Electron Paramagnetic Resonance Signature of Tetragonal Low Spin Iron(V)-Nitrido and -Oxo Complexes Derived from the Electronic Structure Analysis of Heme and Non-Heme Archetypes

Iron(V)-nitrido and -oxo complexes have been proposed as key intermediates in a diverse array of chemical transformations. Herein we present a detailed electronic-structure analysis of [FeV(N)(TPP)] (1, TPP2– = tetraphenylporphyrinato), and [FeV(N)(cyclam-ac)]+ (2, cyclam-ac = 1,4,8,11-tetraazacyclotetradecane-1-acetato) using electron paramagnetic resonance (EPR) and 57Fe Mössbauer spectroscopy coupled with wave function based complete active-space self-consistent field (CASSCF) calculations. The findings were compared with all other well-characterized genuine iron(V)-nitrido and -oxo complexes, [FeV(N)(MePy2tacn)](PF6)2 (3, MePy2tacn = methyl-N′,N″-bis(2-picolyl)-1,4,7-triazacyclononane), [FeV(N){PhB(t-BuIm)3}]+ (4, PhB(tBuIm)3– = phenyltris(3-tert-butylimidazol-2-ylidene)borate), and [FeV(O)(TAML)]− (5, TAML4– = tetraamido macrocyclic ligand). Our results revealed that complex 1 is an authenticated iron(V)-nitrido species and contrasts with its oxo congener, compound I, which contains a ferryl unit interacting with a porphyrin radical. More importantly, tetragonal iron(V)-nitrido and -oxo complexes 1–3 and 5 all possess an orbitally nearly doubly degenerate S = 1/2 ground state. Consequently, analogous near-axial EPR spectra with g|| < g⊥ ≤ 2 were measured for them, and their g|| and g⊥ values were found to obey a simple relation of g⊥2 + (2 – g∥)2 = 4. However, the bonding situation for trigonal iron(V)-nitrido complex 4 is completely different as evidenced by its distinct EPR spectrum with g|| < 2 < g⊥. Further in-depth analyses suggested that tetragonal low spin iron(V)-nitrido and -oxo complexes feature electronic structures akin to those found for complexes 1–3 and 5. Therefore, the characteristic EPR signals determined for 1–3 and 5 can be used as a spectroscopic marker to identify such highly reactive intermediates in catalytic processes.


■ INTRODUCTION
High-valent iron complexes featuring oxo (O 2− ) or nitrido (N 3− ) coordination are invoked as key intermediates in O 2 and N 2 activation processes. 1 In biology, several nonheme iron(IV)-oxo intermediates have been trapped in the reactions of a series of O 2 -activating iron enzymes, and were thoroughly characterized by absorption, resonance Raman (rR), and 57 Fe Mossbauer spectroscopy. 2 In parallel, synthetic chemists have prepared dozens of nonheme iron(IV)-oxo models in order to understand their structure−function relation. 3 Perferryl (Fe V = O) complexes have also been proposed in the chemistry of nonheme iron enzymes. 4 Compound I, formally an iron(V)oxo heme species, is pivotal intermediate of many hemecontaining oxygenases and peroxidases (e.g., chloroperoxidase, horseradish peroxidase, and cytochrome P450 family), 5 which play crucial roles in a range of biological processes including mitochondrial respiration, steroid regulation and degradation of xenobiotics. 5b−e However, 57 Fe Mossbauer measurements revealed that one of the oxidizing equivalents of compound I, in fact, is allocated to the porphyrin ligand, because its Mossbauer spectroscopic features are essentially identical to those of its one-electron reduced species, compound II consisting of a triplet Fe(IV)O unit (Chart 1). 6 EPR investigations showed that the ferryl moiety and the porphyrin π radical of compound I are weakly antiferromagnetically coupled, thus yielding an overall doublet ground state (S tot = 1/2). 7 However, model complexes of compound I all feature an S tot = 3/2 ground state due to moderately strong ferromagnetic coupling. 8 preparation and/or the availability of sophisticated facilities. More importantly, to reach unequivocal assignments of electronic structures, reference compounds, which are often homologous iron complexes with different oxidation states, are usually needed. Because of these limitations, alternative spectroscopic technique that allows to detect transient iron(V)-nitrido and -oxo complexes with higher efficiency and higher sensitivity is highly desirable.
The present work serves as a dual purpose. We first present a combined spectroscopic and computational study of the electronic structure of complex 1 in comparison with wellcharacterized iron(V) complexes 2−5. This enables us to identify the unique bonding feature of tetragonal low spin iron(V)-nitrido and -oxo complexes. On the basis of that, we propose characteristic EPR signatures for such species. Note that correlation of the electronic structure of trigonal iron(V)nitrido complex 4 with its g factors was published earlier by Smith, Kirk and Hoffman and co-workers. 30 ■ MATERIALS AND METHODS Sample Preparation and Photolysis. The ferric azido complexes, [Fe III (N 3 )(TPP)] (1 pro ) 31 and [Fe III (N 3 )(cyclam-ac)]-(PF 6 ) (2 pro ), 13a were synthesized by following the published procedures. Dry and degassed solvents were used to prepare the samples. The ferric azido precursors were dissolved in a 1:9 dichloromethane:toluene mixture for 1 pro or 1:9 methanol:nbutyronitrile for 2 pro to give 2 mM stock solutions. Aliquots of the azide solutions were loaded into standard 4 mm quartz EPR tubes before freezing in liquid nitrogen. Then, the tubes were placed in a finger Dewar filled with liquid nitrogen and photolyzed by an LED LUXEON III Star LED lamp (dominant wavelength of 470 nm). The entire photolysis to generate complex 2 in the EPR tubes was completed within 30 min, whereas for complex 1, the irradiation had to last for ca. 20 h. To prepare Mossbauer samples, droplets of the frozen solution of fully 57 Fe-enriched 1 pro (1.7 mM in the solvent mixture) were collected in liquid nitrogen and crushed into fine powder, which was then photolyzed for 18 h accompanied by periodic manual stirring. The powder was subsequently recovered from liquid nitrogen slurry and transferred to Mossbauer sample cups (ca. 0.7 mL). The photolyzed samples were always stored in liquid nitrogen to avoid decomposition of the desired iron(V)-nitrido species. An EPR sample of photolyzed 1 pro was subjected to rR measurements to validate the formation of 1.
