Kβ X‐Ray Emission Spectroscopic Study of a Second‐Row Transition Metal (Mo) and Its Application to Nitrogenase‐Related Model Complexes

Abstract In recent years, X‐ray emission spectroscopy (XES) in the Kβ (3p‐1s) and valence‐to‐core (valence‐1s) regions has been increasingly used to study metal active sites in (bio)inorganic chemistry and catalysis, providing information about the metal spin state, oxidation state and the identity of coordinated ligands. However, to date this technique has been limited almost exclusively to first‐row transition metals. In this work, we present an extension of Kβ XES (in both the 4p‐1s and valence‐to‐1s [or VtC] regions) to the second transition row by performing a detailed experimental and theoretical analysis of the molybdenum emission lines. It is demonstrated in this work that Kβ2 lines are dominated by spin state effects, while VtC XES of a 4d transition metal provides access to metal oxidation state and ligand identity. An extension of Mo Kβ XES to nitrogenase‐relevant model complexes shows that the method is sufficiently sensitive to act as a spectator probe for redox events that are localized at the Fe atoms. Mo VtC XES thus has promise for future applications to nitrogenase, as well as a range of other Mo‐containing biological cofactors. Further, the clear assignment of the origins of Mo VtC XES features opens up the possibility of applying this method to a wide range of second‐row transition metals, thus providing chemists with a site‐specific tool for the elucidation of 4d transition metal electronic structure.

However,p arallel studies on 4d TM complexes are exceedingly limited. Herein, we perform ad etailed Kb XES study on as eries of Mo complexes,s hown in Figure 1a nd Table 1. While this work is mainly focused on Mo Kb XES,we also present Mo Kb 1 high-energy resolution fluorescence detected (HERFD) XAS as ac omplementary electronic structure probe.
In order to better understand the significance of the results presented here,i ti su seful to first briefly summarize the previous Kb XES work done on 3d TMs and to compare this to the existing assignments for Kb XES on 4d TMs.
X-ray emission spectroscopy, 1 st vs. 2 nd row transition metals. Figure 2s hows ac omparison between the emission lines of 3d (A) and 4d (B) TMs.F igure 2A includes the wellestablished emission lines in increasing energy order:K a 2 , Ka 1 ,K b',K b 1,3 and the VtC transitions (Kb'' and Kb 2,5 ). A representative energy level diagram is displayed below the emission spectrum in Figure 2C.F igure 2C shows the nonresonant emission processes that result from the ionization of the 1s core electron to the continuum. Thea nalogous processes for 4d TMs are shown in Figure 2B and D. In the present study,w ef ocus on the Kb 3 ,K b 1 ,K b 2 Kb'',a nd Kb 4 emission lines,ini ncreasing energy order. TheKb 1 and Kb 3 emission lines in Mo XES correspond to the electric dipole allowed 3p!1s transitions.The splitting of these features is due to 3p core hole spin-orbit coupling  (SOC, % 18 eV splitting). This may be contrasted with the Kb mainline XES of the 3d TMs,w hich splits into Kb 1,3 and Kb' features predominantly due to 3p-3d exchange coupling,with the 3p SOC (< 1eV)) remaining as only aminor perturbation.
