (the triplet, S = 1), or even low spin (the singlet, S = 0), which is generally considered to be much higher © XXXX American Chemical Society

Received: January 26, 2016

A

DOI: 10.1021/acs.inorgchem.6b00169 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

and thus exhibited S = 1 ground states. Other workers have recently reported similar tetragonal oxidoiron(IV) complexes with pentadentate N5-donor ligands.11,31 These complexes were not characterized by any magnetic-field-dependent measurements but likely exhibit spin triplet ground states, consistent with the simple model. However, use of TMG3tren (see Scheme 332), a sterically bulky tripodal tetradentate ligand

Scheme 1. Qualitative MO Diagrams for (Left) [FeO(Leq)3(Lax)] with Idealized Trigonal-Bipyramidal Symmetry and (Right) [FeO(Leq)4(Lax)] with Idealized Square-Bipyramidal Symmetrya

Scheme 3. Representative Trigonal Iron(IV) Oxido Complexes: [FeO(TMG3tren)]2+ (Left) and [FeO(H3buea)]− (Right)a

a

In the more realistic point group symmetries C3v (left) and C4v (right), the prime/double prime and g designations of the respective MOs would be removed. The dz2 and dxz,yz orbitals in both geometries correspond primarily to the FeO σ* and π* MOs, respectively (as labeled for the tetragonal case); the dx2−y2 orbital is a Fe−Leq σ* MO in both geometries, with dxy also being σ* in the trigonal case but nonbonding in the tetragonal. a

The OFe−N axis (idealized C3 axis) defines the z axis (θ = 0°) for the AOM, and the three equatorial nitrogen donors are located at θ ≈ 98° and ϕ ≈ 0, 120, and 240°). The actual metrics for both complexes are given in Table S1. See also Scheme S1 for a generic diagram relevant to the AOM employed here.

which presents the d-based molecular orbital (MO) ordering in the two common types of idealized coordination geometry about the ferryl unit, trigonal [3-fold idealized symmetry about the FeO (z) axis] and tetragonal (4-fold idealized symmetry about the FeO axis). As can be seen in Scheme 1, the d electronic configuration of the tetragonal complexes is dxy2dxz,yz2dx2−y20dz20, giving a 3A2g ground state (in D4h idealized point group symmetry; 3A2 in C4v), and that for the trigonal complexes is dxy,x2−y22dxz,yz2dz20, giving a 5A1′ ground state (in D3h idealized point group symmetry; 5A1 in C3v). The basis for this MO ordering will be discussed below, and further information is provided in the Supporting Information, including the rationale for using here the higher-order groups Dnh. Earlier reported model complexes, such as [FeO(TMC)(CH 3 CN)](OTf) 2 22,23 and [FeO(N4Py)](X)2, where X = ClO4−24 and OTf = CF3SO3−,25 as well as others26−29 (see Scheme 230), each contained nitrogendonor ligands that supported approximate tetragonal symmetry

to enforce C3 symmetry, by Que and co-workers afforded the oxidoiron(IV) complex [FeO(TMG3tren)]2+,14−16 which was shown to have trigonal-bipyramidal geometry by X-ray crystallography. A tridentate variant of TMG3tren, TMG2dien, also afforded an oxidoiron(IV) complex spectroscopically characterized in solution.33 Borovik and co-workers, employing a tripodal anionic ligand, also reported a trigonal oxidoiron(IV) complex, [FeO(H3buea)]−, which was characterized structurally34 and shown to exhibit an S = 2 ground state by magnetic Mö ssbauer and EPR spectroscopies.29 The switch from tetragonal to trigonal symmetry thus results in a spin S = 2 ground state for the oxidoiron(IV) unit, which corresponds to that associated with oxidoiron(IV) intermediates of nonheme iron oxygenases described thus far. High-frequency and -field electron paramagnetic resonance (HFEPR) has been applied to a wide variety of transition-metal complexes, most commonly in the solid state, both as powders35,36 and as single crystals.37 However, the applicability of HFEPR to investigate samples in frozen solutions, both aqueous and organic solvents, has also been demonstrated.38−40 Therefore, in addition to extracting information of (bio)chemical interest in an enzyme model complex in a frozen solution, we wished also to demonstrate the applicability of HFEPR to species that are only transient, such as reactive intermediates. Oxidoiron(IV) species generated in solution by the oxidation of iron(II) and/or iron(III) precursors have been identified in frozen solutions by long known techniques such as resonance Raman, Mössbauer, and conventional EPR spectroscopies. Such species present an ideal challenge for the application of HFEPR. We note that conventional frequency and field EPR, especially with the use of parallel-mode detection, can extract zero-field-splitting (zfs) values from S = 2 complexes, as has been done for several oxidoiron(IV) complexes in a frozen solution.29,33 Of the over 70 nonheme oxidoiron(IV) complexes reported thus far,1 only two, [FeO(TMC)-

Scheme 2. Representative Tetragonal Iron(IV) Oxido Complexes: [FeO(TMC)(CH3CN)]2+ (Top Left), [FeO(N4Py)]2+ (Top Right), [FeO(TPA)(NCCH3)]2+ (Bottom Left), and [Fe(O)(BPMCN)(NCCH3)]2+ (Bottom Right)a

a

The 2+ charge on each complex is not shown. B


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Inorganic Chemistry

parameters. Free-ion values for the spin−orbit coupling (SOC) parameter, ζ, and Racah interelectronic repulsion parameters, B and C, were taken from those reported by Brorson, Bendix, and coworkers.50,51 Quantum-Chemical Theory (QCT). Geometry optimizations of [FeO(TMG3tren)]2+ in various spin states and of its simplified versions (obtained by modification of the TMG3tren ligand; see Scheme 4) in a quintet spin state were performed using the Gaussian

(CH3CN)](OTf)2 and [FeO(N4Py)](OTf)2, have been studied by HFEPR.41 These two complexes are relatively stable S = 1 complexes and can be obtained as solids, making their investigation by HFEPR more feasible. For this effort, we chose to investigate the S = 2 complex [FeO(TMG3tren)]2+ in a frozen solution to demonstrate the forte of HFEPR40 in the extraction of the spin-Hamiltonian parameters of a complex and describe the electronic structure of this complex to high precision.

