Metal-ligand covalency of iron complexes from high-resolution resonant inelastic X-ray scattering

Tracking Coordination Environment and Reaction Intermediates in Homogeneous and Heterogeneous Epoxidation Catalysts via Ti L2,3-Edge Near-Edge X-ray Absorption Fine Structures

Ti-based molecules and materials are ubiquitous and play a major role in both homogeneous and heterogeneous catalytic processes. Understanding the electronic structures of their active sites (oxidation state, local symmetry, and ligand environment) is key to developing molecular-level structure-property relationships. In that context, X-ray absorption spectroscopy (XAS) offers a unique combination of elemental selectivity and sensitivity to local symmetry. Commonly, for early transition metals such as Ti, K-edge XAS is applied for in situ characterization and subsequent structural analysis with high sensitivity toward tetrahedral species. Ti L2,3-edge spectroscopy is in principle complementary and offers specific opportunities to interrogate the electronic structure of five-and six-coordinated species. It is, however, much more rarely implemented because the use of soft X-rays implies ultrahigh vacuum conditions. Furthermore, the interpretation of the data can be challenging. Here, we show how Ti L2,3-edge spectroscopy can help to obtain unique information about both homogeneous and heterogeneous epoxidation catalysts and develop a molecular-level relationship between spectroscopic signatures and electronic structures. Toward this goal, we first establish a spectral library of molecular Ti reference compounds, comprising various coordination environments with mono- and dimeric Ti species having O, N, and Cl ligands. We next implemented a computational methodology based on multiplet ligand field theory and maximally localized Wannier orbitals benchmarked on our library to understand Ti L2,3-edge spectroscopic signatures. We finally used this approach to track and predict the spectra of catalytically relevant intermediates, focusing on Ti-based olefin epoxidation catalysts.

Iron Kβ X-ray Emission Spectroscopy: The Origin of Spectral Features from Atomic to Molecular Systems Using Multi-configurational Calculations

Kβ X-ray emission spectroscopy (XES) is widely used to fingerprint the local spin of transition-metal ions, including in pump-probe experiments, to identify excited states or in chemical and biological reactions to characterize short-lived intermediates. In this study, the spectra of ferrous and ferric complexes for various spin states were measured experimentally and described theoretically through restricted active space (RAS) calculations including dynamic correlations. Through the RAS calculations from simple atomic models to complex molecular systems, spectral effects such as the exchange interactions, crystal-field strength, and covalent orbital mixing were evaluated and discussed. The calculations find that only the spectral features of low-spin cases show a dependence on the crystal-field strength, particularly for ferrous low spin. The effect of the covalent orbital mixing strength on the first moment of the Kβ1,3 main line and the Kβ1,3-Kβ' energy splitting is quantitatively described. Clear relationships are found within a given nominal spin but less between different spin states, which calls for careful selection of reference spectra in future experiments. This study further advances our understanding of the correlation between changes in experimental spectral features and their corresponding electronic structure information.

Unraveling Metal-Ligand Bonding in an HNO-Evolving {FeNO}6 Complex with a Combined X-ray Spectroscopic Approach

Photolytic delivery of nitric oxide and nitroxide has substantial biomedical and phototherapeutic applications. Here, we utilized hard X-ray spectroscopic methods to identify key geometric and electronic structural features of two photolabile {FeNO}6 complexes where the compounds differ in the presence of a pendant thiol in [Fe(NO)(TMSPS2)(TMSPS2H)] and thioether in [Fe(NO)(TMSPS2)(TMSPS2CH3)] with the former complex being the only transition metal system to photolytically generate HNO. Fe Kβ XES identifies the photoreactant systems as essentially Fe(II)-NO+, while valence-to-core XES extracts a NO oxidation state of +0.5. Finally, the pre-edge of the Fe high-energy-resolution fluorescence detected (HERFD) XAS spectra is shown to be acutely sensitive to perturbation of the Fe-NO covalency enhanced by the 3d-4p orbital mixing dipole intensity contribution. Collectively, this X-ray spectroscopic approach enables future time-resolved insights in these systems and extensions to other challenging redox noninnocent {FeNO}x systems.

X-ray Spectroscopic Study of the Electronic Structure of a Trigonal High-Spin Fe(IV)═O Complex Modeling Non-Heme Enzyme Intermediates and Their Reactivity

Fe K-edge X-ray absorption spectroscopy (XAS) has long been used for the study of high-valent iron intermediates in biological and artificial catalysts. 4p-mixing into the 3d orbitals complicates the pre-edge analysis but when correctly understood via 1s2p resonant inelastic X-ray scattering and Fe L-edge XAS, it enables deeper insight into the geometric structure and correlates with the electronic structure and reactivity. This study shows that in addition to the 4p-mixing into the 3dz2 orbital due to the short iron-oxo bond, the loss of inversion in the equatorial plane leads to 4p mixing into the 3dx2-y2,xy, providing structural insight and allowing the distinction of 6- vs 5-coordinate active sites as shown through application to the Fe(IV)═O intermediate of taurine dioxygenase. Combined with O K-edge XAS, this study gives an unprecedented experimental insight into the electronic structure of Fe(IV)═O active sites and their selectivity for reactivity enabled by the π-pathway involving the 3dxz/yz orbitals. Finally, the large effect of spin polarization is experimentally assigned in the pre-edge (i.e., the α/β splitting) and found to be better modeled by multiplet simulations rather than by commonly used time-dependent density functional theory.