To % 300 eV higher in energy there is the Mo Kb 2 emission line,which arises from a4pto1stransition. Thefinal state of the Kb 2 decay process has ah ole in the 4p shell, which interacts with the unpaired electrons in the 4d shell. Hence, the Kb 2 line for 4d TMs is analogous to the Kb 1,3 emission line for 3d TMs.However,4dTMKb 2 XES spectra do not exhibit well-resolved splitting due in part to the smaller 4d-4p exchange integrals,r elative to 3p-3d exchange integrals.I n addition, the spectrum is further modulated relative to 3d TMs due to 1) the 4p 5 final state SOC of a4dTMbeing larger than the corresponding 3p 5 final state SOC for 3d TMs and 2) the increased 1s core-hole lifetime broadening of 4d TMs relative to 3d TMs (1.2 eV for Fe and 4.52 eV for Mo). [49] VtC XES results from electrons in primarily ligand-based valence orbitals refilling the 1s core hole at the metal with the intensity due to the percent npmetal character mixed into the valence orbitals. [34,37] In 3d TMs,t he Kb'' results from ligand ns to metal 1s transitions,w hile the Kb 2,5 results from ligand np to metal 1s transitions.I np rinciple,a nalogous transitions should exist for the 4d TMs,and based on the energetics,these should be the Kb'' and Kb 4 transitions.Recently,Ravel et al. demonstrated that this analogy holds for the Kb'' features in niobium complexes, [25] where the energy of the Kb'' features were shown to depend on ligand identity.Incontrast, the Kb 4 feature remains relatively unexplored, and previous studies have assigned it as arising from orbitals possessing primarily metal 4d character,r ather than al igand npt om etal 1s transition. [27] It is clear that amore detailed exploration as to the exact origin of the Kb 4 features is warranted.
Herein, we carry out asystematic study of molecular Mo complexes and examine how the local geometric and electronic structures impact the Mo Kb 2 ,K b'',a nd Kb 4 features. Theresults are correlated to density functional theory (DFT) calculations in order to obtain more detailed insight. Complexes 0-VI (Table 1, Figure 1) will first be presented to provide ad etailed description of the Mo emission lines.W e then utilize Mo Kb XES together with Mo Kb HERFD XAS to contrast the sensitivity of XES and XAS approaches for understanding electronic structural changes in two nitrogenase FeMoco related model complexes.T he results allow for ab etter understanding of the origins of 4d TMs emission lines and also establish the utility of Mo XES for future applications in bioinorganic chemistry and catalysis.

Results and Discussion
Mo Kb XES. Then ormalized Mo Kb XES spectra of compounds 0-VI are presented in Figure 3(top). Thespectra consist of an intense Kb 2 feature at % 19970 eV and weaker higher energy peaks in the range of 19 980-20 003 eV representing the VtC region (Kb'' and Kb 4 ).
Kb 2 XES. Figure 3( bottom) shows an expansion of the Kb 2 feature.The Kb 2 spectra were fit with three pseudo-Voigt function line shapes,where Peak 1( Table 2)    III,for which the Kb 2max is at 19 967.2 eV.Asthe Kb 2 feature corresponds to a4pto1stransition with a4p 5 4d n final state,it will be influenced by 4p-4d exchange coupling,a nd thus should be sensitive to the number of unpaired 4d electrons. The S = 3/2 compound III,a ppears at highest energy due to the high-spin d 3 configuration.
Using the isostructural models 0 and I for comparison, the energy of the Kb 2max increases by % 0.3 eV per unpaired electron for all S 1c omplexes.T he apparent, albeit, small shifts in the Kb 2 emission energy as af unction of Mo oxidation-state clearly demonstrates the contribution of 4p-4d exchange coupling. However,t his trend is significantly smaller than the 0.5-0.7 eV shift per unpaired electron shifts observed for 3d TMs. [50][51][52] This is aresult of the smaller 4p-4d exchange integrals relative to the corresponding 3p-3d integrals. [53] We note that the shift will, of course,b ef urther modulated by changes in the Mo 1s energy.
Although the shifts in the Kb 2 maxima are modest, the fits reveal an asymmetric profile in the Kb 2 feature (Table S1 and Figure S1), consistent with previous reports by Hoszowska et al. [28] Due to the significant 1s core hole broadening for Mo, the position and intensity of the low energy shoulder is not well-defined. However,wecan discuss the possible origins of this asymmetry based on Russel Sanders terms in the atomic limit, in asimilar fashion as previously done for 3d TM.