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Scheme 4. Structures of [FeO(L)]2+ Complexes, Where L = TMG3tren, and Its Simplified Versions Employed in Computational Analyses: Upper Left, G3tren (1,1,1-Tris[2(N2-guanidino)ethyl]amine); Upper Right, TMG3tren (1,1,1-Tris{2-[N2-(1,1,3,3Tetramethylguanidino)]ethyl}amine); Middle Left, tren [Tris(2-aminoethyl)amine]; Middle Right, Me6tren (Tris[2(N,N-dimethyl)aminoethyl]amine); Lower Left, I3tren [Tris(2-iminoethyl)amine]; Lower Right, DMI3tren (Tris[(dimethylimino)ethyl]amine)

EXPERIMENTAL SECTION

Synthesis and HFEPR Sample Preparation. A dichloromethane (DCM) solution of [FeO(TMG3tren)](OTf)2 (approximately 25 mM) was generated in situ by adding a solution of 2 equiv of 2-(tertbutylsulfonyl)iodosylbenzene42 in DCM to 15 mg of [Fe(TMG3tren)(OTf)](OTf).15 All solutions were handled under an inert atmosphere and at temperatures below −40 °C. The dark red-orange solution was rapidly transferred to HFEPR sample holders and immediately frozen in liquid nitrogen. A separately prepared sample in DCM/toluene (1:1, v/v) was also investigated. This solution, which should give a better glass than neat DCM, did not, in fact, yield spectra that were superior in terms of resolution to those recorded in neat DCM and had lower signal-to-noise ratios. We have found that in HFEPR the glass quality is of minor consideration, if at all; e.g., aqueous (i.e., pure water) solutions give spectra indistinguishable from those of water/ ethylene glycol glasses. This observation is in sharp contrast to that for EPR spectroscopy at conventional fields and frequencies, and even more so for conventional field ENDOR spectroscopy, where a glassed solvent is a requirement. HFEPR Instrumentation. The HFEPR spectrometer at the Electron Magnetic Resonance (EMR) Facility at the National High Magnetic Field Laboratory (NHMFL, Tallahassee, FL) is identical with that described in ref 43 with the exception of employment of a Virginia Diodes (Charlottesville, VA) source operating at a base frequency of 12−14 GHz and multiplied by a cascade of multipliers. The spectrometer is associated with a 15/17 T superconducting magnet. Phase-sensitive detection was used, with the magnetic field modulated at 50 kHz. The alternating-current response was fed into a Stanford SR830 lock-in amplifier to obtain a direct-current signal. Low-temperature control was provided by an Oxford Instruments (Oxford, U.K.) continuous-flow cryostat. EPR Simulation. EPR spectra were simulated using a locally written program, SPIN, available from A. Ozarowski. For S ≥ 2, the spin Hamiltonian contains not only the commonly used second-order zfs terms D (uniaxial zfs, D = 1/3B02) and E (rhombic zfs, E = B22) but m also the fourth-order terms BnmOn̂ , where n = 4 and m = 0, 2, and 44,45 4. Thus, the Hamiltonian used here is given in eq 1: ⎛ 2 1 ⎞ 2 2 / = βeB · g · S ̂ + D⎜Sẑ − S(S + 1)⎟ + E(Sx̂ − Sŷ ) ⎝ ⎠ 3 0 3 0 2 2 ̂ − B4 {O4 + 20 2 O4̂ } + B40 O4̂ + B42 O4̂ 3

09 program suite52 employing the B3LYP/6-311G*53−59 and/or MP260−62 levels of theory (starting from experimental X-ray diffraction structures) without any symmetry restrictions. The stability of the obtained structures has been tested by vibrational analysis (no imaginary vibrations). Singlet spin states of the compounds under study have been treated using an unrestricted formalism (“broken symmetry” treatment). The atomic charges of relevant atoms and d-electron populations of iron atoms (dx) were evaluated using natural bond orbital (NBO) analysis.63,64 The relative energies of various charge and spin states of the same complex have been corrected using restricted open-shell single-point calculations (replacing the electron energy in unrestricted energy data) except “broken symmetry” (BS) singlet state, where the energy difference between the singlet (ES) and quintet (EQ) states is evaluated as given in eq 2:

(1)

where B4 is a cubic fourth-order zfs parameter, B04 is a uniaxial fourthorder parameter, and B24 is a rhombic one. Fourth-order terms have been determined previously by HFEPR, such as in a manganese(III) coordination complex studied as a powder46 and manganese(III) as a dopant in a cesium gallium alum host.47,48 Fits were performed and restricted to both uniaxial symmetry (E ≡ 0; B24 ≡ 0) and rhombic symmetry (E ≠ 0; B24 ≠ 0); the cubic zfs terms had no effect on the fit quality, nor did the fourth-order rhombic term; however, inclusion of a uniaxial fourth-order zfs (B24 ≠ 0) did lead to a significantly improved fit of the field-frequency dependence of the HFEPR resonances, based on a reduction in the fit error as defined using a Hessian error matrix. Ligand-Field Theory (LFT). Calculations using the entire d4 basis set were performed using the program Ligf ield,49 by J. Bendix, and the locally written programs DDN and DDNFIT, the latter of which allows fitting of experimental d−d electronic absorption bands to LFT

ES − EQ =

E BS − EuQ 1 − 0.5⟨S2⟩BS

(2)

where EuQ is an open-shell energy of the quintet state and EBS and ⟨S2⟩BS are the energy and spin expectation values of the “broken symmetry” singlet state, respectively.65,66 The zfs parameters67 and g tensors68,69 were evaluated using the ORCA software package.70 The UBLYP/6-311G*53,54 zfs parameters have been calculated with either the coupled-perturbed (CP)71 and/or quasi-restricted-orbital (QRO)67 methods for comparison completeC


Article

Inorganic Chemistry ness. The complete active space self-consistent field (CASSCF)67,72−74 results were based on active spaces of 10 electrons in 8 orbitals (10,8) and/or 16 electrons in 11 orbitals (16,11) to account for the four d electrons in five d orbitals of iron, including the σ and π interactions within the [Fe−O]2+ moiety and/or σ(Fe−N) dative interactions. The D and E contributions are calculated based on the state average formalism, using a reasonable number of configurations, i.e., 50 quintet and 200 triplet states (either for the state-specific or state-averaged CASSCF wave function; see the Discussion and Theory). The minimalistic 4 electrons in 5 shells CASSCF calculation will be considered from the perspective of the d4 configuration when targeting the state-specific ground-state wave function, which is isoelectronic with the presented restricted open-shell Hartree−Fock (ROHF) results. Nevertheless, the state-averaged CASSCF(4,5) calculation features also the antibonding σ*(Fe−O) and π*(Fe−O) interactions and is no longer a pure d4 configuration (see below). State-averaged CASSCF(4,5) calculations are performed in the full configuration space, including 5 quintet and 35 triplet states, with assessment of the spin−spin coupling (SSC) interaction via the multireference configuration interaction (MRCI) approach, keeping only the (4,5) configuration space active. The electronic structure of the complex under study has been explored at the UBLYP/6-311G*, ROB3LYP/6-311G*, ROHF/6311G*, and CASSCF/6-311G* levels of theory. The electronic structure was elucidated via localized orbitals,75 natural orbitals, and Mulliken population analysis of atomic d and s orbitals, as well as Quantum Theory of Atoms in Molecules (QTAIM) analysis.76 Aside from the QTAIM net atomic charges and spins, QTAIM bond characteristics are evaluated in terms of the electron density, ρ, and its Laplacian, ∇2ρ, as given by eq 3: ∇2 ρ = λ1 + λ 2 + λ3

Figure 1. 203.2 GHz HFEPR spectrum of a frozen CH2Cl2 solution of [FeO(TMG3tren)]2+ at 5 K (black trace) accompanied by powderpattern simulations using slightly modified spin-Hamiltonian parameters relative to those in the text: |D| = 5.1 cm−1, E = 0, and giso = 2.00. Blue trace: negative D. Red trace: positive D. The single-crystal line width used in the simulations was 25, 150, and 100 mT, respectively, for the three prominent perpendicular turning points between 1 and 6 T.