Fitting Multiplet Simulations to L-Edge XAS Spectra of Transition-Metal Complexes Using an Adaptive Grid Algorithm

A new methodology based on an adaptive grid algorithm followed by an analysis of the ground state from the fit parameters is presented to analyze and interpret experimental XAS L_2,3-edge data. The fitting method is tested first in a series of multiplet calculations for d⁰-d⁷ systems and for which the solution is known. In most cases, the algorithm is able to find the solution, except for a mixed-spin Co²⁺ O_h complex, where it instead revealed a correlation between the crystal field and the electron repulsion parameters near spin-crossover transition points. Furthermore, the results for the fitting of previously published experimental data sets on CaO, CaF₂, MnO, LiMnO₂, and Mn₂O₃ are presented and their solution discussed. The presented methodology has allowed the evaluation of the Jahn-Teller distortion in LiMnO₂, which is consistent with the observed implications in the development of batteries, which use this material. Moreover, a follow-up analysis of the ground state in Mn₂O₃ has demonstrated an unusual ground state for the highly distorted site which would be impossible to optimize in a perfect octahedral environment. Ultimately, the presented methodology can be used in the analysis of X-ray absorption spectroscopy data measured at the L_2,3-edge for a large number of materials and molecular complexes of first-row transition metals and can be expanded to the analysis of other X-ray spectroscopic data in future studies.

Local Coordination and Electronic Structure Ramifications of Guest-Dependent Spin Crossover in a Metal-Organic Framework: A Combined X-ray Absorption and Emission Spectroscopy Study

The porous Hoffman-type 3D lattice Fe(pz)[Ni^II(CN)₄] exhibits thermally induced spin-crossover (SCO) behavior that is dependent on the solvent guest species occupying the pores. Here, in situ Fe K-edge X-ray absorption spectroscopy (XAS) and both non-resonant and resonant Kβ X-ray emission spectroscopy (XES) methods are used to probe this framework under two solvent environments that yield different extremes of spin crossover temperature: acetonitrile and toluene. While the acetonitrile pore environment engenders an SCO response around room temperature, toluene guests stabilize the high spin state and effectively suppress SCO behavior throughout the ambient temperature range. The multipronged X-ray spectroscopy approach simultaneously confirmed this spin crossover behavior and provided new local coordination and electronic structural insights of the framework under these two solvent environments. Extended X-ray absorption fine structure analysis revealed spin state and solvent guest-dependent differences in coordination bond lengths and structural disorder. Resonant XES measurements produced high-resolution XAS spectra with distinct pre-edge and edge features, whose assignment was established using both simple ligand field theory and time-dependent density-functional theory calculations and further supported by their observed resonance behavior in the 2D RXES plane. Edge feature variation with the Fe spin state was interpreted to reveal changes in specific metal-linker bond covalency.

Beyond structural insight: a deep neural network for the prediction of Pt L2/3-edge X-ray absorption spectra

X-ray absorption spectroscopy at the L_2/3 edge can be used to obtain detailed information about the local electronic and geometric structure of transition metal complexes. By virtue of the dipole selection rules, the transition metal L_2/3 edge usually exhibits two distinct spectral regions: (i) the "white line", which is dominated by bound electronic transitions from metal-centred 2p orbitals into unoccupied orbitals with d character; the intensity and shape of this band consequently reflects the d density of states (d-DOS), which is strongly modulated by mixing with ligand orbitals involved in chemical bonding, and (ii) the post-edge, where oscillations encode the local geometric structure around the X-ray absorption site. In this Article, we extend our recently-developed XANESNET deep neural network (DNN) beyond the K-edge to predict X-ray absorption spectra at the Pt L_2/3 edge. We demonstrate that XANESNET is able to predict Pt L_2/3 -edge X-ray absorption spectra, including both the parts containing electronic and geometric structural information. The performance of our DNN in practical situations is demonstrated by application to two Pt complexes, and by simulating the transient spectrum of a photoexcited dimeric Pt complex. Our discussion includes an analysis of the feature importance in our DNN which demonstrates the role of key features and assists with interpreting the performance of the network.

Capturing Atom-Specific Electronic Structural Dynamics of Transition-Metal Complexes with Ultrafast Soft X-Ray Spectroscopy

The atomic specificity of X-ray spectroscopies provides a distinct perspective on molecular electronic structure. For 3 d metal coordination and organometallic complexes, the combination of metal- and ligand-specific X-ray spectroscopies directly interrogates metal–ligand covalency—the hybridization of metal and ligand electronic states. Resonant inelastic X-ray scattering (RIXS), the X-ray analog of resonance Raman scattering, provides access to all classes of valence excited states in transition-metal complexes, making it a particularly powerful means of characterizing the valence electronic structure of 3 d metal complexes. Recent advances in X-ray free-electron laser sources have enabled RIXS to be extended to the ultrafast time domain. We review RIXS studies of two archetypical photochemical processes: charge-transfer excitation in ferricyanide and ligand photodissociation in iron pentacarbonyl. These studies demonstrate femtosecond-resolution RIXS can directly characterize the time-evolving electronic structure, including the evolution of the metal–ligand covalency.

Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Spiers Memorial Lecture: Activating Metal Sites for Biological Electron Transfer

Metal sites in biology often exhibit unique spectroscopic features that reflect novel geometric and electronic structures imposed by the protein that are key to reactivity. The Blue copper active site...

Deconvolving Contributions to Decoherence in Molecular Electron Spin Qubits: A Dynamic Ligand Field Approach

In the past decade, transition metal complexes have gained momentum as electron spin-based quantum bit (qubit) candidates due to their synthetic tunability and long achievable coherence times. The decoherence of magnetic quantum states imposes a limit on the use of these qubits for quantum information technologies, such as quantum computing, sensing, and communication. With rapid recent development in the field of molecular quantum information science, a variety of chemical design principles for prolonging coherence in molecular transition metal qubits have been proposed. Here the spin-spin, motional, and spin-phonon regimes of decoherence are delineated, outlining design principles for each. It is shown how dynamic ligand field models can provide insights into the intramolecular vibrational contributions in the spin-phonon decoherence regime. This minireview aims to inform the development of molecular quantum technologies tailored for different environments and conditions.