For3 dT Ms,i ti sw ell-established that the Kb 1,3 spectral shape,i ncluding the Kb' intensity,i sd ominated by the final state multiplet structure. [50,52,54] More specifically,p revious systematic studies of the contribution of the Slater-Condon parameters F 2,4 dd ,F 2 pd and G 1,3 pd have shown that the p-d exchange integrals G 1,3 pd dominate the spectral shape of 3d TMs.Inorder to assess whether or not asimilar picture can be assumed for 4d TMs,w ec alculated the Kb 1,3 and Kb 2 XES spectra of Cr 3+ and Mo 3+ ,r espectively ( Figure S2), using ligand field multiplet calculations.T he Slater-Condon parameters F 2,4 dd ,F 2 pd and G 1,3 pd were individually varied between 100 and 50 %o ft heir atomic values.T he F 2 pd and F 2,4 dd parameters were shown to result in only minor perturbations for the Cr 3+ spectra, and made essentially no contributions to the Mo 3+ spectra. In contrast, the p-d exchange integral (G 1,3 pd )h as ap ronounced effect on the spectral shape for both Cr 3+ and Mo 3+ .T his agrees with previous interpretations of 3d TM XES, [49] and indicates that Kb 2 spectra are dominated by 4p-4d exchange.W et hus use this simple picture for further discussion of the spectral trends.
Examination of the fits reveals that compound III exhibits the greatest redistribution of intensity to lower energy,again consistent with increased 4p-4d exchange contributions for an S = 3/2 complex relative to the S = 0t o1c omplexes.T his exchange interaction redistributes the multiplet intensity into two families of features,c orresponding mainly to final state triplet and quintet states,a si ndicated in Table 3. The remaining compounds exhibit more comparable intensity distributions,c onsistent with the reduced d-counts and the presence of p-accepting carbonyl ligands in 0, I and II,which results in delocalization of d-character onto ligand p*orbitals.
In order to understand the observed relatively modest changes in Mo Kb 2 compared to the reported effect of d-count on the Kb 1,3 lines of 3d TMs,NEVPT2 CASSCF calculations were performed on Mo 3+ and Cr 3+ free ions.T he XES final state 1s 2 np 5 nd n can be reached in the 1 st excited state of ap!d CASSCF calculation utilizing a1s 2 np 6 nd nÀ1 ground state.This first excited state will correspond to all multiplets allowed for np 6 nd nÀ1 !np 5 nd n ,f rom where only the multiplets that correspond to the final states XES processes were selected. Thecalculated XES final states (without SOC contributions) are shown in Figure 4, with the 3 G states shown in blue and the 5 G states shown in red. TheCASSCF + NEVPT2 calculations for Group 6Cr 3+ and Mo 3+ ions have the same dipole-allowed XES final states.H owever,t he final state XES multiplet energy distribution between these ions exhibits striking differences.I nt he case of Cr 3+ ,t he allowed XES final states span % 23 eV,w hile for Mo 3+ the final states span only % 17 eV.
Thed ecreased p-d exchange contribution to the Kb 2 spectra of 4d TMs relative to that observed in the Kb 1,3 spectra of 3d TMs is due to the increased delocalization of the 4d electrons.T he inclusion of SOC in these calculations, and its influence on the 1s 2 np 5 nd 3 final states,are included in Figure S3A,B.T he energy span of the final states remains  Asimilar computational study was used to investigate the distribution of final states by varying the oxidation state. Figure S4 A,B shows an increase in the energy spread of the XES final states by % 2.5 eV on going from Mo 1+ (S = 1/2) to Mo 2+ (S = 1) and by % 5eVongoing from Mo 2+ to Mo 3+ (S = 3/2). This suggests an expansion of % 2.5 eV per unpaired electron in the purely ionic limit. Due to delocalization of dcharacter onto the ligands,however,the effect is expected to diminish. This is clearly seen in the case of the carbonyl coordinated compounds where changes in spin state are effectively not observed at the Kb 2 line due to the strong paccepting nature of the ligand, as noted above and also previously observed in the Kb 1,3 mainline of 3d TMs. [55] Mo valence-to-core Kb 4 and Kb' '' '. Resolved but far less intense Kb 4 and Kb'' transitions appear on the high-energy tail of the Kb 2 mainline.T ogether, these transitions make up the Mo VtC region as shown in Figure 5( top). If we assume that the classical 3d TMs VtC transition assignments are transferable to the Mo VtC,t he following hypothetical assignments can be made: 1) TheK b 4 