(3)

and by bond ellipticity, ε, as given by eq 4: ε=

λ1 −1 λ2

(4)

each calculated at bond critical points (BCP), which are defined as λ1 < λ2 < 0 < λ3, where λi are the eigenvalues of the Hessian of the BCP electron density. The BCP electron density, ρBCP, is proportional to the bond strength; the value and sign of its BCP Laplacian, ∇2ρBCP, describes the relative electron density contribution of the bonded atoms to the bond (covalent vs dative bonding); its BCP bond ellipticity, εBCP, describes its deviation from cylindrical symmetry (such as in ideal single or triple bonds) due to its double-bond character, mechanical strain, and other perturbations. Atomic d- and s-orbital populations are considered for a rotated geometry of the complex, with the oxido ligand defining the z-axis direction and one equatorial nitrogen ligand defining the xz plane. QTAIM analysis was performed in the AIMAll package77 using the wave function from the G09 fchk file. Localized and natural orbitals were visualized in the Molekel software package.78

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Figure 2. Two-dimensional (field vs frequency or energy) map of HFEPR resonances in [FeO(TMG3tren)]2+ at 5 K (squares) with simulations using the best-fitted spin Hamiltonian as in the text. Red lines: calculated perpendicular turning points (B0 ⊥ zfs tensor z axis). Black lines: calculated parallel turning points (B0 ∥ zfs tensor z axis). The vertical dotted lines indicate the frequencies at which spectra shown in Figures S1, 1, and S2, respectively, in increasing frequency, were recorded.

EXPERIMENTAL RESULTS

The 25 mM solution of [FeO(TMG3tren)]2+ in DCM produced a fairly strong EPR response in the ∼100−400 GHz frequency range and at low temperatures (5−30 K). Figure 1 shows a HFEPR spectrum recorded at 203.2 GHz and 5 K. Figures S1 and S2 show spectra at lower and higher frequencies, respectively. The spectra are accompanied by simulations that were generated using spinHamiltonian parameters obtained from tunable-frequency methodology; these are discussed in greater detail below. Rather than obtaining the spin-Hamiltonian parameters from singlefrequency spectra, such as that shown in Figure 1, we followed the tunable-frequency EPR procedure by taking spectra at multiple frequencies and fitting the parameters to a two-dimensional field versus frequency (or energy) map consisting of turning points recorded at each frequency.79 This procedure is illustrated by Figure 2. The least-squares fit of the parameters (details of the procedure are given in the Experimental Section) to the array of resonances yielded

the values S = 2, |D| = 4.940(5) cm−1, |E| = 0.000(5), B40 = −14(1) × 10−4 cm−1, g⊥ = 2.006(2), and g∥ = 2.03(2). The sign of D was obtained through simulating single-frequency spectra, as shown in Figures 1 and S1 and S2. The comparison of the simulations with experiment proves that D is positive in [FeO(TMG3tren)]2+.

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DISCUSSION AND THEORY The zfs of [FeO(TMG3tren)]2+ was determined previously by Mössbauer spectroscopy in high applied magnetic fields and given as D = 5.0(3) cm−1 and E/D = 0.02(1) [E = 0.10(5) cm−1].15 The present study has essentially confirmed these D


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Inorganic Chemistry results, with HFEPR providing D = +4.940(5) cm−1 and E = 0. The higher precision of the HFEPR technique is the result of fitting the entire two-dimensional field-frequency dependence of multiple observed resonances.79 The difference in magnitude between the Mössbauer- and HFEPR-derived D values is insignificant, but what is significant is that HFEPR has determined the positive sign of D unequivocally and that the system is axial. Rhombic zfs is readily observable by HFEPR of high-spin systems by virtue of the splitting of perpendicular turning points. Although the crystal structure lacks true trigonal symmetry (Table S1), the sample was studied in solution, so solid-state constraints may have become relaxed upon dissolution. HFEPR also provided the g values for [FeO(TMG3tren)]2+, which cannot be deduced from Mössbauer analysis. In contrast to the zfs parameters, the g values are not particularly informative; however, it is interesting to note that, consistent with the earlier HFEPR study on S = 1 oxidoiron(IV) complexes,41 the g values are close to, but slightly above, 2.00: g⊥ = 2.006(2) and g∥ = 2.03(2).80 Moreover, in ribonucleotide reductase (RNR) intermediate X, which is comprised of a high-spin iron(III) antiferromagnetically coupled to a high-spin iron(IV), the g tensor is nearly isotropic and very close to 2.00 (g = [2.006, 1.998, 1.993]), which suggests that the single-ion g values of iron(IV) are themselves roughly isotropic and close to 2.00.81−83 These results for iron(IV) contrast with the standard expectation from simple LFT that less than half-filled electronic configurations (with orbital contributions) exhibit g < 2.00 (=ge). More sophisticated LFT modeling suggests that one of the two g values in an axially symmetric system should be much less than 2.00.84 We have explored this by our own LFT calculations given below. Nevertheless, LFT demonstrates how oxidoiron(IV) complexes with tetragonal symmetry and spin triplet ground states exhibit very large magnitude zfs (16 < D < 28 cm−1),84 while those with trigonal symmetry and spin quintet ground states exhibit much smaller zfs (D ≈ 5 cm−1); see, e.g., Table 3 in Jensen et al.27 and Table 1 in Puri and Que.1,85 We note that a study by some of us on manganese(III), isoelectronic with