EPR Measurements. Continuous-wave (cw) X-band EPR measurements were performed on a Bruker E500 ELEXSYS spectrometer equipped with the Bruker dual-mode cavity (ER4116DM) or a standard cavity (ER4102ST) and an Oxford Instruments helium flow cryostat (ESR 900). The microwave bridge was a high-sensitivity Super-X bridge (Bruker ER-049X) with integrated microwave frequency counter. The magnetic field controller (ER032T) was calibrated with a Bruker NMR field probe (ER035M). EPR simulations have been done with our own routines, esim_gfit and esim_sx. For spin quantitation, the experimental derivative spectra were numerically integrated by using the routine eview, and the results were corrected for their g value dependence for field-swept spectra by using Aasa and Vanngard approximation,32 i.e. dividing the integrals by the factor, 3 9 i i i i P av 2 57 Fe Mossbauer Measurements. 57 Fe Mossbauer spectra were recorded on a conventional spectrometer with alternating constant acceleration of the γ-source ( 57 Co/Rh, 1.8 GBq), which was kept at room temperature. The minimum experimental line width was 0.24 mm/s (full width at half-height). The sample temperature was maintained constant in an Oxford Instruments Variox cryostat. Isomer shifts are quoted relative to iron metal at 300 K.
Computational Setup. All calculations were performed by using the ORCA quantum chemical program. 33 For geometry optimizations, the BP86 34 functional was used in combination with the resolution of the identity (RI) 35 approximation. All atoms were described by the triple-ζ quality def2-TZVP basis set in conjunction with the def2-TZV/J auxiliary basis set required for the RI approximation. 36 Solvation effects were taken into account by employing the conductor like polarizable continuum model (CPCM), 37 for which, to be consistent with the experiment, acetonitrile (ε = 36.6) was chosen as the solvent. Numerical frequency calculations verified the optimized structures to be local minima on the potential energy surface.
The complete active space self-consistent field (CASSCF) calculations 38 were performed with the def2-TZVPP basis set along with the def2-TZVPP/C auxiliary basis set for the RI approximation. In the case of complexes 1−3 and 5, we first tested CASSCF (11,9) calculations, for which the active space consists of five d-orbitals, three nitrido-or oxo-2p based orbitals, respectively, and the bonding combination (σ eq ) with respect to the interaction between the Fe d x 2 −y 2 orbital and the equatorial ligands. It turned out that the CASSCF(11,9) computations predicted an erroneous ground state with an electron configuration of (nb) 2 (σ* eq ) 1 instead of (nb) 2 (π* Fe−N ) 1 . As a consequence, the computed g-values deviate from the experiment values significantly. We then enlarged the active space by adding three t 2g -derived 4d orbitals (4d xy , 4d xz , and 4d yz ), and the resulting CASSCF(11,12) computations provided a correct ground state as evidenced by the calculated g-values closely matching the experiment. For complex 1, in order to allow development of radical character in the porphyrin ligand, we also added four porphyrin π-orbitals, namely, a 1u , a 2u , and two e g orbitals on top of CASSCF (11,12). The resulting CASSCF (15,16) calculations with an active space containing more than 14 orbitals were treated by iterative-configuration expansion configuration interaction (ICE-CI), an approximated version of the full configuration interaction recently developed by our group. For complex 4, we employed an active space distributed 13 electrons into 14 orbitals CASSCF(13,14), including five Fe d-orbitals, three nitrido 2p based orbitals, two bonding partners of the d xy and d x 2 −y 2 orbitals, and four 4d orbitals (4d xy, 4d x 2 −y 2 , 4d xz and 4d yz ). To capture dynamic correlation effects, Nelectron valence perturbation theory of second order (NEVPT2) 39 calculations were performed on top of the CASSCF wave functions.
For g-value calculations using the multireference CASSCF/ NEVPT2 method, 40 we first diagonalized the spin−orbit coupling (SOC) matrix constructed by the five roots from the state-average CASSCF calculation, for which the diagonal elements were replaced by the NEVPT2 excitation energies. The g-values were then computed by using Gerloch−McMeeking equation in the basis of the relativistic wave functions, the eigenvectors of the SOC matrix. 41 ■ RESULTS AND DISCUSSION Spectroscopic Characterizations of Iron(V)-Nitrido Species. In the earlier work, the electronic structure of complex 1 was deduced only from its vibrational frequencies determined by the rR measurements. 11 In order to gain more insights into its nature, we carried out more thorough spectroscopic characterizations. In the present work, complex 1 was prepared by irradiating frozen solutions of 1 pro in quartz EPR tubes for 20 h. The samples thus obtained are closer to the usual conditions of chemical reactions in comparison with the previous work, where complex 1 was generated by photolysis of a solid thin film of 1 pro deposited on a cold tip in the incident Raman beam at 30 K. 11 Despite the different preparation protocol employed, the rR spectra measured for our photolyzed samples revealed signals at 883, 1371, and 1569 cm −1 ( Figure S5), which reasonably match the FeN stretching vibration and the marker bands of the porphyrin ligand reported before for 1 (876, 1373, 1576 cm −1 ,

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Article respectively). 11b The difference can be attributed to the solvent effect. Thus, the rR investigations confirmed the successful generation of complex 1.