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

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.

Effect of 3d/4p Mixing on 1s2p Resonant Inelastic X-ray Scattering: Electronic Structure of Oxo-Bridged Iron Dimers

1s2p resonant inelastic X-ray scattering (1s2p RIXS) has proven successful in the determination of the differential orbital covalency (DOC, the amount of metal vs ligand character in each d molecular orbital) of highly covalent centrosymmetric iron environments including heme models and enzymes. However, many reactive intermediates have noncentrosymmetric environments, e.g., the presence of strong metal-oxo bonds, which results in the mixing of metal 4p character into the 3d orbitals. This leads to significant intensity enhancement in the metal K-pre-edge and as shown here, the associated 1s2p RIXS features, which impact their insight into electronic structure. Binuclear oxo bridged high spin Fe(III) complexes are used to determine the effects of 4p mixing on 1s2p RIXS spectra. In addition to developing the analysis of 4p mixing on K-edge XAS and 1s2p RIXS data, this study explains the selective nature of the 4p mixing that also enhances the analysis of L-edge XAS intensity in terms of DOC. These 1s2p RIXS biferric model studies enable new structural insight from related data on peroxo bridged biferric enzyme intermediates. The dimeric nature of the oxo bridged Fe(III) complexes further results in ligand-to-ligand interactions between the Fe(III) sites and angle dependent features just above the pre-edge that reflect the superexchange pathway of the oxo bridge. Finally, we present a methodology that enables DOC to be obtained when L-edge XAS is inaccessible and only 1s2p RIXS experiments can be performed as in many metalloenzyme intermediates in solution.

Direct structural and mechanistic insights into fast bimolecular chemical reactions in solution through a coupled XAS/UV–Vis multivariate statistical analysis

A combined multivariate and theoretical analysis of coupled XAS/UV–Vis data was proven to be an innovative method to obtain direct structural and mechanistic evidence for bimolecular reactions in solution involving organic substrates.

3d-4f Resonant Inelastic X-ray Scattering of Actinide Dioxides: Crystal-Field Multiplet Description

A theoretical overview of the core-to-core (3d-4f) resonant inelastic X-ray scattering (RIXS) spectra of actinide dioxides AnO₂ (An = Th, U, Np, Pu, Am, Cu, Bk, Cf) is provided. The 3d-4f RIXS maps were calculated using crystal-field multiplet theory and turned out to be significantly different at the An M₅ vs M₄ edges, because of selection rules and final state effects. The results of the calculations allowed for a general analysis of so-called high-energy-resolution fluorescence-detected X-ray absorption (HERFD-XAS) spectra. The cuts of the calculated RIXS maps along the incident energy axis at the constant emitted energy, corresponding to the maximum of the RIXS intensity, represented the HERFD spectra and provided their comparison with calculated conventional X-ray absorption (XAS) spectra with a reduced core-hole lifetime broadening at the An M₅ and M₄ edges. Although the An M₅ HERFD profiles were found to depart from the X-ray absorption cross-section, in terms of appearing additional transitions, the results of calculations for the An M₄ edges demonstrate overall better agreement between the HERFD and XAS spectra for most dioxides, keeping in mind a restricted HERFD resolution, because of the core–hole lifetime broadening in the final state. The results confirm the utility of HERFD for the An chemical state determination and indicate the importance of calculating the entire RIXS process in order to interpret the HERFD data correctly.

A theoretical overview of the core-to-core resonant inelastic X-ray scattering of actinide dioxides is provided using crystal-field multiplet theory. The calculations allowed for a general analysis of high-energy-resolution fluorescence-detected X-ray absorption (HERFD-XAS) spectra and their comparison with conventional XAS.

Femtosecond X-ray emission study of the spin cross-over dynamics in haem proteins

In haemoglobin the change from the low-spin (LS) hexacoordinated haem to the high spin (HS, S = 2) pentacoordinated domed deoxy-myoglobin (deoxyMb) form upon ligand detachment from the haem and the reverse process upon ligand binding are what ultimately drives the respiratory function. Here we probe them in the case of Myoglobin-NO (MbNO) using element- and spin-sensitive femtosecond Fe K_α and K_β X-ray emission spectroscopy at an X-ray free-electron laser (FEL). We find that the change from the LS (S = 1/2) MbNO to the HS haem occurs in ~800 fs, and that it proceeds via an intermediate (S = 1) spin state. We also show that upon NO recombination, the return to the planar MbNO ground state is an electronic relaxation from HS to LS taking place in ~30 ps. Thus, the entire ligand dissociation-recombination cycle in MbNO is a spin cross-over followed by a reverse spin cross-over process.

The change from low-spin hexacoordinated to high-spin pentacoordinated domed form in heam upon ligand detachment and the reverse process underlie the respiratory function. The authors, using femtosecond time-resolved X-ray emission spectroscopy, capture the transient states connecting the two forms in myoglobin-NO upon NO photoinduced detachment.