feature is primarily due to transitions from np ligand valence orbitals to the metal 1s core hole.T he intensity of this feature is dominated by the amount of metal pc haracter mixed into these valence orbitals.T he Kb 4 feature is the equivalent of the L(np)!M(1s) Kb 2,5 feature for 3d TMs,where the intensities of the peak have been previously correlated with the MÀLbond length 2) TheM oK b'' peak is primarily due to transitions from ns ligand valence orbitals to the metal 1s core hole.I ti s dominated by ligand identity and the intensity is modulated by metal-ligand bond length. [27] Experimental data were fit for all compounds,i ncluding the main peak positions and amplitudes,a nd are included in Table 2. Them ost intense peaks correspond to the Kb 4 features,l ocated between 19 995-20 010 eV for compounds 0 to VI,with total areas of 0.2-0.4 as indicated in Table 2(Peak 4and Peak 5). Theenergy of the Kb 4 feature appears to track with oxidation state,with the feature increasing in energy by % 5eVongoing from 0 to VI.This likely reflects,inlarge part, the stabilization of the Mo 1s energy upon increasing Z eff . Similar trends have been previously observed for 3d TM. [56] As the weak Kb'' features appear on the high-energy tail of the more intense Kb 2 mainline,the Kb'' features are either obscured or poorly resolved (between 19 975-19 990 eV, Peaks 2a nd 3, Table 2). However,f or the molybdenum oxides IVand VI relatively intense Kb'' features are observed.
To further test the assignment of these transitions and gain additional insight into their molecular origin, the Mo VtC of  each compound was calculated by ground-state DFT methods. [34] Thecalculated VtC spectra were obtained by allowing for electric dipole,m agnetic dipole and quadrupole contributions.T he resultant spectra were found to be comprised of 99.9 %d ipole contributions.T he DFT results well-reproduce the experimental data, replicating the observed energy trends and transition intensities ( Figure 5, bottom). Thec alculated spectra allow the donor molecular orbitals of each transition to be assigned. Figure 6s hows the primary contributing molecular orbitals (MO) for the Kb'' and the more intense Kb 4 transitions for compounds 0, III and IV.Aquantitative orbital analysis for all compounds is included in Table S2.
Qualitative inspection of the MOs contributing to the intensity of the Kb 4 peak demonstrate that this transition is mainly from npligand valence orbitals and that the calculated intensity is dominated by the amount of metal pc haracter mixed into these valence orbitals.F or instance,t he most intense transition for III is in the Kb 4 region and is attributed to aC l3 p! Mo 1s transition ( % 19 999.4 eV with at otal integrated area of 0.22 units Figure 6). TheKb 4 transitions for both IV and VI are from O2pligand MOs ( Figure 5) with Mo 4p/5p dipole contributions.A sIV and VI each have oxygen ligands,but different delectron counts,their comparison most directly tests the Kb 4 origin. TheKb 4 energy positions for IV and VI are % 1.3 eV shifted and their total integrated areas are 0.36 and 0.33 units.I tw as previously suggested that the Kb 4 feature is formally a4 d! 1s transition. [27] However, complex VI is formally d 0 with no available donor d-electrons for the Kb 4 transition. Therefore,t his further supports the assignment of the Kb 4 feature as al igand np ! Mo 1s transition, which gains intensity through metal npc haracter mixing into the ligand orbitals.Only complexes III, IV,and VI have well-resolved Kb'' features.T he MOs which correspond to these transitions are ligand ns based. Thec alculated spectrum for complex III shows one main feature due to the Cl 3s ! Mo 1s transition between 19 987-19 990 eV and contributions from the ttcn ligand, found at 19 990 eV but with low intensity.Calculated XES spectra of IV and VI show one main Kb'' feature due mainly to O2 s-based molecular orbitals.These transitions possess slightly different intensities due to varying Mo À Od istances.C omplex VI,M oO 3 ,h as an orthorhombic crystal distorted bulk unit with strong anisotropy in MoÀOb onding that is also responsible for ah igher dipole contribution relative to the monoclinic MoO 2 complex IV.The shortest MoÀObond distance in MoO 3 is 1.67 while the shortest Mo À Ob ond length for MoO 2 is 2.023 .T hese calculations validate the aforementioned hypothesized transition assignments (see above).