The zero-field Mossbauer spectrum (Figure 1) of the photolyzed sample, which is prepared in a similar way by starting from 57 Fe-enriched 1 pro , exhibits two quadrupole doublets. The minor component can be attributed to the unreacted precursor as compared to the Mossbauer spectrum independently measured for 1 pro ( Figure S6). The newly formed major component that is assigned to 1 accounting for 67% of the total iron content in the sample has an isomer shift of 0.02 mm/s and a quadruple splitting of 2.49 mm/s. Notably, the isomer shift of 1 is comparable to those found for complexes 2, 2′, 2″, and 3 (Table 1), indicating that the iron oxidation states of 1 is also +V. The more negative isomer shifts observed for complexes 4, 5, 5′, and 5″ mainly originate from the more contracted FeN/O bonds. Typically, the iron-ligand distance is a more critical factor than the d N configuration of the iron center to determine the isomer shift, i.e. the shorter the iron-ligand distance, the more negative the isomer shift. 42 Consequently, to reach more reliable conclusion about the iron oxidation state, it is necessary to compare the isomer shifts of related complexes with similar chemical bonding.
Complex 1 pro produces a nearly axial EPR spectrum with effective g factors of 6.02, 5.89, and 2.01 ( Figure 2, traces a), typical for high spin iron(III) porphyrin complexes (S = 5/2) with a positive axial zero-field splitting. After 20 h of photolysis, the signal of 1 pro is attenuated, and a weak yet perceptible asymmetric zero-crossing signal around 400 mT appears with a very shallow trough extending to the high field ( Figure 2, traces b), rendering an almost axial spectrum with g || < g ⊥ ≤ 2. The resonances are attributed to complex 1. A reasonable fit gave g factors of 1.83, 1.70, and 1.0 for 1, Figure 1. Mossbauer spectrum of 18 h-photolyzed 1 pro measured at 80 K. The simulation (red line) is composed of two components. Parameters: δ = 0.02, |ΔE Q | = 2.49, Γ = 0.40 mm/s, w 2/1 = 1.32 (67%, green line), and δ = 0.40, |ΔE Q | = 0.59, Γ = 0.30 mm/s, w 2/1 = 1.10 (33%, blue line). Γ is the full-width at half-maximum of the Lorentzian lines and w 2/1 is the asymmetric broadening factor for the high-energy line of the doublets. The asymmetric broadening is introduced to mimics the effects of not perfectly fast spin relaxation for a half-integer spin species.

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Article wherein g min was estimated on the basis of the integrated absorption spectrum and fixed in the simulation. Double integration of the spectra, for which the g-dependence of the field-swept spectra was adjusted by Aasa-Vaenngard factors, 32 revealed that the yield of the 1 pro -to-1 conversion is 71% ( Figures S3 and S4), comparable to that determined by the Mossbauer measurements. This observation hence confirms our assignment of the emerged EPR signal to 1. For comparison, photolysis of 2 pro was carried out at the same conditions. Unlike that of 1 pro , the photoreaction of 2 pro in the EPR tubes completed within half an hour. Low spin ferric azido complex 2 pro elicits a rhombic spectrum with large g-anisotropy 13a (Figure 2, traces c, g max = 2.60, g mid = 2.29, and g min = 1.82). After photolysis, it completely changed into a wide-split spectrum at low g values that we attributed to the photolysis product, 2 ( Figure 2, traces d). The simulations yield g factors of 1.75, 1.64, and 1.0 for 2, similar to those detected for 1. Double integration of the spectra demonstrated nearly full recovery of the spin in the conversion of 2 pro to 2. Remarkably, such unconventional EPR spectra with three g factors all significantly lower than 2 were also observed for complexes 2′, 2″, 14 and 3 16a (Table 1).
Taken together, complex 1 must feature qualitatively the same electronic structure as those determined for 2 and 3. This notion is consistent with the observation that the FeN stretching frequency measured for 1 (883 cm −1 ) is comparable to those for 2 (864 cm −1 ) 13c and 3 (866 cm −1 ). 16b Therefore, complex 1 is a genuine iron(V)-nitrido species and possesses a low spin rather than high spin ground state. Different from complexes 2 and 3 whose precursors are both low spin complexes, 1 is evolved from a high spin complex. Thus, the formation of 1 must involve a change in the spin state. Our B3LYP calculations predicted the quartet state to be ∼15 kcal/ mol higher in energy than the doublet ground state. One can anticipate an even large gap for the sextet state in which all iron-nitrido antibonding orbitals are singly occupied. As such, the large driving force and the efficient spin-orbit coupling (SOC) of the iron center may render the required spin transition easily occur. Clearly, our findings show that low spin state of the ferric azido precursors is not the prerequisite for the photochemical generation of iron(V)-nitrido species. 43 The EPR spectrum of 1 differs markedly from those of the various forms of compound I, whose S tot = 1/2 ground state results from (weak) antiferromagnetic coupling between a triplet ferryl core and a porphyrin π-radical. 7 Because the isotropic exchange coupling (J) competes with the axial zerofield splitting of the ferryl moiety (D FeO ), the nature of the ground state depends on the degree of the resulting mixing of S tot = 1/2 and 3/2. As a consequence, the EPR spectra of the variants of compound I in different enzymes vary depending on the relative magnitudes of J and D FeO . For instance, g factors below 2 have been observed for compound I in chloroperoxidase 6c (g || = 2 and broad g ⊥ ≈ 1.73, J/D ≈ 1), and the EPR spectrum of horseradish peroxidase shows an exceedingly broad feature at g ≈ 1.99 due to a much smaller J/D FeO value and conformational strains. 7a In general, the spin Hamiltonian analyses 7a,c render the sharp g || feature close to 2 nearly independent of the J/D FeO value, whereas g ⊥ can be much smaller. Interestingly, the synthetic porphyrin model complexes of compound I show distinct S tot = 3/2 ground states with effective g values of g ⊥ eff ≈ 4 and g || eff = 2, independent of various porphyrin substitutions. 8 The situation for compound I and its models is thus distinct from that observed for 1, which features g || < g ⊥ ≤ 2. This finding further corroborates that complex 1 and compound I possess different electronic structures.