iron(IV), also in trigonal-bipyramidal geometry, similarly gave a relatively small, positive zfs, D ≈ +3.0 cm−1, which was validated using LFT.86 In this system, manganese(III) was a dopant in an oxide lattice and thus in a homoleptic coordination environment, which qualitatively leads to a smaller zfs. Correspondingly, for S = 1 manganese(III), in the example of hexacoordinated bis(scorpionate) complexes, the zfs is much larger (D ≥ 15 cm−1), approaching that for S = 1 iron(IV) complexes.87,88 Our goal at present is to apply both LFT and QCT [both density functional theory (DFT) and ab initio methods] to understand the electronic structure of [FeO(TMG3tren)]2+. A detailed study on the observed electronic transitions of this complex by MCD has been reported by Srnec et al.14 For the purposes of a simple LFT picture, using the angular overlap model (AOM),89−91 we primarily make use of the single electronic band that has been clearly identified and assigned as a primarily d−d transition, namely, that at 11500 cm−1 (timedependent DFT calculated this transition to be at 18100 cm−1),14 which corresponds to 5A1g → 5E(″) (d2xy,x2−y2d2xz,yzd0z2) → (d2xy,x2−y2d1xz,yzd1z2).92 There are other, higher-energy bands that are ligand-to-metal charge transfer in nature, specifically (Fe)O [π(px,y)) → Fe(O)(π*(dxz,yz)], observed at 19500 cm−1, which clearly shows a vibronic progression due to ν(Fe O).14 Unfortunately, the possible d−d transition 5A1g → 5E(′) (d2xy,x2−y2d2xz,yzd0z2) → (d2xy,x2−y2d2xz,yzd1z2) was not observed. Therefore, we use the experimental band at 11500 cm−1 with its assignment fixed as (d2xy,x2−y2d2xz,yzd0z2) → (d2xy,x2−y2d1xz,yzd1z2) and make estimates as to the energy of the other d−d transition. With this method, as detailed in the Supporting Information, it is possible to obtain rough estimates of the bonding parameters for the ligands in [FeO(TMG3tren)]2+. These show that, in addition to imposing the crucial trigonal symmetry that stabilizes the spin quintet ground state, TMG3tren provides imino nitrogen atoms that are moderate σ donors and strong π donors, which may assist in the reactivity of this complex toward oxidation and hydrogen-atom-abstraction reactions. Moreover, the use of these bonding parameters from the AOM, combined with reasonable estimates (80% of the freeion single-electron SOC constant, ζ)51 and Racah parameters B and C50 for Fe4+ reproduces the experimental D value remarkably well: +5.2 cm−1 (E must be zero with the trigonal symmetry of this AOM). The use of parameters that are 75% of the free ion give D = +4.8 cm−1 (70% gives D = +4.3 cm−1).93 Thus, despite the approximate nature of our LFT model, the zfs of [FeO(TMG3tren)]2+ is also well-reproduced, as was the case for manganese(III) in an oxide lattice with trigonal-bipyramidal geometry.86 As described in the Supporting Information (Figure S3 and associated text), it was also possible to estimate the g values from LFT by inclusion of the Zeeman interaction. In this case, the experimental g∥ value of ∼2.0 was moderately well-reproduced (see Table 3), but g⊥ was calculated to be much lower than that found. We have not applied our LFT approach to the related complex [FeO(H3buea)]−;29,34 however, the fact that its geometry is very close to that of [FeO(TMG3tren)]2+ (see Table S1) suggests that the results would be similar. A more sophisticated analysis of the electronic structure of [FeO(TMG3tren)]2+ was performed using QCT, with both the DFT and ab initio methods, following the work of Srnec et al.14 B3LYP/6-311G*-optimized geometries of [FeO(TMG3tren)]2+ structures in various spin states (Table 1) confirmed the quintet spin state to be its ground state, with

Table 1. DFT Energies (EDFT), Total Spin Squares (⟨S2⟩), and Free Energies at 298 K (G298) of B3LYP/6-311G*Optimized [FeO(TMG3tren)]2+ Structures in Various Spin States, S S 1

2

3a

2.040 −2715.40091

6.049 −2715.44306

12.017 −2715.39728

−2714.74250

−2714.78480

−2714.74320

−2715.38550

−2715.43400

−2715.39044

127

0

114

128

0

103

0 Unrestricted Formalism ⟨S2⟩ 0.717 EDFT −2715.39563 [hartree] G298 −2714.73595 [hartree] Restricted Formalism EDFT −2715.38780 [hartree] Relative Energies 189 EDFT [kJ/mol] 193 G298 [kJ/mol] a

Calculation using an alternative model to [FeIVO2−]2+, namely, [FeIIIO•−]2+, in which high-spin iron(III) is ferromagnetically coupled to O•−, to give total spin S = SFe + SO = 5/2 + 1/2 = 3. E


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Inorganic Chemistry

Table 2. Selected Metrical Parameters of Iron Inner Coordination Sphere for B3LYP/6-311G*-Optimized [FeO(TMG3tren)]2+ Structures in Various Spin States S 0 Distances [Å] Fe−O Fe−Neq

Fe−Nax (O···H)minc

Angles [deg] Neq−Fe−Neq

1

2

3a

1.605 1.966 2.002 2.009

1.599 1.985 2.024 2.032

1.622 2.037 (×3)

1.877 2.063 2.071 2.078

2.177 2.417 2.439 2.503

2.158 2.426 2.429 2.553

2.129 2.482 (×3)

2.273 2.322 2.437 2.593

113.7 116.8 121.9

Neq−Fe−Nax

80.4 80.7 81.1

Nax−Fe−O Neq−Fe−O

174.7 104.8 97.2 96.1

106.8 119.3 127.6

118.3 (×3)

80.9 81.8 (×2)

175.1 102.4 98.9 94.5

116.3 117.2 (×2)

82.4 (×3)

78.2 80.3 80.4

180.0 97.6 (×3)

170.1 106.0 102.8 92.1

exptl geometryb 1.661(3) 1.994(2) 2.002(3) 2.020(3) 2.005 (avg) 2.112(3) 2.422 2.437 2.522 2.460 (avg) 116.8(1) 118.6(1) 119.2(1) 118.2 (avg) 82.0(1) 82.1(1) 82.5(1) 82.2 (avg) 179.3(1) 98.1(1) 98.0(1) 97.4(1) 97.8 (avg)

a Calculation using the model described in the footnote to Table 1. bStructural data from England et al. (CSD code: ANEXAT);16 standard deviations are in parentheses. cThe X-ray crystal structure was of the perdeuteromethyl ligand (TMG3tren-d36), so these are (O···D)min distances for the experimental values. The deuterium atoms were modeled as an idealized CD3 group riding on the carbon atom.