Probing Solute-Solvent Interactions of Transition Metal Complexes Using L-Edge Absorption Spectroscopy

In order to tailor solution-phase chemical reactions involving transition metal complexes, it is critical to understand how their valence electronic charge distributions are affected by the solution environment. Here, solute-solvent interactions of a solvatochromic mixed-ligand iron complex were investigated using X-ray absorption spectroscopy at the transition metal L_2,3-edge. Due to the selectivity of the corresponding core excitations to the iron 3d orbitals, the method grants direct access to the valence electronic structure around the iron center and its response to interactions with the solvent environment. A linear increase of the total L_2,3-edge absorption cross section as a function of the solvent Lewis acidity is revealed. The effect is caused by relative changes in different metal-ligand-bonding channels, which preserve local charge densities while increasing the density of unoccupied states around the iron center. These conclusions are corroborated by a combination of molecular dynamics and spectrum simulations based on time-dependent density functional theory. The simulations reproduce the spectral trends observed in the X-ray but also optical absorption experiments. Our results underscore the importance of solute-solvent interactions when aiming for an accurate description of the valence electronic structure of solvated transition metal complexes and demonstrate how L_2,3-edge absorption spectroscopy can aid in understanding the impact of the solution environment on intramolecular covalency and the electronic charge distribution.

A simple molecular orbital picture of RIXS distilled from many-body damped response theory

Ab initio calculations of resonant inelastic x-ray scattering (RIXS) often rely on damped response theory, which prevents the divergence of response solutions in the resonant regime. Within the damped response theory formalism, RIXS moments are expressed as the sum over all electronic states of the system [sum-over-states (SOS) expressions]. By invoking resonance arguments, this expression can be reduced to a few terms, an approximation commonly exploited for the interpretation of computed cross sections. We present an alternative approach: a rigorous formalism for deriving a simple molecular orbital picture of the RIXS process from many-body calculations using the damped response theory. In practical implementations, the SOS expressions of RIXS moments are recast in terms of matrix elements between the zero-order wave functions and first-order frequency-dependent response wave functions of the initial and final states such that the RIXS moments can be evaluated using complex response one-particle transition density matrices (1PTDMs). Visualization of these 1PTDMs connects the RIXS process with the changes in electronic density. We demonstrate that the real and imaginary components of the response 1PTDMs can be interpreted as contributions of the undamped off-resonance and damped near-resonance SOS terms, respectively. By analyzing these 1PTDMs in terms of natural transition orbitals, we derive a rigorous, black-box mapping of the RIXS process into a molecular orbital picture. We illustrate the utility of the new tool by analyzing RIXS transitions in the OH radical, benzene, para-nitroaniline, and 4-amino-4'-nitrostilbene. These examples highlight the significance of both the near-resonance and off-resonance channels.

Simulations of valence excited states in coordination complexes reached through hard X-ray scattering

Hard X-ray spectroscopy selectively probes metal sites in complex environments. Resonant inelastic X-ray scattering (RIXS) makes it is possible to directly study metal-ligand interactions through local valence excitations. Here multiconfigurational wavefunction simulations are used to model valence K pre-edge RIXS for three metal-hexacyanide complexes by coupling the electric dipole-forbidden excitations with dipole-allowed valence-to-core emission. Comparisons between experimental and simulated spectra makes it possible to evaluate the simulation accuracy and establish a best-modeling practice. The calculations give correct descriptions of all LMCT excitations in the spectra, although energies and intensities are sensitive to the description of dynamical electron correlation. The consistent treatment of all complexes shows that simulations can rationalize spectral features. The dispersion in the manganese(iii) spectrum comes from unresolved multiple resonances rather than fluorescence, and the splitting is mainly caused by differences in spatial orientation between holes and electrons. The simulations predict spectral features that cannot be resolved in current experimental data sets and the potential for observing d-d excitations is also explored. The latter can be of relevance for non-centrosymmetric systems with more intense K pre-edges. These ab initio simulations can be used to both design and interpret high-resolution X-ray scattering experiments.

HERFD-XANES probes of electronic structures of ironII/III carbene complexes

Iron centered N-heterocyclic carbene (Fe-NHC) complexes have shown long-lived excited states with charge transfer character useful for light harvesting applications. Understanding the nature of the metal-ligand bond is of fundamental importance to rationally tailor the properties of transition metal complexes. The high-energy-resolution fluorescence detected X-ray absorption near edge structure (HERFD-XANES) has been used to probe the valence orbitals of three carbene complexes, [Fe^II(bpy)(btz)₂](PF₆)₂ (bpy = 2,2'-bipyridine, btz = 3,3'-dimethyl-1,1'-bis(p-tolyl)-4,4'-bis(1,2,3-triazol-5-ylidene)), [Fe^III(btz)₃](PF₆)₃, and [Fe^III(phtmeimb)₂]PF₆ (phtmeimb = [phenyl(tris(3-methylimidazol-2-ylidene))borate]^-). The multiconfigurational restrict active space (RAS) approach has been used to simulate the metal K pre-edge X-ray absorption spectroscopy of these carbene complexes, and have reproduced the metal K pre-edge spectral features in terms of relative intensity and peak positions. The evident intensity difference between the Fe^II and the other two Fe^III complexes has been elucidated with different intensity mechanisms in the transition. The smaller splitting between the t_2g and e_g character peak for [Fe^III(btz)₃](PF₆)₃ has been observed in the experimental measurements and been reproduced in the RAS calculations. The results show how the combination of experimental HERFD-XANES measurements and ab initio RAS simulations can give quantitative evaluation of the orbital interactions between metal and ligands for such large and strongly interacting systems and thus allow to understand and predict properties of novel complexes.

Vitamin Derived Nitrogen Doped Carbon Nanotubes for Efficient Oxygen Reduction Reaction and Arsenic Removal from Contaminated Water

Nitrogen doped carbon nanotubes (NCNT) that were prepared by simple microwave pyrolysis of Niacin (Vitamin B₃) as noble metal free electrocatalyst for oxygen reduction reaction (ORR) is reported. Our newly developed technique has the distinct features of sustainable and widely available niacin as a bi-functional source of both carbon and nitrogen, whereas the iron catalyst is cheap and the fourth most common element in the Earth’s crust. The results of the electrochemical tests show that our newly developed iron impregnated NCNT anchored on reduced graphene substrate (Fe@NCNT-rGO) catalyst exhibit: a positive half-wave potential (E_1/2) of 0.75 V vs. RHE (reversible hydrogen electrode), four-electron pathway, and better methanol tolerance when compared to commercial 20% Pt/C. When applied as adsorbent for arsenic removal, our newly discovered NCNT-Fe illustrate the efficient and effective removal of arsenic across a wide range of pH values.