The EPR spectrum of complex 5 displays a near-axial pattern of g || < g ⊥ ≤ 2, 19 similar to that found for complexes 1−3, but has much smaller g shifts, the deviation of the measured g value from spin-only g value, 2. In contrast, a distinct EPR spectrum with g || < 2 < g ⊥ is observed for complex 4. 18 These observations hence give rise to a question about how to correlate the different g factors determined for complexes 1−5 with their electronic structures.
Ligand Field Analysis of Electronic Structures of Iron(V)-Nitrido/-Oxo Complexes and Their g Values. In this section, we first present a ligand-field bonding analysis of iron(V)-nitrido and -oxo complexes in tetragonal and trigonal coordination environments. On the basis of that, a quantitative model to rationalize the g values of tetragonal low spin iron(V)-nitrido and−oxo complexes (1−3 and 5) is developed. In the next two sections, the approximation used to derive this model will be verified by more rigorous multireference electronic-structure calculations using the CASSCF/NEVPT2 approach and finally the validity of the model will be carefully evaluated.
As elaborated elsewhere 44 the interaction of the iron center with oxo and nitrido ligands (E) is rather covalent and entails two π-bonds between the Fe-d xz/yz and E-p x/y orbitals, and one σ-bond involving the Fe-d z 2 and E-p z orbitals. The resulting antibonding molecular orbitals are labeled as π* FeE with a 2fold degeneracy and σ* Fe−E , respectively. For tetragonal coordination geometry, the remaining d xy orbital is essentially a nonbonding (nb) orbital, whereas d x 2 −y 2 interacts strongly with the equatorial donors of the supporting ligand, yielding the σ* eq molecular orbital. Thus, one envisions a 1+2+1+1 ligand field splitting pattern (Scheme 1a) with the energetic ordering of nb < π* FeE < σ* eq (the σ*-orbital in the equatorial plane) < σ* FeE , as proposed for complex [V IV (O)(H 2 O) 5 ] 2+ by Ballhausen and Gray. 45 For low spin d 3 centers, the only unpaired electron must occupy one of the doubly degenerate π* orbitals, and the resulting electron configuration of (nb) 2 (π*) 1 leads to a ground state of 2 E symmetry in the C 4v point group. However, even in ideal cases where the supporting ligands possess 4-fold rotation axes, such as TPP, Jahn−Teller distortions should lower the symmetry of the entire complex and lift the double degeneracy of the 2 E state.
In the case of trigonal coordination geometry, a 2+1+2 ligand field splitting with the energetic ordering of 2σ* eq < σ* FeE ≤ 2π* FeE (Scheme 1b) is often proposed, where σ* eq is the equatorial σ*-combination between the d xy and d x 2 −y 2 Scheme 1. Qualitative Orbital Splitting Pattern for Iron(V) Complexes

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Article orbitals and the equatorial donors of tripodal ligands. Note that the equatorial σ-antibonding interaction in pseudotetrahedral geometry is much weaker than the corresponding one in distorted octahedral or square pyramidal coordination arrangements. In the latter cases, the four lobes of the d x 2 −y 2 orbital all directly point to the donor atoms. Therefore, in a trigonal coordination environment the σ* eq orbitals usually have the lowest energy. Because of the 3d z 2 -4s-4p z mixing, σ* FeE is typically situated at lower energy than π* FeE . 9b Note that for a trigonal iron(IV)-nitrido complex supported by a bulky guanidinate ligand, DFT calculations suggest that the π* FeN orbitals lie above σ* FeN . 46 Despite this complexity, for low spin iron(V) complexes, the singly occupied molecular orbital (SOMO) must be one of the two σ* eq -orbitals. Consequently, the ground state is predicted to feature a (σ* xy, x 2 −y 2 ) 3 electron configuration, and to be of 2 E symmetry in the C 3v point group. Similar to the tetragonal situation discussed above, even when the supporting ligands possess three-fold rotation axes, the double degeneracy of 2 E cannot be maintained.
To gain further insight into the correlation between the electronic structure and the EPR g values of low spin iron(V) complexes, one needs to consider SOC between the ground state and low lying excited states with the same spin as the ground state. The g anisotropy and g shifts are predominantly originated from the mixing of excited states into the ground state under the influence of SOC and the resulting partial restoration of the orbital angular moment. 47 The sign of the g shifts can be predicted by using the following rule. 47 A DOMO-to-SOMO (DOMO = doubly occupied molecular orbital) transition causes a positive g shift, whereas a SOMOto-VMO (VMO = virtual molecular orbital) transition gives a negative g shift. The magnitude of the g shift is inversely proportional to the excitation energy.
As will be verified below, due to the overwhelming ironnitrido and−oxo interaction, complexes 1−3 and 5 feature an orbitally near doubly degenerate ground state. More importantly, the energy separation between the ground state with an electron configuration of (nb) 2 (π* y ) 1 and the first excited state (nb) 2 (π* x ) 1 is comparable to the effective SOC constant of iron(V) (∼578 cm −1 ). 48 Thus, we assume that the SOC within the effective 2 E ground state essentially dictates the g values, and the contributions from the higher lying excited states are negligible. According to the above rule, for 1−3, 5, the lowest-energy SOMO-to-VMO excitation (nb) 2 (π* y ) 1 → (nb) 2 (π* x ) 1 should give a dominant downshift of one g value (g || ), as experimentally measured, whereas for trigonal complex 4, the lowest-energy DOMO-to-SOMO excitation of σ* xy → σ* x 2 −y 2 should introduce a positive g shift in the z direction along the FeN bond. The (smaller) negative shift found for g ⊥ is in accord with the two higher lying SOMO-to-VMO excitations of σ* x 2 −y 2 → π* x/y .