An iron(IV) oxidation state might be alternatively described as iron(III) combined with a ligand-centered radical cation, i.e., a consequence of “noninnocent” ligand (NIL) behavior. According to Jørgensen,95 ligands are innocent when they allow oxidation states of the central atom to be defined. NILs are able to delocalize part of the electronic density of the complexes to which they belong, becoming, in addition to the metal center, a place where redox processes can also take place. The above-mentioned self-decay mechanism raises the suspicion that the TMG3tren ligand might be “noninnocent”, in contrast to a ligand such as TMC, with its tertiary amine donors (see Scheme 2). The real oxidation state of transition metals might be deduced from their d-electron population.65 Unlike free ions with d-electron populations corresponding to their formal oxidation states, the d-electron populations in their complexes are higher because of electron density transfer from neighboring atoms/ligands and subsequent electron density redistribution at the central atom. To provide a basis for comparison, we have performed B3LYP/6-311G* geometry optimization of trigonal tetraammineiron oxido complexes [FeO(NH3)4)]q in quintet spin states with total charges q = 2+ and 0, in which the supporting ammine ligands are truly innocent (the structure for q = 2+ is shown in Figure S6). For neutral [FeO(NH3)4)] in the quintet spin state, corresponding to iron(II), we have obtained a d-electron population at iron, dx(Fe), of 6.37 and, for [FeO(NH3)4)]2+ in the quintet spin state, corresponding to iron(IV), dx(Fe) of 6.06, which is in perfect agreement with the dx(Fe) value calculated for

vanishing contributions of other spin states (because the energy differences are over 100 kJ/mol). Except in the “broken symmetry” singlet state, we have obtained nearly pure higher spin states as indicated by their spin squares, so their energies calculated by an unrestricted formalism with a small spin contamination are close to the pure spin restricted ones. The experimental structural data are best reproduced by the quintet spin state (Table 2; see, e.g., ∠Nax−Fe−O and ∠Neq−Fe−O), and the minor differences among the metrics may be explained by neglecting the environmental influences in quantumchemical calculations.94 The optimized spin quintet structure (5A state within the C3 symmetry group) has preserved a trigonal rotation axis, while the triplet states lack trigonal symmetry as a consequence of the Jahn−Teller effect on the degenerate 3E state in the unstable parent C3 structure. The symmetry descent of the nondegenerate 1A state may be explained by a pseudo-Jahn−Teller effect within the same parent C3 structure. The excited states of lower spin multiplicity (see Table 1 for the energies of triplet and singlet spin states relative to the quintet ground state) are very high in energy and thus practically unpopulated at ambient temperature. Despite their negligible populations, these excited states might be relevant in connection with the self-decay of [FeO(TMG3tren)]2+ even at low temperatures, wherein the oxygen atom attacks a ligand methyl C−H bond, leading to the formation of FeIIIOH and FeIIIOR products.16 Our calculations indicate that a (pseudo-)Jahn−Teller symmetry descent causes a shortening of the minimal O−H distances and so might enhance the self-decay rate. F


Article

Inorganic Chemistry [FeO(TMG3tren)]2+ in the quintet spin state (Table S6; the extent of the electron density transfer from ligands may be deduced from the iron and oxygen natural charges and from their comparison with the total charge of the complex). Thus, we can conclude that iron(IV) in our complex is as real an oxidation state with TMG3tren as with the genuinely innocent ammine ligand. In other words, the oxidoiron(IV) unit is the defining feature of these complexes, and the supporting ligand, while crucial for kinetic stability and spin-state stabilization, need not be noninnocent. In the next step, we have also performed geometry optimizations of [FeO(L)]2+ complexes in the quintet spin state, wherein L is a series of “simplified” variants of the TMG3tren ligand (see Scheme 4), beginning with both tren itself and its methylated form, Me6tren, and including the demethylated form of TMG3tren, namely, G3tren. Also investigated are variants in which the nitrogen atoms of the guanidine moiety are replaced by carbon atoms, I3tren [(CH 2 NCH 2 CH 2 ) 3 N] and DMI 3 tren [((CH 3 )C NCH2CH2)3N]. The purpose of this exercise was to explore specific structural aspects of the tetramethylguanidine moiety in relation to the overall electronic structure of the complex. The synthetic/steric effects of this specific ligand are, of course, dominant in its effectiveness but cannot be easily quantified by our computational methods. The structures of their iron inner coordination sphere do not differ substantially from that of [FeO(TMG3tren)]2+ (see Table S7 and Figures S4 and S5). Except for the MP2/6-311G* data of [FeO(G3tren)]2+, they preserve the C3 symmetry of the parent complex. An interesting aspect of all of these complexes is the interaction between the oxido ligand and hydrogen atoms from the chelating ligand. We note that the reported crystal structure was of TMG3tren with perdeuterated methyl groups,16 the isotopologue of which was thermally more stable than that in natural abundance. Hydrogen bonds involving deuterium have lower zero-point energy than those involving protium.96 The structure showed short C−D···O nonbonded contacts, which was related to the complex’s self-decay by intramolecular hydrogen-atom abstraction.16,97 Our computational results show this structural phenomenon as well for the TMG3tren complex in the quintet spin state (Table 2). In the simplified complexes, the minimal C−D···O distances are generally longer than that in the TMG3tren complex, with the exception of those with G3tren and DMI3tren ligands. In particular, [FeO(G3tren)]2+ in the quintet spin state exhibits extensive hydrogen bonding between the guanidine N−H groups and the oxido ligand (see Figure 3), which could well affect its reactivity/stability. The relatively close (2.20 Å; Table S7) C− H···O contacts calculated in [FeO(DMI3tren)]2+ are also

notable and lead us to speculate that such a complex might be less stable than the TMG3tren complex. We then turn to DFT and CASSCF calculations of the spinHamiltonian parameters, which are presented in Table 3. Table 3. Experimental and Calculated zfs Parameters (in cm−1) and g Tensor Components for Iron(IV) Oxido Complexes with Trigonal Symmetry D experiment UBLYP-CP UBLYP-QRO CASSCF(4,5)a MRCI(4,5)a CASSCF(10,8) CASSCF(10,8)

a

CASSCF(16,11) LFTb experiment B3LYP

E

g∥

[FeO(TMG3tren)]2+ (this work) +4.940(5) 0.000(5) 2.03(2) +2.29 [+2.32] 0.01 2.012 [0.00] [2.013] +3.51 [+3.55] 0.01 [0.00] +4.93 [+4.99] 0.06 2.000 [0.00] [2.000] +5.48 [+5.55] 0.07 [0.00] +3.38 [+3.57] 0.03 2.000 [0.00] [2.000] +3.44 [+3.61] 0.03 2.000 [0.00] [2.000] +3.37 [+3.58] 0.02 2.000 [0.00] [2.000] +4.8 0.00 2.0015(5) [FeO(H3buea)]− (Gupta et al.29) +4.7 0.14 2.02c d +3.9

g⊥ 2.006(2) 2.010 [2.010]

1.985 [1.986]

2.009 [2.008] 2.014 [2.012] 2.009 [2.009] ∼1.6

a

State-averaged calculation. bCalculation using 75% of the Fe4+ freeion Racah and SOC parameters (in cm−1), B = 900, C = 3800, and ζ = 380, and the following AOM bonding parameters (in cm−1): εσO = 19095, επO = 14210, εσN1ax ≡ 7500, εσN2,3,4eq = 5000, and επcN2,3,4eq = 3065. cOnly g∥ was observed, and g values were not calculated. d Estimated from an AOM-like analysis of B3LYP populations. aFor [FeO(TMG3tren)]2+, calculated values are given based on both the experimental and optimized geometries (optimized in brackets).

