Probing Physical Oxidation State by Resonant X‐ray Emission Spectroscopy: Applications to Iron Model Complexes and Nitrogenase

Abstract The ability of resonant X‐ray emission spectroscopy (XES) to recover physical oxidation state information, which may often be ambiguous in conventional X‐ray spectroscopy, is demonstrated. By combining Kβ XES with resonant excitation in the XAS pre‐edge region, resonant Kβ XES (or 1s3p RXES) data are obtained, which probe the 3dn+1 final‐state configuration. Comparison of the non‐resonant and resonant XES for a series of high‐spin ferrous and ferric complexes shows that oxidation state assignments that were previously unclear are now easily made. The present study spans iron tetrachlorides, iron sulfur clusters, and the MoFe protein of nitrogenase. While 1s3p RXES studies have previously been reported, to our knowledge, 1s3p RXES has not been previously utilized to resolve questions of metal valency in highly covalent systems. As such, the approach presented herein provides chemists with means to more rigorously and quantitatively address challenging electronic‐structure questions.


Introduction
Thec oncept of oxidation state is fundamental to how chemists communicate about electronic structure and chemical reactivity.W ed istinguish formal oxidation states,w hich are effectively used for bookkeeping of electrons,f rom physical oxidation states,w hich are assigned based on experimental observables.S pectroscopic methods play ak ey role in the identification of physical oxidation states.X -ray spectroscopy is frequently utilized to assign oxidation states in transition metal (TM) complexes,l argely due to its element selectivity and involvement of core electron excitations which provide an experimental means to probe the changes in effective nuclear charge at the selected photoabsorbing atom. Metal K-edge X-ray absorption spectroscopy (XAS) serves as areasonable fingerprint for changes in metal oxidation state, with the 1s to 4p edge features of first-row transition metals (TMs) shifting up by~1eVp er unit change in oxidation state. [1][2][3][4][5][6][7][8][9][10][11] However,asother factors,including ligand identity, coordination number, and metal spin state,c ontribute to the rising edge position, [10,[12][13][14][15][16][17] caution must be exercised in using the metal K-edge energies as ag eneralized measure of oxidation state.This observation has led to significant debate in the literature as to how edges can be quantitatively interpreted. [18][19][20] Metal L-edge XAS (2p!3d) [21][22][23][24][25][26] can also provide covalencya nd metal oxidation state information, but experimental intensity and covalencyc an only be correlated through computational studies.T hese correlations may be further biased by the computational protocol or individual interpretation. [19,27] In this regard, very similar Cu L-edge data of formal Cu III complexes have been used to both support [27] and dismiss [19] aC u III physical oxidation state assignment.
In addition to XAS,o ne can also utilize X-ray emission spectroscopy (XES) to obtain insight into the physical oxidation state and spin state of aT Ma bsorber. [28][29][30][31][32][33][34][35][36][37][38][39] The Kb mainlines in first-row TMs correspond to the emission process that occurs when an electron in the 3p shell refills the 1s core-hole created upon ionization, resulting in a3 d n 3p 5 final state (FS). Hence,Kb mainlines are dominated by 3p-3d exchange coupling that splits the mainline into Kb 1,3 and Kb' features and provides information about the number of unpaired d-electrons (where al arger number of unpaired delectrons results in larger 3p-3d exchange coupling). [36,[39][40][41] However,d ue to the covalent dilution of 3d character by ligand-based orbitals,adecrease in d-count due to oxidation may be countered by the corresponding increase in metalligand covalency,y ielding as imilar net 3p-3d exchange splitting for