In order to rationalize more quantitatively the g values of 1− 3 and 5, which largely determined by the intra-2 E excitations ((nb) 2 (π* y ) 1 →(nb) 2 (π* x ) 1 ), we first consider an ideal situation where complexes have an exact doubly degenerate 2 E ground state. In this case, one can show that only the lẑ·sẑ term contributes nonvanishing matrix elements to the SOC Hamiltonian (For details, see the Supporting Information), which, hence, can be written as Here to a good approximation the SOC operator is treated as a single-electron operator. 47a Furthermore, to simplify the calculation, one can use complex d-orbitals, which are eigenfunctions of lẑ. These complex d-orbitals are related to the usual real d-orbitals by a unitary transformation. Specifically, the two degenerate real d xz and d yz orbitals in C 4v symmetry correspond to the complex d +1 and d −1 orbitals. Thus, the four basis functions of the 2 E state can be characterized by the orbital and spin magnetic quantum numbers, L M and S M , viz. |L M S M ⟩. Specifically, Here the coefficients α Fe and α N denote the contributions from iron 3d-and nitrido or oxo p-orbitals, and the indices α and β at the d and p functions denote the spin part. Apparently, |L M S M ⟩ is the eigenfunction of the SOC operator, and its energy E is obtained by acting the SOC Hamiltonian on itself. Furthermore, ζ Fe is the effective SOC constant of Fe(V), whereas the SOC of the ligand-atoms is neglected. In summary, as expected, the 2 E ground state in perfect C 4v symmetry is split by the first-order SOC into two Kramers doublets.
Lowering the symmetry from C 4v to the actual symmetry C 1 of the complexes under investigation leads to mixing of |+1S M ⟩ and |−1S M ⟩, because eventually only S M is a good quantum number. Such mixing can be parametrized in terms of a mixing angle φ (φ ∈[0, π/4]), which yields the wave functions of the lowest-energy Kramers doublet as Furthermore, the Zeeman splitting is described by Here μ B is the Bohr magneton, g e ≈ 2 is the spin-only g value, and B is the magnetic field. For a given isolated doublet, one can compute the g values as defined for Kramers doublets in a weak-field approximation by using To this end, the Zeeman matrix for the magnetic field along the Z direction can be computed as follows (2) Note that the final g matrix computed by this approach is only determined by the mixing angle φ and is independent of the metal−ligand covalency parametrized by α values (for details, see the Supporting Information).
One can eliminate φ in eqs 1 and 2, and obtain a direct relation between the two g factors.
This equation represents the lower quadrant of a full cycle with a radius of 2 and the origin at (0,2) ( Figure 3). In the present case, if the energy gap between the two components of 2 E is zero, then g || = g ⊥ = 0. Because the two components of the lowest energy Kramers doublet have orbital angular momenta of ± ℏ and spin angular momenta of ∓ℏ/2, the magnetic moment arising from the orbital angular momentum exactly cancel out that from the spin angular momentum. However, if the energy separation is close to infinity, then g || = g ⊥ = 2, because the orbital angular momentum is completely quenched and the system has an orbitally nondegenerate ground state. The g values determined experimentally for complexes 1−3 and 5 all obey eq 3 nicely.
Ab Initio Calculations of Electronic Structures of Iron(V)-Nitrido/-Oxo Complexes. As analyzed above, to rationalize g values of transition metal complexes, one need to consider the SOC between the ground state and low lying excited states, especially for complexes 1−5 which likely feature orbital near degeneracy. In this regard, DFT is not a method of choice, because it cannot treat the ground and excited states on an equal footing. 49 Therefore, it is necessary to employ wave function based highly correlated CASSCF/ NEVPT2 approach. In our earlier work on the spectroscopy and reactivity of high valent iron-oxo complexes, 22,50 this method has been shown to deliver reliable results not only for the ground state but also for the excited states. The balanced active space should consist of the Fe-centered 3d orbitals and their ligand centered bonding partners. For complexes 1−3, the active space has to include three t 2g derived 4d orbitals (4d xy , 4d xz , and 4d yz ); otherwise, the CASSCF calculations predicted erroneous ground states (for details, see the Supporting Information). To examine the electronic structure of complex 1 in an unbiased manner, we further added four porphyrin π-orbitals, namely, a 1u , a 2u , and two e g , into the active space, which should allow the system to develop a porphyrin radical in the calculations. Hereafter, we first discuss the ground state of complexes 1−5, and then discuss their excited states.

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Article formulated as an iron(IV)-nitrido species interacting with a porphyrin radical. The same bonding picture was delivered by the CASSCF(11,12) calculations ( Figure S13); therefore, in the following we employed the smaller active space to compute its low lying ligand-field excited states. The predicted groundstate electron configuration of complex 1 corresponds to one component of the 2 E state. To accommodate such a ground state for complex 1, the optimized geometry shows that the Fe center is situated above the porphyrin plane, and that the two Fe−N bonds (1.981, 1.974 Å) along the x-direction are considerably shorter than those (2.000, 1.996 Å) along the ydirection ( Figure S19). These geometric distortions raise the π* x orbital and simultaneously lower the π* y orbital.