How to stay out of trouble in RIXS calculations within equation-of-motion coupled-cluster damped response theory? Safe hitchhiking in the excitation manifold by means of core–valence separation

We present a novel approach with robust convergence of the response equations for computing resonant inelastic X-ray scattering (RIXS) cross sections within the equation-of-motion coupled-cluster (EOM-CC) framework.

Elucidation of the photoaquation reaction mechanism in ferrous hexacyanide using synchrotron x-rays with sub-pulse-duration sensitivity

Ligand substitution reactions are common in solvated transition metal complexes, and harnessing them through initiation with light promises interesting practical applications, driving interest in new means of probing their mechanisms. Using a combination of time-resolved x-ray absorption spectroscopy and hybrid quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations and x-ray absorption near-edge spectroscopy calculations, we elucidate the mechanism of photoaquation in the model system iron(ii) hexacyanide, where UV excitation results in the exchange of a CN^- ligand with a water molecule from the solvent. We take advantage of the high flux and stability of synchrotron x-rays to capture high precision x-ray absorption spectra that allow us to overcome the usual limitation of the relatively long x-ray pulses and extract the spectrum of the short-lived intermediate pentacoordinated species. Additionally, we determine its lifetime to be 19 (±5) ps. The QM/MM simulations support our experimental findings and explain the ∼20 ps time scale for aquation as involving interconversion between the square pyramidal (SP) and trigonal bipyramidal pentacoordinated geometries, with aquation being only active in the SP configuration.

X-ray Raman scattering: a building block for nonlinear spectroscopy

Ultraintense X-ray free-electron laser pulses of attosecond duration can enable new nonlinear X-ray spectroscopic techniques to observe coherent electronic motion. The simplest nonlinear X-ray spectroscopic concept is based on stimulated electronic X-ray Raman scattering. We present a snapshot of recent experimental achievements, paving the way towards the goal of realizing nonlinear X-ray spectroscopy. In particular, we review the first proof-of-principle experiments, demonstrating stimulated X-ray emission and scattering in atomic gases in the soft X-ray regime and first results of stimulated hard X-ray emission spectroscopy on transition metal complexes. We critically asses the challenges that have to be overcome for future successful implementation of nonlinear coherent X-ray Raman spectroscopy. This article is part of the theme issue 'Measurement of ultrafast electronic and structural dynamics with X-rays'.

Resonant inelastic X-ray scattering determination of the electronic structure of oxyhemoglobin and its model complex

Hemoglobin and myoglobin are oxygen-binding proteins with S = 0 heme {FeO₂}⁸ active sites. The electronic structure of these sites has been the subject of much debate. This study utilizes Fe K-edge X-ray absorption spectroscopy (XAS) and 1s2p resonant inelastic X-ray scattering (RIXS) to study oxyhemoglobin and a related heme {FeO₂}⁸ model compound, [(pfp)Fe(1-MeIm)(O₂)] (pfp = meso-tetra(α,α,α,α-o-pivalamido-phenyl)porphyrin, or TpivPP, 1-MeIm = 1-methylimidazole) (pfpO₂), which was previously analyzed using L-edge XAS. The K-edge XAS and RIXS data of pfpO₂ and oxyhemoglobin are compared with the data for low-spin Fe^II and Fe^III [Fe(tpp)(Im)₂]^0/+ (tpp = tetra-phenyl porphyrin) compounds, which serve as heme references. The X-ray data show that pfpO₂ is similar to Fe^II, while oxyhemoglobin is qualitatively similar to Fe^III, but with significant quantitative differences. Density-functional theory (DFT) calculations show that the difference between pfpO₂ and oxyhemoglobin is due to a distal histidine H bond to O₂ and the less hydrophobic environment in the protein, which lead to more backbonding into the O₂ A valence bond configuration interaction multiplet model is used to analyze the RIXS data and show that pfpO₂ is dominantly Fe^II with 6-8% Fe^III character, while oxyhemoglobin has a very mixed wave function that has 50-77% Fe^III character and a partially polarized Fe-O₂ π-bond.

Disentangling Transient Charge Density and Metal-Ligand Covalency in Photoexcited Ferricyanide with Femtosecond Resonant Inelastic Soft X-ray Scattering

Soft X-ray spectroscopies are ideal probes of the local valence electronic structure of photocatalytically active metal sites. Here, we apply the selectivity of time-resolved resonant inelastic X-ray scattering at the iron L-edge to the transient charge distribution of an optically excited charge-transfer state in aqueous ferricyanide. Through comparison to steady-state spectra and quantum chemical calculations, the coupled effects of valence-shell closing and ligand-hole creation are experimentally and theoretically disentangled and described in terms of orbital occupancy, metal-ligand covalency, and ligand field splitting, thereby extending established steady-state concepts to the excited-state domain. π-Back-donation is found to be mainly determined by the metal site occupation, whereas the ligand hole instead influences σ-donation. Our results demonstrate how ultrafast resonant inelastic X-ray scattering can help characterize local charge distributions around catalytic metal centers in short-lived charge-transfer excited states, as a step toward future rationalization and tailoring of photocatalytic capabilities of transition-metal complexes.