molecules of different d-counts. [14,42] Consequently,itappears that there are many ways for Xray spectroscopic measurements to lead to ambiguous conclusions.Inour view,this issue is best addressed by taking aholistic view of all available spectroscopic data (both X-ray based and other methods) to arrive at aconsistent picture of the electronic structure.I narecent study [14] of dimeric [Fe 2 S 2 ] 2+/1+/0 complexes spanning three oxidation states,w e showed that the rising edges of the diferrous and mixed valent iron dimers are nearly superimposable and that the Kb XES mainlines of the full [Fe 2 S 2 ] 2+/1+/0 series are essentially identical. Despite this,c rystallographic data, Mçssbauer, and calculations of spectroscopic data supported diferrous, mixed-valent, and diferric oxidation states assignments for these complexes,r espectively.B yc ombining spectroscopic results with computation, we were able to highlight the relative strengths and weaknesses of each spectroscopic approach in assessing the oxidation state.
This however, raises an important question:isthere aspectroscopic approach that allows our concepts of metal valency, covalency, and oxidation state to be more rigorously tested and experimentally assessed? It is here that we draw inspiration from the words of Linus Pauling in his 1948 Liversidge lecture where he stated with regard to our understanding of valency, "…and we may hope that powerful methods of investigation that are not yet known will be discovered". [43] In our view, resonant X-ray emission spectroscopy (RXES also known as resonant inelastic X-ray scattering (RIXS)) is atool with the potential to fulfill this role.R XES has historically been at ool for physicists, [44][45][46][47][48] and, while various types of RXES experiments have recently been utilized by the chemistry community, [49][50][51][52][53][54][55][56][57] it is clear that we are still evolving our understanding of the rich chemical information content of these spectra. In particular,s ignificant progress has been made utilizing 2p3d and 1s2p RXES to extract d-d transition energies and L-edgelike information, respectively. [49,52,53,58,59] Additionally,1 s3p RXES has been utilized to obtain spin and oxidation state selective XAS,o ften referred to as Kb-detected XAS. [60][61][62][63][64] However,t oo ur knowledge the detailed chemical and electronic structural information contained in the 1s3p RXES spectra themselves has yet to be fully explored.
Below,wepresent 1s3p RXES (Kb RXES) as ameans to recover physical oxidation state information, which may be lost in classical non-resonant emission (Kb XES) measurements due to the countering effects of covalency and metal dcount ( Figure 1). As ystematic series,i ncluding ferrous and ferric tetrachlorides,aswell as iron sulfur dimers,tetranuclear clusters,and the MoFeprotein of nitrogenase (Figure 2), was studied by non-resonant and resonant Kb XES,aswell as Kbdetected high energy resolution fluorescence detected (Kb HERFD) XAS,w hich allows for higher resolution than standard XAS. [5,9] In aKb RXES experiment, the 1s electron is excited into specific unoccupied orbitals by tuning the incident excitation energy.F or instance,w hen resonantly exciting into the preedge region of the XAS spectra (dominated by 1s to 3d transitions), 1s3p RXES spectra are obtained, with 3p 5 3d n+1 FS.B yp erforming both resonant and non-resonant XES,w e are able to experimentally differentiate between different 3d n counts despite the changes in covalency. As such, the presented 1s3p RXES approach provides chemists with atool for more rigorously assigning physical oxidation states.T oour knowledge the ability to use 1s3p RXES to assess oxidation states in highly covalent systems has not previously been reported. Thee xtension of 1s3p RXES to the MoFep rotein of nitrogenase further establishes the viability of this method for studying electronic structural questions in biological systems.