Calculations of the zfs of [FeO(TMG3tren)]2+ (using the crystal structure16) employing the UBLYP level of theory show that the QRO method yields better agreement with the experimental D values, compared to the more rigorous CP method. While the D value is not sensitive to the choice of geometry (experimental or optimized), the E value is zero for the optimized geometry (as found in the experiment). The spin−spin contribution to the zfs, DSSC, equals ∼0.39 cm−1 at the UBLYP level for both CP and QRO methods, i.e., the choice of the particular method affects only the spin−orbit contribution, DSOC. The CASSCF(16,11) method yields the following zfs values for the experimental (optimized) geometry D = +3.37 (+3.58) cm−1 and E = 0.02 (0.00) cm−1, respectively. The quintet contribution to the D CASSCF(16,11) value is only +0.83 cm−1, indicating the importance of triplet excited states. Similar results are also obtained for the CASSCF(10,8) calculations (irrespective of the usage of state-specific or stateaveraged wave function; see Table 3). The discrepancy between the CASSCF results and the experimental zfs can be attributed to the missing spin−spin interaction and dynamic electron correlation, which are currently technically out of reach for the size of the (10,8) and (16,11) active spaces and the particular number of configurations.98 Herein we shall mention also the minimalistic state-averaged CASSCF(4,5), with the d4 configuration accounting for the antibonding σ*(Fe−O) and π*(Fe− O) interactions; see parts a and b of Figure 5, respectively. For

Figure 3. Structures of FeO(TMG3tren)]2+ (left) and [FeO(G3tren)]2+ (right) in the quintet spin state from geometry optimizations (Fe, white; O, red; N, blue; C, black; H, gray). G


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Inorganic Chemistry Table 4. Atomic s- and d-Orbital Mulliken Populations (Experimental Geometry) UB3LYP ROB3LYP UBLYP ROHF CASSCF(4,5)a CASSCF(10,8) CASSCF(16,11) a

α β α β α β α β α β α β α β

dz2

dxz

dyz

dx2−y2

dxy

s

0.556 0.373 0.460 0.460 0.533 0.408 0.648 0.648 0.724 0.425 0.649 0.341 0.640 0.341

0.992 0.375 0.993 0.378 0.986 0.386 1.008 0.060 0.747 0.426 1.003 0.245 1.002 0.261

0.992 0.378 0.992 0.382 0.986 0.388 1.008 0.061 0.748 0.430 1.003 0.246 1.002 0.262

0.989 0.178 0.991 0.179 0.978 0.231 1.007 0.065 0.709 0.305 0.998 0.069 0.997 0.085

0.990 0.180 0.992 0.181 0.979 0.233 1.008 0.067 0.710 0.306 0.998 0.070 0.998 0.087

0.156 0.141 0.148 0.148 0.168 0.148 0.113 0.113 0.125 0.120 0.096 0.098 0.093 0.094

State-averaged calculation.

Figure 4. Selected BLYP/6-311G* central atom−ligand atom localized β orbitals (experimental geometry). All localized orbitals have an occupation number equal to 1. The numbers in parentheses show the MO percentage contributions for a particular AO type. These orbitals may be visualized in the LFT model as (a) an equatorial Fe−N σ-bonding orbital, (b) an Fe−O σ-bonding orbital, and (c) an Fe−O π-bonding orbital.

the D value obtained from state-averaged CASSCF(4,5) (see Table 3), the contribution of the quintet states is +1.16 (+1.16) cm−1 for the experimental (optimal) geometry. The essential quintet contributions arise from excitations for the two d orbitals involved in the π*(Fe−O) interactions (see Figure 5b) into the empty dz2 orbital involved in σ*(Fe−O) interactions (see Figure 5a). The essential triplet contribution is obtained from the linear combination of the [2110] determinant manifold with a contribution of the [1111] d4 reference state determinant of about 7% (3%) for the experimental (optimized) geometry. It should be highlighted that the D value from the state-averaged CASSCF(4,5) agrees the closest with the experimental value, but this agreement should be taken with care because of the lack of Fe−O bonding interactions within the [Fe−O]2+ moiety. This can also be seen for the state-averaged CASSCF(4,5)-based MRCI results, which overestimate the D value when spin−spin contributions are added to the spin−orbit contributions from the CASSCF(4,5) calculations. On the other hand, the use of the CASSCF(4,5) calculations is qualitatively in agreement with experimentally measured g values, while the CASSCF(16,11) and CASSCF(10,8) g values are exchanged with respect to spin-Hamiltonian parameters best fitted to the experimentally measured HFEPR data (irrespective of geometry and/or state averaging). To obtain insight into the formal versus physical picture of the electronic d configuration of the central atom, the Mulliken atomic orbital (AO) populations are worth consideration. It can be seen from Table 4 that the atomic d-orbital populations of α AOs are indeed in line with the LFT picture where the dz2 population is to be interpreted as the acceptor site of the charge density within the dative bonding picture (as is the case for the

s orbitals), while the dxz(α), dyz(α), dxy(α), and dx2−y2(α) populations are close to 1, which is in line with the formal model of four fully populated open-shell d orbitals on iron (see Scheme 1). The exception is for the state-averaged CASSCF(4,5) level of theory because it reflects an averaging among all of the quintet and triplet states accounting also for the σ* and π* Fe−O interactions. For the β AO populations, the ROHF results confirm underestimation of the donor character of the central atom to ligand atoms, as documented in the literature.99 On the other hand, there is no qualitative difference between the DFT and state-specific CASSCF(16,11) d(β) populations. Note that the formally empty AO d(β) orbitals are involved in the donor (bonding, nonbonding, and antibonding) interactions with the ligands. Obviously, the dx2−y2(β) and dxy(β) populations are lower compared to the dxz(β) and dxz(β) populations. This can be interpreted in light of LFT because the former pair of AOs are lower in energy compared to the latter, so that the energetically lower-lying d AOs will be less involved in donor interactions (especially with respect to the oxido ligand). Nevertheless, from the MO-LCAO and/or orbital representation picture, one has to note that the oxido ligand (formally O2−) has a considerable excess of charge density (comparing to, e.g., Cl−), with a favorable π interaction between the 3dxz and dyz AOs of iron and 2px and py AOs of oxygen (both pO AOs having a Mulliken population of about 1.6). The small differences between CASSCF(16,11) and CASSCF(10,8) populations are also worth highlighting, as seen in Table 4. To further elucidate interactions in the [Fe−O]2+ moiety, DFT localized orbitals and CASSCF(16,11) natural orbitals merit further inspection. For an alternative and more detailed H