Unexpectedly, the computed spin population of the iron center in complex 1 is less than that of the nitrido ligand. In line with this observation, the π* x,y orbitals contains more Np x,y contribution than that from the Fe-d xz,yz atomic orbitals. Thus, the iron-nitrido interaction features so-called "inverted" bonding, 44c,51 in contrast to usual situations where the metal d character prevails in metal−ligand antibonding orbitals. Thus, there is substantial radical character in the nitrido ligand of complex 1, and its electronic structure is best described as a resonance hybrid between two limiting bonding situations, Fe V (S Fe = 1/2)N 3− ↔ Fe II (S Fe = 0)N • (S N = 1/2), in the latter case the iron center featuring an electron configuration of (d xy ) 2 (d xz ) 2 (d yz ) 2 . This bonding description is consistent with that deduced from the earlier ground-state DFT calculations. 13b However, for iron(V)-oxo complex 5, the spin population of the iron center is higher than that of the oxo group ( Figure S17). The difference clearly originates from considerably higher energy of the nitrido p-orbitals than the oxo p-orbitals. Furthermore, as analyzed in our earlier work on related iron(IV)-oxo complexes, 22,50 the unpaired electron in the SOMO (π* y ) is expected to contribute positive spin density in the Fe-d yz and N-p y atomic orbitals, while negative spin density on the iron center, which reduces the total spin population, mainly stems from the spin polarization. Because in the present case, the nitrido ligand has a larger spin population than the iron center, spin polarization induces some marginal negative spin density in the Fe-d xz and -d z 2 atomic orbitals as suggested by the occupation numbers of the DOMOs (π x and σ z ) substantially deviating from their anticipated value (2), and those of the corresponding VMOs (π* x and σ* z ) considerably differing from 0. Consequently, the spin density does not exactly resemble the shape of the SOMO and shows a negative fraction in the xz plane (Figure 4b). The situation found for complex 1 is exclusively different from those for 6, 7, and 7-H + where the peripheral groups of the central Fe IV O unit possess sizable negative spin density. 22 Relative to 1, similar leading electron configurations were found for the ground states of complexes 2, 3, and 5 (Figures S14, S15, and S17). For complex 2, the double degeneracy of the effective 2 E ground state is lifted by the interaction of the iron center with the trans π-donating acetate ligand. The optimized geometries of complexes 3 and 5 reveals that the iron centers move out of the equatorial plane and that the computed equatorial metal−ligand bond distances along the xdirection substantially differ from those along the y-direction ( Figure S19), an analogous situation found for complex 1. Such geometric distortions stabilize one of the two components of the 2 E ground states, and destabilize the other. Table 2 summarizes the calculated energies of important excited states for all complexes under investigation. Complexes 1−3 feature a very low-lying excited state with an electron configuration of (nb) 2 (π* x ) 1 , which lies above the ground state by only several hundred wavenumbers. Thus, complexes 1−3 possess an orbitally near degenerate ground state of effectively 2 E symmetry, consistent with the ligand field analysis. It should be noted that adjusting the FeN distance in the (FeN) 2+ core, the only geometric freedom of this moiety, cannot lift the double degeneracy of the two FeN π-bonds. Therefore, the small energy separation must arise from much weaker interactions between the iron center and the supporting ligand as found for 1−3. The excitation energy of π* y →σ* z computed for 1 is much lower than those for 2 and 3, mainly because the lack of a trans ligand in 1 stabilizes the σ z * orbital. In line with this reasoning, the Fenitrido bond length (1.56 Å) estimated for complex 1 is slightly shorter than those (∼1.60 Å) for complexes 2 and 3.
Complex 5 features a similar electronic structure as 1−3, except for the considerably larger energy separation between the two components of 2 E. Furthermore, for complex 5, the excitation energy of π* y →σ* eq was predicted to be much higher than that of π* y →σ* z . This is due to the strong σdonating capability of TAML, which raises the σ* eq orbital above σ* z . 52 The excitation from the nb d xy orbital to the Fe E π* orbital can be used to gauge the differential bonding strength between the iron-nitrido and -oxo π-interactions. 53 These excited states of complexes 1−3 were found to lie much higher in energy than that of 5, thereby suggesting that the πbond of iron(V)-nitrido complexes is substantially stronger than that of iron(V)-oxo species. For complexes 1 and 5, both species featuring the same coordination geometry, our calculations showed that the excitation from π* y to the vacant σ* z orbital requires similar energy, although the π* y orbital of 1 is by far more destabilized than that of 5. These findings show that iron(V)-nitrido complexes have stronger σ-bonds than iron(V)-oxo compounds. As a consequence, the iron-oxo interaction is more vulnerable to subtle perturbations. To test the ligand effect, we calculated the gap between the two components of the effective 2 E ground state of the hypothetical nitrido congener of 5, [Fe V (N)(TAML)] 2− (5-N). The obtained value of 1000 cm −1 is higher than those found for complexes 1−3 but lower than that for 5. Therefore, not only the distinct iron(V)-nitrido and -oxo bonding strengths but also the strong donating capability of the TAML ligand lead to the larger energy separation for complex 5 compared to 1−3. Because there are four negatively charged donors in TAML, Table 2. CASSCF/NEVPT2 Excitation Energy (cm −1 ) for Complexes 1−5 Excitation π* y →π* x π* y →σ* eq nb→π* y π* y →σ* z Excited state (nb) 2 (π* x ) 1 (nb) 2 (σ* eq ) 1 (nb) 1 (π* y ) 2 (nb) 2 (σ* z ) 1 Excitation σ* xy →σ* x 2 −y 2 σ* x 2 −y 2 → π* x σ* x 2 −y 2 → π* y σ* x 2 −y 2 → σ z * Excited state (σ* xy ) 1 (σ* x 2 −y 2 ) 2 (σ* xy ) 2 (π* x ) 1 (σ* xy ) 2 (π* y ) 1 (σ* xy ) 2 (σ* z ) 1 4 4220 20020 22500 22280

Journal of the American Chemical Society
Article the gap estimated for 5 is probably close to the maximum value that can be reached in the iron(V)-nitrido and -oxo chemistry. The differential bonding strength between the iron-nitrido and -oxo interactions explain why complex 1 features a distinctly different electronic structure compared to compound I. Our calculations show that, due to the much stronger ironnitrido π-interactions, the two π* FeN orbitals (−3.8 eV) of the hypothetical one-electron reduced form of complex 1 are situated at higher energy than the porphyrin a 1u (−5.2 eV) and a 2u (−5.0 eV) orbitals ( Figure S18). Consequently, the electron residing in the π* FeN orbital is more likely to be removed in the one-electron oxidation process. In other words, if a species formulated as [Fe IV (N)(TPP •+ )] 0 were to be generated in the photolysis, the electron transfer from the singly occupied π* FeN orbitals to the vacant porphyrin π*orbital would have a tremendous driving force and would happen spontaneously. Further experimental investigations are required to verify this interpretation.