Fe K-Edge XAS and (Non-resonant) Kb XES
In order to discuss the advantages of 1s3p RXES,i ti s helpful first to illustrate how changes in oxidation state manifest in Fe Kb HERFD-XAS and Kb XES,and how these changes are modulated by covalency. Figure 3A  TheX AS spectra show the classic changes that one expects to see upon oxidation of the metal center.Namely,the Fe K-edge shifts up in energy by~1.2 eV,r eflecting the increase in effective nuclear charge on going from Fe 2+ to Fe 3+ .I nc ontrast, the changes in the Kb mainlines are more subtle,w ith am odest decrease in the intensity of the Kb' feature (at ca. 7045 eV) and aslight decrease in the energy of the Kb 1,3 maximum (by À0.4 eV) on going from d 6 S = 2F e 2+ to d 5 S = 5/2 Fe 3+ .I nas imple picture,o ne would expect the

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Forschungsartikel 10202 www.angewandte.de splitting between the Kb 1,3 and Kb' to increase with an increasing number of unpaired de lectrons.T he fact that the splitting of the Kb mainline features is somewhat smaller in the S = 5/2 ferric case than the S = 2f errous case indicates that the increase in covalency( resulting from the FeÀCl bonds contracting from (2.30 AE 0.01) to (2.18 AE 0.01) upon oxidation) counters the increase in spin. [65] Figure 3B shows ac omparison of the Fe K-edge XAS (top) and Kb XES (bottom) for aseries of sulfide bridged iron dimers clusters,i dentified by their formal oxidation state as diferrous L 2 Fe II Fe II S, mixed valent [L 2 Fe II Fe III S 2 ] 1À and diferric L 2 Fe III Fe III S 2 .T he assignment of oxidation states in this series is based on both structural changes and Mçssbauer parameters (Figures S1,2 and Tables S1,2). While the diferrous complex has the expected lowest energy rising edge,the mixed-valent and diferric complexes are nearly superimposable.Consequently,inthis case,the use of the Fe K-edge as an isolated measure of oxidation state could lead to an incorrect assignment of the physical oxidation state.F or the Kb mainlines,t he changes are even smaller. Upon going from the diferrous to the diferric,t he Kb 1,3 maxima shift by < 0.3 eV and the Kb' for all three complexes remains constant at 7059.3 eV.T his is once again attributed to the canceling effects of covalencya nd changing d-count, as has been previously established. [29,37,61,65,66] These observations clearly limit the information content of Kb XES,a nd also provide acautionary note against using these data to assess radiation damage.
Given the ambiguity in both the XAS and XES for the iron sulfur dimer,tetramers and MoFeprotein, as well as the small changes in the XES of the iron chlorides,o ne can reasonably question how useful either method is for assessing oxidation states.D ot he data suggest that discussions of specific oxidation state assignments become meaningless in the limit of high covalency, as is sometimes suggested in the literature? [70,71] Fort he iron chloride and iron sulfur series, this is clearly not the case.B oth the structural changes and Mçssbauer parameters are fully consistent with assigned oxidation states ( Figures S1,2 and Tables S1,2). Similarly, combined spectroscopic and computational studies have also clearly established oxidation state differences in the cubanes relative to the all-ferrous P-cluster and FeMoco cofactors in the MoFep rotein. [72] Hence,t he question is,c an meaningful and quantifiable differences be obtained from X-ray spectro-scopic approaches in order to assess the electronic structural changes?

1s3p RXES of Iron Tetrachlorides
As shown in Figure 1, in a1s3p RXES experiment, rather than ionizing a1 se lectron to the continuum, the electron is resonantly excited to a3 do rbital. This produces a1 s 1 3d n+1 intermediate state (IS), and a3 p 5 3d n+1 final state (FS). Thus, the contrasting electronic configurations accessed via resonant (d n+1 )a nd non-resonant (d n )X ES will result in distinct multiplet structures,a nalysis of which could allow for unambiguous assignment of physical oxidation states.
In order to illustrate this hypothesis and show the dependence of RXES on the excitation energy,w ep resent 1s3p RXES of [Fe II Cl 4 ] 2À ,a nd [Fe III Cl 4 ] 1À ,a tt hree different incident excitation energies:o ne in the pre-edge and two in the rising edge ( Figure 4). Examination of the 1s3p RXES data for [Fe II Cl 4 ] 2À ,when exciting into the rising edge region at 7119.2 eV and 7123.2 eV shows that the spectra are essentially identical to the Kb XES,w ith Kb 1,3 maximum at 7161 eV and aK b' at~7047 eV.T his indicates that at the rising edge energies,the 1s electron is being excited into high energy unoccupied orbitals with no impact on the p-d exchange interactions that dominate the Kb mainline region and there is no added information from the 1s3p RXES.I n contrast, the 1s3p RXES spectra of [Fe II Cl 4 ] 2À change dramatically upon resonant excitation into the pre-edge (1s to 3d). Tw oc lear features appear in the Kb 1,3 region with maxima at~7059.3 and~7061.4 eV,i na ddition, aw eak shoulder is observed at~7051.4 eV.T he differences in the RXES spectra in the pre-edge region relative to those in the rising edge clearly demonstrate that adifferent FS (3p 5 3d 7 for [Fe II Cl 4 ] 2À )h as been reached. Figure 4(right panel) shows the parallel 1s3p RXES from [Fe III Cl 4 ] 1À with resonant excitations in both the edge and preedge region. Once again, the data obtained with resonant excitation into the edge region are essentially identical to the Kb XES indicating that, at these energies,the FS is equivalent to the non-resonant process.I nterestingly,f or resonant excitation into the pre-edge region, one observes aK b 1,3 maximum at 7060.6 eV and aw eak shoulder at 7057.9 eV. Similar to the ferrous case,u pon resonant excitation in the pre-edge region, no well-defined Kb' feature is observed, distinctly demonstrating that the 1s3p RXES of the ferric species is not simply the equivalent of Kb XES on af errous complex, despite their seemingly equivalent 1s 2 3p 5 3d 6 FS. This indicates that one must consider the IS that are available to be populated by resonant excitation. In the section that follows,the detailed origins of the differences in Kb XES and 1s3p RXES are evaluated.