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Inorganic Chemistry

Figure 5. Selected CASSCF(16,11)/6-311G* central atom−ligand atom natural orbitals (experimental geometry). Orbital numbers−occupation numbers follow the given alphabetical figure label. The numbers in parentheses show the MO percentage contribution of a particular AO type. These orbitals may be visualized in the LFT model as (a) an Fe−O σ*-antibonding orbital, (b) an Fe−O π*-antibonding orbital, (c) an equatorial Fe−N σ*-antibonding orbital, (d) an Fe−O σ-bonding orbital, (e) an Fe−O π-bonding orbital, and (f) an equatorial Fe−N σ*-antibonding orbital.

accounts for a population of about 0.2 electrons, which is in good accordance with the presented CASSCF(16,11) dxz/dyz β populations compiled in Table 4. Quantitatively, CASSCF(16,11) yields a weaker bonding π(Fe−O) interaction than that in the case of the DFT picture. For comparison, similar Fe−O interactions are also found in the tetragonal model system, [FeO(NH3)5]2+, studied by Neese,99 although this hexacoordinated species shows stronger π(Fe−O) interactions in comparison to the pentacoordinated compound under investigation here. Because of this difference, a consistency check for [FeO(NH3)4]2+ has been performed (not shown), leading to the same picture of DFT and/or CASSSF(16,11) orbitals as those found for [FeO(TMG3tren)]2+, and weaker π(Fe−O) interactions with respect to the [FeO(NH3)5]2+ study of Neese99 have been confirmed. Alternatively, the CASSCF(16,11) e and e* natural orbitals can be rationalized as representing respectively a stabilizing, dative contribution of the oxido ligand px/py AOs into the Fe dxz/dyz AOs (bonding character) and a dative interaction of the Fe dxz/dyz AOs with the oxido ligand px/py AOs (nonbonding/antibonding character). Note also that the extended CASSCF(16,11) active space leads to differences within interactions between the nitrogen donors and the iron compared to the DFT picture, which treats equally all p orbitals of the donor atoms (see also the comparison of the DFT and CASSCF charges and spin populations). As shown in Table 5, UBLYP/6-311G* QTAIM BCP characteristics agree well with the localized orbital picture (see also the description in the Quantum-Chemical Theory (QCT) section). The Fe−O dative bond is the shortest and has the highest BCP electron density ρBCP and corresponding Laplacian

analysis of the canonical B3LYP orbitals, see the earlier study by Srnec et al.14 The localized orbitals are well suited to give insight into the bonding situation; i.e., the bonding density is lowered by antibonding contributions and formally free of nonbonding interactions. It can be concluded that the DFT localized orbitals are in acceptable agreement with the CASSCF(16,11) results, as demonstrated by the shape of the orbitals in the [Fe−O]2+ moiety. Figure 4 presents the relevant localized bonding MOs generated from DFT calculations (the four localized d orbitals on iron are omitted), and Figure 5 presents natural orbitals from CASSCF(16,11) calculations. A comparison of the [Fe−O]2+ a1 symmetry orbitals shows the similarity between the DFT and CASSCF(16,11) results. In particular, in the DFT localized orbital (Figure 4b), about 25% of the dative bond is found in the dz2 β orbital (40% for the α orbital) of the iron atom. This corresponds well with the net contribution in the CASSCF(16,11) regime considering either subtraction (to evaluate the β contributions) or addition (to evaluate the α contributions) of the bonding (Figure 5c) and antibonding (Figure 5a) CASSCF orbital contributions, including the orbital occupation number and AO contribution of the dz2 orbital.100 On the other hand, in the case of the nearly doubly degenerate e-like symmetry orbitals, which describe the π interaction between dxz/dyz AOs of the iron and px/py AOs of the oxido ligand, the formal picture in the DFT and canonical CASSCF(16,11) localized orbitals is different. In the DFT picture, one has both 3dxz/3dyz α orbitals singly occupied and localized on the iron (not shown). In addition, the bonding contributions are present only in the DFT β-localized orbitals (Figure 4c). The essentially antibonding character in the CASSCF(16,11) Fe−O natural orbitals (Figure 5b) is in counterbalance with higher Fe d populations in the bonding π(Fe−O) natural orbitals (Figure 5d). Thus, if one wants to compare qualitatively the canonical CASSCF π(Fe−O) natural orbitals with the localized DFT picture, one has to build the 3dxz/3dyz single occupied shell on the iron by means of moving ca. 0.2 electron of the d population of the bonding π(Fe−O) natural orbital to the appropriate antibonding π*(Fe−O) MO, i.e., from the orbital in Figure 5e to that in Figure 5b. In this way, one part of the π(Fe−O) bonding interaction is formally canceled by the antibonding interactions in π*(Fe−O). Hence, the net bonding interaction from the CASSCF perspective

Table 5. UBLYP/6-311G* BCP Characteristics from QTAIM Analysis

I

Fe1−X

ρBCP [e/bohr3]

∇2ρBCP [e/bohr5]

ellipticity

Fe1−O2 Fe1−N3 Fe1−N4 Fe1−N5 Fe1−N6

0.209 0.076 0.095 0.096 0.091

0.802 0.270 0.348 0.358 0.333

0.001 0.002 0.096 0.094 0.092


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Inorganic Chemistry

Table 6. QTAIM and Mulliken Charges and Spin Populations at Different Levels of Theory (Experimental Geometry) theory level employed

a

Fe1

O2

UBLYP UB3LYP

1.455 1.578

−0.683 −0.696

UBLYP UB3LYP

2.811 3.024

0.664 0.613

UBLYP UB3LYP ROHF CASSCF(4,5)a CASSCF(10,8) CASSCF(16,11)

1.491 1.608 2.095 2.116 2.093 2.053

−0.489 −0.508 −0.650 −0.726 −0.558 −0.553

UBLYP UB3LYP ROHF CASSCF(4,5)a CASSCF(10,8) CASSCF(16,11)

2.848 3.061 3.782 1.757 3.679 3.605

0.673 0.627 0.088 0.320 0.189 0.235

N3 QTAIM Charge −0.915 −0.992 QTAIM Spin −0.018 −0.024 Mulliken Charge −0.470 −0.522 −0.735 −0.737 −0.740 −0.733 Mulliken Spin −0.032 −0.037 0.001 0.018 0.007 0.004

N4

N5

N6

−1.064 −1.150

−1.068 −1.155

−1.061 −1.147

0.114 0.089

0.114 0.090

0.112 0.088

−0.624 −0.693 −0.962 −0.944 −0.965 −0.953

−0.615 −0.685 −0.954 −0.934 −0.956 −0.944

−0.617 −0.686 −0.954 −0.936 −0.956 −0.944

0.099 0.075 0.033 0.041 0.032 0.040

0.100 0.076 0.034 0.041 0.032 0.040

0.097 0.074 0.032 0.038 0.030 0.038

State-averaged calculation.