Theback-bonding character of the carbonyl ligands yields VtC transitions that are more mixed in character. Therich Fe VtC spectra of Fe carbonyl complexes exhibit features arising from s*2s-2s (CO) and s 2p z -2p z (CO) interactions with the metal. [55] Fort he Mo carbonyl-containing compounds,w ellresolved contributions from the carbonyl ligands are not observed. However,the calculations reproduce experimental trends,with the energy of the Kb 4 increasing and the intensity decreasing going from 0 to II.The s-type bonding interactions are capable of mixing with Mo po rbitals to form available donor orbitals that are major contributors to the Kb 4 region, Figure 6. Thet ransitions in the Kb 4 region with the highest dipole contribution to the emissionoscillator strength correspond to transitions from s 2p z -2p z (CO) + s N(Tp) MOs.The lessening of p back-donation from the Mo 4d shell is reflected in Mo-CO bond lengthening from 0 to II.The increase in MoÀ CO bond length affects the intensity of VtC features as the np Mo-ligand mixing decreases.T his same distance dependence is observed in the Kb 2,5 feature of 3d TMs. [34,37] Forc ompounds 0 to II,t hree distinguishable peaks are found to be part of the Kb'' calculated transitions.T he two transitions between 19 980-19 985 eV are of significantly lower intensity than the other calculated Kb'' features and not observed in the experimental data. Thel ow intensity features are due to Nand C2sorbital delocalization over the tris(pyrazolyl)borate (Tp) ligand. From an MO description, both features can be assigned as transitions from MOs of the chelating pyrazole rings in the Tp ligand with little contribution of the Mo(CO) 3 fragment. Theminimal amount of metal pcharacter mixed into these MOs results in very small dipole contributions to the calculated oscillator strength. This explains why these transitions are not observed in the experimental spectra.
Despite the disparate ligand character of the studied Mo complexes,c lear trends in the Mo VtC emerge:t he Kb 4 feature provides am arker of Mo oxidation-state and is sensitive to ligand identity and metal ligand bond length.
XAS measurements. Figure 7d isplays the Mo Kb 1 HERFD XAS of the complexes grouped by ligand identity, with the Mo compounds with Tp and CO ligands (0, I, Ib and II)atthe top and the oxides (IV and VI)atthe bottom. Metal K-edge positions shift towards higher energies with increasing oxidation state,a st he effective nuclear charge varies. [57,58] Figure 7( bottom) shows an energy shift of + 2.6 eV in the rising edge on going from compound IV to VI. Figure 7(top) shows a % 1eVenergy shift at the white lines,consistent with the increase in oxidation state from 0 ! I ! II.H owever, identification of the Mo oxidation state of these compounds by the inflection points of their corresponding rising edges has aless intuitive interpretation. In this particular case,the rising edge of each compound is modulated by the strong backbonding nature of the carbonyl ligands,w ith an increase in back-bonding resulting in an edge shift toward higher energy. Interestingly,f or the present series,t he Kb 4 XES features seem to more clearly correlate with the oxidation states of the compounds than the rising edge positions. [56] Ap ractical case:m olybdenum-iron-sulfurc lusters. Having established in the preceding sections the complementary information that can be obtained by the use Mo Kb XES and Kb 1 HERFD XAS,wenow go on to utilize these methods to understand synthetic MoFec ubanes. [59] These serve as examples of more complex models with relevance to ab iological system, in this particular case the FeMoco active site of nitrogenase.T wo MoFec ubanes, [59] [MoFe 3 S 4 ] 3+ and [MoFe 3 S 4 ] 2+ ,w ere studied to determine the sensitivity of each method to one electron cluster reductions.I na ddition, Fe Kb 1,3 HERFD experiments are also presented in order to obtain insight into the location of the redox event.  [60,61] Both MoFec ubanes overlap in the whiteline region of the Mo K-edge XAS spectra, suggesting there is no change in oxidation state at the Mo site.This is consistent with reduction occurring at the iron, as supported by the Fe K-edge data and previous Mçssbauer studies. [62] Just before the rising edge,both compounds III and [MoFe 3 S 4 ] 2+ overlap in the preedge area, while [MoFe 3 S 4 ] 3+ has ahigher intensity pre-edge. This may reflect greater p-d mixing in the [MoFe 3 S 4 ] 3+ cubane due to increased covalencya nd/or the presence of MMCT transitions. Figure 9d isplays the Mo Kb 2 and VtC for III and both MoFecubanes.The Kb 2max of compound III (S = 3/2) is found at 19 967.2 eV while both MoFec ubanes (S loc (Mo) = 1/2) show their Kb 2max % 0.6 eV downshifted from the Kb 2max of III. This translates to a0 .3 eV energy shift per unpaired electron in Mo Kb 2max ,and is fully consistent with the shifts determined for compounds 0-VI.W en ote,h owever,t hat the shift may also be attributed to an increase in covalencyupon replacing the thioethers in III with the more covalent sulfides in the cubane clusters. [50]   XES spectra were calculated by DFT in order to understand the origin of these differences ( Figure 10, Figure 11). In both experimental and calculated spectra, compound III shows aKb 4 peak with lower intensity than the MoFecubanes. In III,t he intensity of this peak is mainly due to transitions from 3p Cl and thioether sulfur MOs ( Figure 6). However, for both MoFec ubanes the origin of the Kb 4 transitions is less straight forward as the calculated transitions are modulated by covalency( via Mo À S(thiolate) and Mo À Fe bonding). Thep utative effect of metal-ligand bonding on the XES VtC spectra of both cubanes was investigated by replacing the Fe sites with closed shell atoms without changing overall geometry or local Mo spin. Figure 11 Figure S6).
This computational study demonstrates that Mo VtC is moderately sensitive to metal-metal interactions,b ut relatively insensitive to the Mo local spin state.

Conclusion
As ystematic experimental and theoretical study of Mo Kb XES has been performed for ar ange of molecular and extended lattice Mo materials.T he ability of this method to provide local information on Mo oxidation state,s pin state, and identity of coordinated ligands has been established. The trends elucidated here should be readily transferable to other 4d TMs.
Having established the strong correlations between experimental and calculated Mo Kb XES spectra, the method was extended to MoFe 3 cubane clusters with relevance to the FeMo cofactor of nitrogenase.T hese studies highlight the ability of Mo Kb XES to report on subtle changes in cubane electronic structure.Bycombining the XES studies with XAS measurements at the Mo and Fe K-edge,i ti sd emonstrated that the Mo Kb XES is sufficiently sensitive to show changes upon iron-based reduction. This suggests that Mo Kb XES could be useful for studies of FeMoco and might provide greater selectivity than Fe Kb XES,where contributions from the 7iron of FeMoco and the 8irons of the P-cluster greatly complicate the spectral interpretation.
Thep resent study forms the basis for applying Mo Kb XES in homogeneous and heterogenous catalysis.W hile Mo Kb XES suffers from relatively large Mo 1s core-hole lifetime broadening, [22,27] this technique may be particularly useful for Mo-containing enzymes with al arge number of Sa toms present. Due to the overlap of the Mo L-edges and SK-edges, it is difficult to deconvolute the Mo and Scontributions in the tender X-ray spectra. [63]  Thea pproach presented here may provide am eans to more readily access electronic structural changes at the Mo in biological systems where molybdenum is involved either as amononuclear active site (DMSO reductase,sulfite oxidase, etc) or as part of multinuclear metal centres,l ike Cu,Mocontaining CO dehydrogenases. [64]