In agreement with an earlier study reported by Cutsail III et al.,30 complex 4 has essentially an orbitally nondegenerate ground state with a leading electron configuration (78%) of (σ* xy ) 2 (σ* x 2 −y 2 ) 1 ( Figure S16). The considerably large energy gap (4220 cm −1 ) of the two components of 2 E mainly results from the strong Jahn−Teller distortion in the equatorial plane, as evidenced by three distinct FeC bond lengths (1.932, 1.947, and 1.969 Å) shown in the crystal structure of 4. As depicted in Figure S16, both σ* xy and σ* x 2 −y 2 orbitals are essentially nonbonding in nature, because they contain predominant iron 3d character (94% and 84%, respectively) and rather limited C lone-pair character (<5%). The excitations of σ* x 2 −y 2 → π* x/y for complex 4 are, in fact, equivalent to those of nb→π* y for complexes 1−3, because in both transitions one electron is promoted from the nb orbital to the FeN π* orbital. These excitations of 1−4 were estimated to have comparable energy despite their different iron-nitrido bond orders. This observation is consistent with the notion that the SOMO (σ* x 2 −y 2 ) of complex 4 is raised to higher energy due to the significant Jahn−Teller distortion. For complex 4, the excitation energy of σ* x 2 −y 2 → π* x/y is comparable to that of σ* x 2 −y 2 → σ* z , thereby suggesting that the π-bond in 4 is as strong as its σ-bond. This finding is due to the 3d z 2 -4s-4p z mixing, 30 which significantly drops the energy of the σ z * orbital.
Ab Initio Calculations of the g Values of Iron(V)-Nitrido and -Oxo Complexes. The computed g values of complexes 1−5 by using CASSCF/NEVPT2 approach are summarized in Table 1. The theoretical results of complexes 1, 4, and 5 are in reasonable agreement with the experiment. However, for complexes 2 and 3, our computations do not achieve quantitative agreement, especially for the lowest g components. Nevertheless, the estimated g values of complexes 1−3 and 5 reproduced the near-axial pattern with g || < g ⊥ ≤ 2 and the lowest g factors (g || ) were found to align along the FeE bonds ( Figure S22). For complex 4, the largest g value was predicted along the FeN bond, and the other two are situated in the equatorial plane ( Figure S22). In contrast to the ab initio results, the DFT computed g factors of complexes 1− 3 and 5 are all very close to 2 (Table S1), further corroborating the notion that often DFT methods cannot be applied to orbitally near degenerate systems.
As discussed above, complexes 1−3 and 5 all possess a lowlying excited state. Thus, the large deviations of the estimated g values likely result from the error in the computed excitation energy of this state. Taking complex 1 as an example, we examined its influence on the g values. In a series of five-root CASSCF/NEVPT2 calculations, we systematically varied the transition energy of π* y →π* x from 0 to 6000 cm −1 and kept the energy of other excited states fixed at the initially calculated values (Figure 5b). In parallel, we also carried out similar tworoot CASSCF/NEVPT2 computations, where only the SOC of the effective 2 E ground state was taken into account ( Figure  5a). The results obtained from both calculations are essentially identical. A similar behavior was also found for complex 2 ( Figure S21). These findings suggest that the g values of complexes 1 and 2 are almost completely determined by the SOC between the two components of 2 E, which verifies the assumption of the ligand field model. Specifically, as the excitation energy changes from 0 to 3000 cm −1 , the g || and g ⊥ values rocket from 0 to 1.8 and 2.0, respectively. As the excitation energy further increases, the g || component slowly approaches to 2, while g ⊥ levels off at 2. Thus, the g || value is Figure 5. g values of complex 1 as a function of the excitation energy of π* y →π* x calculated by using CASSCF(11,12)/NEVPT2 calculations averaging two doublets (a) and five doublets (b). The experimental g values are denoted by dashed lines at g = 1.00, 1.70, and 1.83.

Journal of the American Chemical Society
Article more sensitive to the variation of the excitation energy, because it gets saturated at higher excitation energy than g ⊥ . To achieve better agreement with the experimental g values of complex 1 indicated by gray dashed lines in Figure 5, the excitation energy should be in the range of 600−800 cm −1 , at most 200 cm −1 above the calculated excitation energy (Table 2). This error is definitely beyond the accuracy of any quantum chemical calculations. Thus, our theoretical results clearly demonstrated that a minor change in the excitation energy of π* y →π* x has drastic influence on the g values, in particular g || . This explains the large error in the calculated g values of complexes 2 and 3, because their first excited states are below 2500 cm −1 .