Direct Observation of Cr3+ 3d States in Ruby: Toward Experimental Mechanistic Evidence of Metal Chemistry

The role of transition metals in chemical reactions is often derived from probing the metal 3d states. However, the relation between metal site geometry and 3d electronic states, arising from multielectronic effects, makes the spectral data interpretation and modeling of these optical excited states a challenge. Here we show, using the well-known case of red ruby, that unique insights into the density of transition metal 3d excited states can be gained with 2p3d resonant inelastic X-ray scattering (RIXS). We compare the experimental determination of the 3d excited states of Cr³⁺ impurities in Al₂O₃ with 190 meV resolution 2p3d RIXS to optical absorption spectroscopy and to simulations. Using the crystal field multiplet theory, we calculate jointly for the first time the Cr³⁺ multielectronic states, RIXS, and optical spectra based on a unique set of parameters. We demonstrate that (i) anisotropic 3d multielectronic interactions causes different scaling of Slater integrals, and (ii) a previously not observed doublet excited state exists around 3.35 eV. These results allow to discuss the influence of interferences in the RIXS intermediate state, of core–hole lifetime broadenings, and of selection rules on the RIXS intensities. Finally, our results demonstrate that using an intermediate excitation energy between L₃ and L₂ edges allows measurement of the density of 3d excited states as a fingerprint of the metal local structure. This opens up a new direction to pump-before-destroy investigations of transition metal complex structures and reaction mechanisms.

Fingerprints of electronic, spin and structural dynamics from resonant inelastic soft X-ray scattering in transient photo-chemical species

We describe how inversion symmetry separation of electronic state manifolds in resonant inelastic soft X-ray scattering (RIXS) can be applied to probe excited-state dynamics with compelling selectivity. In a case study of Fe L3-edge RIXS in the ferricyanide complex Fe(CN)63-, we demonstrate with multi-configurational restricted active space spectrum simulations how the information content of RIXS spectral fingerprints can be used to unambiguously separate species of different electronic configurations, spin multiplicities, and structures, with possible involvement in the decay dynamics of photo-excited ligand-to-metal charge-transfer. Specifically, we propose that this could be applied to confirm or reject the presence of a hitherto elusive transient Quartet species. Thus, RIXS offers a particular possibility to settle a recent controversy regarding the decay pathway, and we expect the technique to be similarly applicable in other model systems of photo-induced dynamics.

Cobalt-to-vanadium charge transfer in polyoxometalate water oxidation catalysts revealed by 2p3d resonant inelastic X-ray scattering

2p3d RIXS spectra reveal electronic structures ofCo4V2WOC, which offers insights into its enhanced catalytic activity thanCo4P2WOC.

Advanced X-ray Spectroscopic Methods for Studying Iron-Sulfur-Containing Proteins and Model Complexes

In this chapter, a brief overview of X-ray spectroscopic methods that may be utilized to obtain insight into the geometric and electronic structure of iron-sulfur proteins is provided. These methods include conventional methods, such as metal and ligand K-edge X-ray absorption, as well as more advanced methods including nonresonant and resonant X-ray emission. In each section, the basic information content of the spectra is highlighted and important experimental considerations are discussed. Throughout the chapter, recent applications to iron-sulfur-containing models and proteins are highlighted.

Local vs Nonlocal States in FeTiO3 Probed with 1s2pRIXS: Implications for Photochemistry

Metal-metal charge transfer (MMCT) is expected to be the main mechanism that enables the harvesting of solar light by iron-titanium oxides for photocatalysis. We have studied FeTiO3 as a model compound for MMCT with 1s2pRIXS at the Fe K-edge. The high-energy resolution XANES enables distinguishing five pre-edge features. The three first well distinct RIXS features are assigned to electric quadrupole transitions to the localized Fe* 3d states, shifted to lower energy by the 1s core-hole. Crystal field multiplet calculations confirm the speciation of divalent iron. The contribution of electric dipole absorption due to local p-d mixing allowed by the trigonal distortion of the cation site is supported by DFT and CFM calculations. The two other nonlocal features are assigned to electric dipole transitions to excited Fe* 4p states mixed with the neighboring Ti 3d states. The comparison with DFT calculations demonstrates that MMCT in ilmenite is favored by the hybridization between the Fe 4p and delocalized Ti 3d orbitals via the O 2p orbitals.

Effective intermediate-spin iron in O2-transporting heme proteins

Proteins carrying an iron-porphyrin (heme) cofactor are essential for biological O2 management. The nature of Fe-O2 bonding in hemoproteins is debated for decades. We used energy-sampling and rapid-scan X-ray Kβ emission and K-edge absorption spectroscopy as well as quantum chemistry to determine molecular and electronic structures of unligated (deoxy), CO-inhibited (carboxy), and O2-bound (oxy) hemes in myoglobin (MB) and hemoglobin (HB) solutions and in porphyrin compounds at 20-260 K. Similar metrical and spectral features revealed analogous heme sites in MB and HB and the absence of low-spin (LS) to high-spin (HS) conversion. Amplitudes of Kβ main-line emission spectra were directly related to the formal unpaired Fe(d) spin count, indicating HS Fe(II) in deoxy and LS Fe(II) in carboxy. For oxy, two unpaired Fe(d) spins and, thus by definition, an intermediate-spin iron center, were revealed by our static and kinetic X-ray data, as supported by (time-dependent) density functional theory and complete-active-space self-consistent-field calculations. The emerging Fe-O2 bonding situation includes in essence a ferrous iron center, minor superoxide character of the noninnocent ligand, significant double-bond properties of the interaction, and three-center electron delocalization as in ozone. It resolves the apparently contradictory classical models of Pauling, Weiss, and McClure/Goddard into a unifying view of O2 bonding, tuned toward reversible oxygen transport.