∇2ρBCP values. The low ellipticity of the Fe−O (as well as of the Fe−N3) bond agrees with the symmetrical distribution of the perpendicular π(Fe−O) [and σ(Fe−N3)] interaction. Nevertheless, the perpendicular π(Fe−O) [and π(Fe−N3)] interactions affect the ellipticity of the remaining Fe1−N4, Fe1−N5, and Fe1−N6 dative bonds. Last, Table 6 provides the QTAIM and Mulliken charges and spin populations of the central and ligating atoms. Overall, DFT charges and spin populations for iron from QTAIM and Mulliken analyses agree qualitatively with each other, providing a good quality test of the reliability of the Mulliken AO dpopulation analysis, although the DFT Mulliken populations of the remaining ligand-field atoms are underestimated with respect to the QTAIM results. Apparently, the CASSCF(16,11) Mulliken charge and spin on iron is higher compared to the DFT results. Similarly, the charges of nitrogen atoms are larger at the CASSCF(16,11) level compared to DFT and the spin population of oxygen is lower for the CASSCF(16,11) calculation. This points out the overestimation of bonding interactions within the [Fe−O]2+ moiety in the DFT picture, causing the spin density excess (decrease) on oxygen (iron) when the DFT and CASSCF(16,11) spin populations are compared. Again, the Mulliken charge and spin populations of the CASSCF(16,11) and CASSCF(10,8) calculations agree well with each other.

in good agreement with previous Mössbauer studies but is of higher precision, and the axial nature of this trigonally symmetric complex in solution is demonstrated unequivocally. The g values were also determined, which is not possible from Mössbauer, and are found to be quite close to 2.00. Fourthorder zfs could also be extracted from the HFEPR data and has its origin in higher-order SOC effects. The spin-Hamiltonian parameters obtained from HFEPR were reproduced computationally in a rather qualitative manner, demonstrating the conceptual applicability of DFT and even ab initio methods to the relatively large [FeO(TMG3tren)]2+ molecular ion. Nevertheless, the presence of the [Fe−O]2+ moiety necessarily complicates the performance of CASSCF methods [with both (16,11) and (10,8) active spaces]. The physically more limited d4-like state-averaged CASSCF(4,5) representation does yield D and E values very close to those of the experiment, but this may be fortuitous due to error cancellation because this representation omits the bonding σ and π Fe−O interactions, thus providing only a limited active space for static correlation and leaving out the dynamic correlation and spin−spin interactions. It is further noteworthy that the CASSCF(4,5) g tensor components are in better agreement with the experiment than those provided by the physically more appropriate larger active spaces; however, experimental g values for oxidoiron(IV), whether in tetragonal geometry as shown earlier41 or in trigonal geometry as shown here, are close to 2.0 and thus relatively uninformative, in contrast to the expectations from LFT. In contrast to the CASSCF(4,5) results, the Fe−O π-bonding interactions are to be thought of as the dominating dative (bonding/antibonding) interactions in the [Fe−O]2+ moiety for both DFT and CASSCF(16,11) levels of theory. The CASSCF(16,11) calculation recovers this feature of the px and py AOs of the oxido (O2−) ligand (with populations up to 74%) in the bonding π Fe−O interaction (occupation number of close to 2), while the antibonding interaction is featured by the open-shell MOs (occupation number of close to 1) with the dxz and dyz AOs populated by roughly 80%. The net qualitative comparison between the DFT

■

CONCLUSIONS Nonheme iron enzymes catalyze many important biochemical processes. The ferryl [oxidoiron(IV)] active species in these enzymes has been the object of much synthetic modeling. Many such models exhibit S = 1 spin ground states, in contrast to the enzymes, which have S = 2 ground states. Recently, oxidoiron(IV) model complexes with spin quintet ground states have been prepared.15,16,29,33,34 One such complex, [FeO(TMG3tren)]2+, has now been investigated by HFEPR in a frozen solution and analyzed by classical LFT as well as modern QCT. The HFEPR studies confirm the S = 2 ground state with modest uniaxial, positive zfs, D = +4.940(5) cm−1. This value is J


Article

Inorganic Chemistry

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and CASSCF(16,11) pictures recovers an overestimation of π(Fe−O) bonding interactions at the DFT level of theory. The physical oxidation state of iron within the strongly covalent [Fe−O]2+ moiety is the same in [FeO(TMG3tren)]2+ as in the trigonal model complex [FeO(NH3)4]2+, demonstrating that the TMG3tren ligand is as innocent as the ammine ligand. This is further confirmed by the presence of the d4 configuration recovered in the localized and/or natural orbitals and Mulliken analysis of individual d populations in the DFT as well as CASSSCF(16,11) realms. In combination with previous spectroscopic (primarily MCD and Mössbauer) and theoretical work,4,14,16,101 a comprehensive picture of the electronic structure of a trigonally symmetric oxidoiron(IV) complex is now available. We hope that this information will lead to further synthetic efforts and an enhanced understanding of the nonheme iron enzymes that inspired the development of [FeO(TMG3tren)]2+ and related complexes.

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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.6b00169. Additional HFEPR spectra of [FeO(TMG3tren)]2+, figure of a generic trigonal complex for use with AOM, tables of LFT matrices, discussion of the application of LFT to the calculation of spin-Hamiltonian parameters of [FeO(TMG3tren)]2+, listings of energy levels calculated from LFT, results of NBO population analysis, and optimized structures of simplified ligand variants of [FeO(TMG3tren)]2+ (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 The work carried out at the University of Minnesota was supported by the U.S. National Science Foundation (Grant CHE-1361773 to L.Q.) and a University of Minnesota graduate dissertation fellowship (to G.T.R.). The HFEPR studies were supported by the NHMFL, which is funded by the U.S. National Science Foundation (Cooperative Agreement DMR 1157490), State of Florida, and U.S. Department of Energy. The computational studies were supported by the Slovak Grant Agency VEGA under Contract 1/0598/16. We thank the HPC Center at the Slovak University of Technology in Bratislava, which is a part of the Slovak Infrastructure of High Performance Computing (SIVVP Project 26230120002, funded by the European Region Development Funds), for computing facilities.

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REFERENCES

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Article

Inorganic Chemistry

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HFEPR and Computational Studies on the Electronic Structure of a

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