Given the electronic-structures of complexes 1−3 and 5, we surmise that probably all tetragonal low spin iron(V)-nitrido and -oxo complexes feature effective 2 E ground states. Because of the exceedingly strong σand π-donating capability of the nitrido and oxo ligands, the overwhelming iron-nitrido and -oxo bonding overrides any other metal−ligand interactions, which in turn slightly lift the double degeneracy of 2 E. Bendix et al. proposed that the π* orbitals in [Cr V (N)Cl 4 ] 2− can be significantly destabilized and hence lie higher in energy than the σ* eq orbital. 54 Consequently, the classical 1−2−1−1 orbital splitting (Scheme 1a) does not hold true for [Cr V (N)Cl 4 ] 2− . Thus, one can envisage a ground-state electron configuration of (nb) 2 (σ* eq ) 1 for a low-spin iron(V)-nitrido and -oxo complex with a very weak equatorial coordination. To test this hypothesis, we computationally examined the corresponding hypothetical iron(V) complexes, [Fe V (N)Cl 4 ] 2− and [Fe V (O)Cl 4 ] − ( Figure S20). It turns out that both complexes feature qualitatively the same electronic structure as those found for complexes 1−3 and 5. This finding further corroborates our proposed general bonding feature for tetragonal low spin iron(V)-nitrido and -oxo complexes. As a consequence, their EPR spectra would show a near-axial pattern with g || considerably less than 2, and, more critically, the g || and g ⊥ values fit eq 3, in analogy to those measured for complexes 1−3 and 5.
Eq 3 has been shown to succeed in correlating the g || and g ⊥ values of complexes 1−3 and 5, because our numerical calculations revealed that the contributions from the higher lying excited states, other than the first excited state, to the g shifts are negligible ( Figure 5). On the basis of the electronic structures found for complexes 1−3 and 5, tetragonal low spin iron(V)-nitrido and -oxo complexes may be classified into two classes according to their equatorial coordination strength. On one hand, if complexes feature weak equatorial coordination, as exemplified by complexes 1−3, they typically have a small energy gap of ∼1000 cm −1 for the effective 2 E ground state. Their closely lying excited states likely arise from promoting the α-electron residing in the SOMO (π* Fe-E ) to the equatorial σ-antibonding orbital (σ* eq ). These excited states were computed to be situated at ∼5000 cm −1 above the ground state for complexes 1−3. Because the π-bonds of iron(V)-oxo complexes are much weaker than those of iron(V)-nitrido compounds, the corresponding excitations (π* Fe−O →σ* eq ) for iron(V)-oxo complexes should have much higher energy. On the other hand, if tetragonal low spin iron(V)-nitrido and -oxo complexes, such as 5, are supported by very strong equatorial ligands, such systems often possess an energy separation of at most 2500 cm −1 for the effective 2 E ground state. However, different from the situation discussed above, the closely lying excited states probably originate from exciting the β-electron in the doubly occupied nb orbitals to the SOMO (π* Fe-E ). Our calculations on complexes 1−3 and 5 show the lower bound of the energy of these excited states is ∼14000 cm −1 . Taken together, for both classes the energy of other excited states is at least four times higher than the energy separation of the effective 2 E ground state. Therefore, the in-state SOC essentially determines the g values of tetragonal iron(V)nitrido and -oxo complexes, which provides a rationale for the general applicability of eq 3.
As elaborated in our earlier work, 22 complexes 6, 7, and 7-H + feature different bonding situations from those found for 1−3 and 5. As a consequence of their distinct electronic structures, the g values of 6, 7, and 7-H + are all close to 2. More importantly, our theoretical studies revealed that complexes 5 and 5′ only can initiate one-electron chemistry, in agreement with experimental findings, 28 whereas 6 can function as a two-electron oxidant. 22 The reactions of CH and CC bond oxidation with complex 6 proceed without an intervening intermediate, which nicely explains the stereospecificity observed experimentally.

■ CONCLUSION
Our experimental and theoretical investigations evidence that complex 1, a nitrido congener of compound I, is a bona fide low spin (S = 1/2) iron(V)-nitrido complex. The multireference CASSCF/NEVPT2 calculations revealed that tetragonal iron(V)-nitrido complexes 1−3 all feature a unique electronic structure having an orbitally near degenerate ground state with an electron configuration of (nb) 2 (π* FeN ) 1 . A similar bonding situation was also found for tetragonal iron(V)-oxo complex 5, but the gap between the two components of the effective 2 E ground state is larger. As a manifestation of their analogous electronic structures, their EPR spectra exhibit a near-axial pattern with g || < g ⊥ ≤ 2, and the lowest g component is considerably lower than 2. On the basis of their unique bonding features, a simple equation to correlate their g || and g ⊥ values, g ⊥ 2 + (2 − g ∥ ) 2 = 4, was derived. However, an electron configuration of (σ* xy ) 2 (σ* x 2 −y 2 ) 1 was predicted for trigonal iron(V)-nitrido complex 4, and due to strong Jahn−Teller distortions the system has essentially an orbitally nondegenerate ground state.

Chart 3. Open-Shell Square Planar Nitrido Complexes
Journal of the American Chemical Society Article Consequently, complex 4 exhibits a distinct EPR spectrum with g || < 2 < g ⊥ .
Further in-depth electronic-structure analysis suggested that tetragonal low spin iron(V)-nitrido and -oxo complexes possess electronic structures akin to those found for complexes 1−3 and 5. Thus, the EPR signatures determined for complexes 1−3 and 5 can be used as a spectroscopic marker to identify analogous species in future studies.
This work provides deep insight into the electronic structures of iron(V)-nitrido and -oxo complexes, particularly in tetragonal coordination environments. The results should aid in detecting such important, yet usually short-lived, intermediates and understanding their functions in complex biological or industrial processes.

* S Supporting Information
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.8b11429.
EPR spectra of azide precursors (1 pro and 2 pro ) and the samples after photolysis, Raman spectrum of photolyzed 1 pro , Mossbauer spectrum of 1 pro , the effect of the double d-shell on the ground state of complex 2, CASSCF electronic structures of complexes 1−5, key geometrical parameters of complexes 1−5 and the hypothetical complexes, dependence of g-tensors on the π* y → π* x excitation energy for complex 2, orientation of the g matrices for complexes 1−5 (PDF)