Highly efficient soft X-ray spectrometer based on a reflection zone plate for resonant inelastic X-ray scattering measurements

We present a newly designed compact and flexible soft X-ray spectrometer for resonant inelastic X-ray scattering (RIXS) studies within an energy range from 380 eV to 410 eV, which would include the K alpha emission lines of vital elements like nitrogen. We utilized an off-axis reflection zone plate (RZP) as the wavelength selective element with a maximum line density of 10000 l/mm. A higher energy resolution over a broader range of ± 15 eV around the designed energy was achieved by displacing the RZP. Additionally, for the first time, an actual optical side effect, the so-called comatic aberration was exploited to increase the energy resolution. First results show a resolving power in the order of 1300 for photon energy of 395 eV, which is comparable to a commercial varied line spacing grating (VLS).

K- and L-edge X-ray Absorption Spectroscopy (XAS) and Resonant Inelastic X-ray Scattering (RIXS) Determination of Differential Orbital Covalency (DOC) of Transition Metal Sites

Continual advancements in the development of synchrotron radiation sources have resulted in X-ray based spectroscopic techniques capable of probing the electronic and structural properties of numerous systems. This review gives an overview of the application of metal K-edge and L-edge X-ray absorption spectroscopy (XAS), as well as K resonant inelastic X-ray scattering (RIXS), to the study of electronic structure in transition metal sites with emphasis on experimentally quantifying 3d orbital covalency. The specific sensitivities of K-edge XAS, L-edge XAS, and RIXS are discussed emphasizing the complementary nature of the methods. L-edge XAS and RIXS are sensitive to mixing between 3d orbitals and ligand valence orbitals, and to the differential orbital covalency (DOC), that is, the difference in the covalencies for different symmetry sets of the d orbitals. Both L-edge XAS and RIXS are highly sensitive to and enable separation of and donor bonding and back bonding contributions to bonding. Applying ligand field multiplet simulations, including charge transfer via valence bond configuration interactions, DOC can be obtained for direct comparison with density functional theory calculations and to understand chemical trends. The application of RIXS as a probe of frontier molecular orbitals in a heme enzyme demonstrates the potential of this method for the study of metal sites in highly covalent coordination sites in bioinorganic chemistry.

Chemical bonding in aqueous hexacyano cobaltate from photon- and electron-detection perspectives

The electronic structure of the [Co(CN)₆]^3- complex dissolved in water is studied using X-ray spectroscopy techniques. By combining electron and photon detection methods from the solutions ionized or excited by soft X-rays we experimentally identify chemical bonding between the metal center and the CN ligand. Non-resonant photoelectron spectroscopy provides solute electron binding energies, and nitrogen 1 s and cobalt 2p resonant core-level photoelectron spectroscopy identifies overlap between metal and ligand orbitals. By probing resonances we are able to qualitatively determine the ligand versus metal character of the respective occupied and non-occupied orbitals, purely by experiment. For the same excitations we also detect the emitted X-rays, yielding the complementary resonant inelastic X-ray scattering spectra. For a quantitative interpretation of the spectra, we perform theoretical electronic-structure calculations. The latter provide both orbital energies and orbital character which are found to be in good agreement with experimental energies and with experimentally inferred orbital mixing. We also report calculated X-ray absorption spectra, which in conjunction with our orbital-structure analysis, enables us to quantify various bonding interactions with a particular focus on the water-solvent - ligand interaction and the strength of π-backbonding between metal and ligand.

CTM4DOC: electronic structure analysis from X-ray spectroscopy

Two electronic structure descriptions, one based on orbitals and the other based on term symbols, have been implemented in a new Matlab-based program, CTM4DOC. The program includes a graphical user interface that allows the user to explore the dependence of details of electronic structure in transition metal systems, both in the ground and core-hole excited states, on intra-atomic electron-electron, crystal-field and charge-transfer interactions. The program can also track the evolution of electronic structure features as the crystal-field parameters are systematically varied, generating Tanabe-Sugano-type diagrams. Examples on first-row transition metal systems are presented and the implications on the interpretation of X-ray spectra and on the understanding of low-spin, high-spin and mixed-spin systems are discussed.

X-ray Spectroscopic Characterization of Co(IV) and Metal-Metal Interactions in Co4O4: Electronic Structure Contributions to the Formation of High-Valent States Relevant to the Oxygen Evolution Reaction

The formation of high-valent states is a key factor in making highly active transition-metal-based catalysts of the oxygen evolution reaction (OER). These high oxidation states will be strongly influenced by the local geometric and electronic structures of the metal ion, which are difficult to study due to spectroscopically active and complex backgrounds, short lifetimes, and limited concentrations. Here, we use a wide range of complementary X-ray spectroscopies coupled to DFT calculations to study Co(III)4O4 cubanes and their first oxidized derivatives, which provide insight into the high-valent Co(IV) centers responsible for the activity of molecular and heterogeneous OER catalysts. The combination of X-ray absorption and 1s3p resonant inelastic X-ray scattering (Kβ RIXS) allows Co(IV) to be isolated and studied against a spectroscopically active Co(III) background. Co K- and L-edge X-ray absorption data allow for a detailed characterization of the 3d-manifold of effectively localized Co(IV) centers and provide a direct handle on the t2g-based redox-active molecular orbital. Kβ RIXS is also shown to provide a powerful probe of Co(IV), and specific spectral features are sensitive to the degree of oxo-mediated metal-metal coupling across Co4O4. Guided by the data, calculations show that electron-hole delocalization can actually oppose Co(IV) formation. Computational extension of Co4O4 to CoM3O4 structures (M = redox-inactive metal) defines electronic structure contributions to Co(IV) formation. Redox activity is shown to be linearly related to covalency, and M(III) oxo inductive effects on Co(IV) oxo bonding can tune the covalency of high-valent sites over a large range and thereby tune E(0) over hundreds of millivolts. Additionally, redox-inactive metal substitution can also switch the ground state and modify metal-metal and antibonding interactions across the cluster.