Non-resonant versus Resonant XES Multiplets in Iron Tetrachlorides
In order to more rigorously understand the differences in the Kb XES and 1s3p RXES,i ti su seful to examine the FS Angewandte Chemie Forschungsartikel multiplets which are reached in each process.F or simplicity, we begin by computing the multiplets involved in the d 6 and d 5 Kb XES spectra ( Figure S3). Atomic Russell Saunders terms for these processes are given in Table S4. Forthe high-spin d 6 ferrous case,t he ground state term symbol is 5 D. When a1 s electron is ionized, a1s 1 3d 6 state is reached, giving rise to 4 D and 6 Dc onfigurations when alpha and beta 1s electrons are ionized, respectively.F ollowing the Kb emission process,a3p hole is created giving rise to a3 p 5 3d 6 electron configuration. Coupling the 2 Pconfiguration of the 3p hole to the 5 Dground state term symbol gives rise to 4,6 P, D, and Ff inal state multiplets (Table S4). Themultiplet splitting is dominated by 3p-3d exchange,which separates the XES spectrum into a 4 G (Kb ' )a nd 6 G (Kb 1,3 ). In the d 5 case,asimilar picture may be derived, where the FS spectra are instead characterized by splitting of the 5 G and 7 G states.T hese simple pen and paper predictions are readily captured by atomic multiplet calculations ( Figure S3 and Figure S4) and fully consistent with previous assignments for Kb XES spectra. [65] The1s3p RXES process at the pre-edge region, preferentially populates a1 s 1 3d n+1 IS (Table 1, Figure 5). Following decay via Kb emission, one arrives at a1s 2 3p 5 3d n+1 FS.Asthere are no a 3d holes in either high-spin Fe II or Fe III ,only b 1s to 3d transitions are spin allowed. Assuming conservation of spin during the radiative decay process,t he b-decay channel will also dominate.T his yields to aK b XES spectrum exhibiting 5 G terms for Fe II and 6 G terms for Fe III (Table 1). Hence,u pon resonant excitation into the pre-edge region, the pronounced 3p-3d exchange coupling is no longer the largest contribution to the spectral shape and instead the Kb' is effectively absent. This is consistent with the full 1s3p RXES planes (Figure S5) [73] where the pre-edge region shows intensity only on the Kb 1,3 channel.

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For1 s3p RXES in the pre-edge region, the ferrous and ferric spectra are dominated by splitting of the FS 5 G and 6 G, respectively.B ut why is the 1s3p RXES spectrum of the ferrous tetrachloride so strongly structured, while that of the ferric is relatively featureless?H ere,o ur conceptual understanding comes from considering the many-electron states accessible in the RXES process.Inthe ferrous case,the 1s3p RXES spectrum comes from ad 7 configuration for the intermediate and final states.I nt he valence space,t he d 7 configuration gives rise to a 4 Ft erm that must be coupled to the 2 Sterm for the IS and a 2 Pterm for the FS.Therefore,the FS have 5 D, 5 F, and 5 Gterms (Table 1). Importantly,there are two 5 G terms that contribute to the spectrum at~7059 eV in the ferrous case yielding greater spectral intensity. This is supported by the multiplet simulation shown in Figure 5A,which highlights the 5 Dterm. This 5 Dterm can be seen as deriving from low-lying 4 Pt erm of d 7 metals that is stabilized by configuration interaction. Figure S6 further describes the role of configuration interaction and the identification of 5 D( 4 P) feature using multiplet simulations.
Forthe ferric case,the 5 Dterm from the d 6 configuration coupled with 2 Softhe 1s core hole results in a 6 DIS. In the Kb XES, 6 F, 6 D, and 6 PFSmultiplets may be accessed. In contrast to the ferrous case,there are no low lying multiplets that the 5 Dp arent term can interact with, resulting in am ore simplified FS multiplet structure relative to that of the ferrous.T hese trends are validated by multiplet calculations, Figure 5. The1 s3p RXES spectra of both iron tetrachlorides clearly show that resonant excitation into the pre-edge region allows for the nearly identical Kb XES spectra to be readily distinguished within the resonant limit. Does this observation continue to hold even for highly covalent iron sulfur clusters? Figure 5. A) Simulated 1s3p RXES spectra for d 6 (left) and d 7 (right) and their corresponding multiplets without ligand field inclusion.Multiplets labeled in black are derived from their corresponding d n ground state parent term, while those labeled in red are due to an energetically higher parent term. B) Experimental 1s3p RXES on ferrous (left) and ferric (right) tetrachlorides, overlaid with simulated spectra includingl igand field and 60 and 45 %SCreduction,respectively.

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Effect of Covalency on 1s3p RXES Spectra Thecontribution of covalencyto1s3p RXES spectra was investigated through computational studies in which the Slater Condon parameters (F 2 pd and G 1,3 pd )w ere systematically scaled from 100 %( e.g. the atomic limit) to 40 % ( Figure S7). These simulations show that though the spectra are modulated by covalency,the general multiplet structure is maintained even for an unphysical 40 %r eduction and the splitting between the 5 Gand 5 F/ 5 Dterms is still large enough to be resolved experimentally.T of urther assess this assumption, data on highly covalent systems are presented in the next section.

RXES on Highly Covalent Systems:Synthetic Iron Sulfur Dimers Clusters, Iron Sulfur Cubanes and the MoFeProtein of Nitrogenase
TheRXES spectra of all molecules are plotted in Figure 6 (positive axis), and difference spectra (D RXES and D XES ) generated by subtracting af erric reference from ferrous species are given following the color of their ferrous parent (negative axis). Theall-ferric reference spectra are chosen to as [Fe III Cl 4 ] 3À for the monomer ( Figure 6A)and L 2 Fe III Fe III S 2 for the dimer and tetramers (Figure 6Band C), to account for the high covalencyp resent in the dimers and tetramers.T o evaluate the presence of Fe II in the mixed-valence clusters and in the MoFeprotein versus the 1s3p RXES for Fe III ,t he incident energy chosen for the mixed-valence samples corresponds to the 1s!3d (Fe II ). Additional RXES cuts can be found in the Supporting Information ( Figure S8 and S9). Figure 6A emphasizes the points already made in the preceding section regarding the similarity of the classical XES versus the clear changes in the RXES,now highlighted too by the difference spectra D XES ,and D RXES .F igure 6B shows 1s3p RXES at the pre-edge of the diferrous,m ixed valent, and diferric dimers.A sw as the case for the iron tetrachlorides, resonant excitation clearly distinguishes these three complexes.T he advantage of 1s3p RXES over conventional XES is again highlighted by the corresponding difference spectra, showing minor differences for D XES in comparison to D RXES . Thec hanges are more pronounced for the diferrous dimer than the mixed valent dimer.I nt he diferrous case,r esonant excitation into the pre-edge gives rise to two features (at 7058.8 and~7060.5 eV), attributed to 5 G derived from the 4 F and 4 Pp arent terms of the d 7 configuration, as discussed above.I nt he mixed valent complex, two features are still present, however, the lower energy feature is reduced in intensity,consistent with the fact that only half the irons are in the ferrous form. This is also highlighted by the difference spectrum D RXES .
Finally,t he biomimetic tetranuclear [MoFe 3 S 4 ] 2+ and [Fe 4 S 4 ] 2+ and the MoFep rotein of nitrogenase were studied ( Figure 6C). All samples contain Fe II ,a nd the resonant excitation into the pre-edge yields two distinct features split by~0.9-1.3 eV at their maxima due to the additional 5 Dterm discussed above.Once again, inspection of the D RXES and D XES highlights the ability of 1s3p RXES at the pre-edge region to identify the presence of ferrous iron, which is not possible using the Kb XES spectra alone.Future studies including 1s3p RXES full planes collected with higher resolution instruments may allow for amore rigorous quantification of the changes in electronic structure,e nabling better distinction between the different intermediate states.N evertheless,t hese results demonstrate that even in highly covalent systems,meaningful differences in 3d metal valencypersist in the 1s3p RXES data.