Viewing the Valence Electronic Structure of Ferric and Ferrous Hexacyanide in Solution from the Fe and Cyanide Perspectives

The valence-excited states of ferric and ferrous hexacyanide ions in aqueous solution were mapped by resonant inelastic X-ray scattering (RIXS) at the Fe L2,3 and N K edges. Probing of both the central Fe and the ligand N atoms enabled identification of the metal- and ligand-centered excited states, as well as ligand-to-metal and metal-to-ligand charge-transfer excited states. Ab initio calculations utilizing the RASPT2 method were used to simulate the Fe L2,3-edge RIXS spectra and enabled quantification of the covalencies of both occupied and empty orbitals of π and σ symmetry. We found that π back-donation in the ferric complex is smaller than that in the ferrous complex. This is evidenced by the relative amounts of Fe 3d character in the nominally 2π CN(-) molecular orbital of 7% and 9% in ferric and ferrous hexacyanide, respectively. Utilizing the direct sensitivity of Fe L3-edge RIXS to the Fe 3d character in the occupied molecular orbitals, we also found that the donation interactions are dominated by σ bonding. The latter was found to be stronger in the ferric complex, with an Fe 3d contribution to the nominally 5σ CN(-) molecular orbitals of 29% compared to 20% in the ferrous complex. These results are consistent with the notion that a higher charge at the central metal atom increases donation and decreases back-donation.

Simulations of iron K pre-edge X-ray absorption spectra using the restricted active space method

The intensities and relative energies of metal K pre-edge features are sensitive to both geometric and electronic structures.

Insights into the geometric and electronic structure of transition metal centers from valence-to-core X-ray emission spectroscopy

A long-standing goal of inorganic chemists is the ability to decipher the geometric and electronic structures of chemical species. This is particularly true for the study of small molecule and biological catalysts, where this knowledge is critical for understanding how these molecules effect chemical transformations. Numerous techniques are available for this task, and collectively they have enabled detailed understanding of many complex chemical systems. Despite this battery of probes, however, challenges still remain, particularly when the structural question involves subtle perturbations of the ligands bound to a metal center, as is often the case during chemical reactions. It is here that, as an emerging probe of chemical structure, valence-to-core (VtC) X-ray emission spectroscopy (XES) holds promise. VtC XES begins with ionization of a 1s electron from a metal ion by high energy X-ray photons. Electrons residing in ligand-localized valence orbitals decay to fill the 1s hole, emitting fluorescent photons in the process; in this manner, VtC XES primarily probes the filled, ligand-based orbitals of a metal complex. This is in contrast to other X-ray based techniques, such as K-edge X-ray absorption and EXAFS, which probe the unoccupied d-manifold orbitals and atomic scatterers surrounding the metal, respectively. As a hard X-ray technique, VtC XES experiments can be performed on a variety of sample states and environments, enabling application to demanding systems, such as high pressure cells and dilute biological samples. VtC XES thus can offer unique insights into the geometric and electronic structures of inorganic complexes. In recent years, we have sought to use VtC XES in the study of inorganic and bioinorganic complexes; doing so, however, first required a thorough and detailed understanding of the information content of these spectra. Extensive experimental surveys of model compounds coupled to the insights provided by DFT calculated spectra of real and hypothetical compounds allowed the development of a framework whereby VtC XES spectra may be understood in terms of a molecular orbital picture. Specifically, VtC spectra may be interpreted as a probe of electronic structure for the ligands bound to a metal center, enabling access to chemical information that can be difficult to obtain with other methods. Examples of this include the ability to (1) assess the identity and number of atomic/small molecule ligands bound to a metal center, (2) quantify the degree of bond activation of a small molecule substrate, and (3) establish the protonation state of donor atoms. With this foundation established, VtC has been meaningfully applied to long-standing questions in bioinorganic chemistry, with the potential for numerous future applications in all areas of metal-mediated catalysis.

Feasibility of Valence-to-Core X-ray Emission Spectroscopy for Tracking Transient Species

X-ray spectroscopies, when combined in laser-pump, X-ray-probe measurement schemes, can be powerful tools for tracking the electronic and geometric structural changes that occur during the course of a photoinitiated chemical reaction. X-ray absorption spectroscopy (XAS) is considered an established technique for such measurements, and X-ray emission spectroscopy (XES) of the strongest core-to-core emission lines (Kα and Kβ) is now being utilized. Flux demanding valence-to-core XES promises to be an important addition to the time-resolved spectroscopic toolkit. In this paper we present measurements and density functional theory calculations on laser-excited, solution-phase ferrocyanide that demonstrate the feasibility of valence-to-core XES for time-resolved experiments. We discuss technical improvements that will make valence-to-core XES a practical pump-probe technique.

Characterizing the Intermediates Compound I and II in the Cytochrome P450 Catalytic Cycle with Nonlinear X-ray Spectroscopy: A Simulation Study

Cytochrome P450 enzymes are an important family of biocatalysts that oxidize chemically inert CH bonds. There are many unresolved questions regarding the catalytic reaction intermediates, in particular P450 Compound I (Cpd-I) and II (Cpd-II). By using simple molecular models, we simulate various X-ray spectroscopy signals, including X-ray absorption near-edge structure (XANES), resonant inelastic X-ray scattering (RIXS), and stimulated X-ray Raman spectroscopy (SXRS) of the low- and high-spin states of Cpd-I and II. Characteristic peak patterns are presented and connected to the corresponding electronic structures. These X-ray spectroscopy techniques are complementary to more conventional infrared and optical spectroscopy and they help to elucidate the evolving electronic structures of transient species along the reaction path.