Conclusion
Thew ork presented here illustrates the ability of 1s3p RXES to identify physical oxidation states which may be hidden in standard Kb XES and K-edge XAS experiments. This is achieved by resonantly exciting into the pre-edge region of the XAS spectrum, giving rise to aF Sw ith ad n+1 configuration. By comparing the multiplet structure of Kb XES to that of 1s3p RXES,b oth the ground state and final state multiplets may be experimentally accessed, allowing for the physical oxidation state to be assigned in afar more robust

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Forschungsartikel manner than is possible in standard XAS or XES experiments.
RXES and XES are complementary in the assessment of the oxidation state.However,there are certain advantages of RXES.F or all d n configuration with n ! 5, only b excitations are allowed in the pre-edge region, resulting in aR XES spectrum in which only the states of maximum multiplicity contribute.C ombined with the higher achievable resolutions in 1s3p RXES relative to Kb XES,t his allows for am ore quantitative assessment of the electronic structure.F urthermore,t he multiplet structure in 1s3p RXES persists upon strong covalent modulation, unlike in the non-resonant Kb XES case.
Theresults presented should be readily translatable to all high-spin first-row TMs of any d n count. Thes plitting of the 1s3p RXES Kb 1,3 feature for Fe II results from the 5 Fterm that is reached in its IS (s 1 d 7 )a nd the existence of al ow-lying excited state with the same spin multiplicity with which mixing can occur via configuration interaction. This same phenomenon should occur for all TMs that reach an Fterm in the IS.Based on these observations,general groupings can be made for all first-row TMs with high-spin configurations: I. As plitting of the 1s3p RXES Kb 1,3 feature will be observed for all TMs in which an Fterm is its IS.E.g.d 1 , d 2 ,d 6 and d 7 ground state configurations. II. Ford n!5 TMs the 1s3p RXES at the pre-edge,w ill be absent from the Kb' feature. III. As plitting of the Kb 1,3 feature in Kb XES should be observed for TMs with Fg round state terms,p roviding experimental resolution is sufficient (e.g.d 2 ,d 3 ,d 7, and d 8 configurations).
Theg eneral pairings of resonant and non-resonant XES multiplet behavior thus provide am eans to distinguish electronic structural ambiguities for arange of 3d n counts.
In recent years,t he literature has seen increasing applications of Kb XES to awide range of TM systems,including in situ and operando studies of catalysts, [74][75][76][77] transformations of materials under high pressure, [78,79] and time-resolved (TR) studies of enzymatic systems. [80,81] However,inmany of these cases the information conveyed by Kb XES is ambiguous and their conclusions are at times controversial. This study makes it clear that 1s3p RXES provides an opportunity to further the chemical information content of XES even on biological systems.T he inclusion of 1s3p RXES to the MoFeprotein of nitrogenase in the present work shows not only the feasibility of the experiment on enzymatic systems (data collection time was 8minutes/incident energy), but also highlights that RXES could significantly increase the information about the electronic structure obtained in TR studies.
In our view,this work brings us one step closer to realizing the vision of Linus Pauling who said, "If scientific progress continues,t he next generation may have at heory of valency that is sufficiently precise and powerful to permit chemistry to be classed along with physics as an exact science." Although we are not there yet, we have added another tool to the chemists toolbox to bring the community one step closer to realizing this goal.