Chemical Bonding in Aqueous Ferrocyanide: Experimental and Theoretical X-ray Spectroscopic Study

Using Iron L-Edge and Nitrogen K-Edge X-ray Absorption Spectroscopy to Improve the Understanding of the Electronic Structure of Iron Carbene Complexes

Iron-centered N-heterocyclic carbene compounds have attracted much attention in recent years due to their long-lived excited states with charge transfer (CT) character. Understanding the orbital interactions between the metal and ligand orbitals is of great importance for the rational tuning of the transition metal compound properties, e.g., for future photovoltaic and photocatalytic applications. Here, we investigate a series of iron-centered N-heterocyclic carbene complexes with +2, + 3, and +4 oxidation states of the central iron ion using iron L-edge and nitrogen K-edge X-ray absorption spectroscopy (XAS). The experimental Fe L-edge XAS data were simulated and interpreted through restricted-active space (RAS) and multiplet calculations. The experimental N K-edge XAS is simulated and compared with time-dependent density functional theory (TDDFT) calculations. Through the combination of the complementary Fe L-edge and N K-edge XAS, direct probing of the complex interplay of the metal and ligand character orbitals was possible. The σ-donating and π-accepting capabilities of different ligands are compared, evaluated, and discussed. The results show how X-ray spectroscopy, together with advanced modeling, can be a powerful tool for understanding the complex interplay of metal and ligand.

Unveiling Hidden Shake-Up Features in the Uranyl M4-Edge Spectrum

The M4,5-edge high energy resolution X-ray absorption near-edge structure (HR-XANES) spectra of actinyls offer valuable insights into the electronic structure and bonding properties of heavy-element complexes. To conduct a comprehensive spectral analysis, it is essential to employ computational methods that accurately account for relativistic effects and electron correlation. In this work, we utilize variational relativistic multireference configurational interaction methods to compute and analyze the X-ray M4-edge absorption spectrum of uranyl. By employing these advanced computational techniques, we achieve excellent agreement between the calculated spectral features and experimental observations. Moreover, the calculations unveil significant shake-up features, which arise from the intricate interplay between strongly correlated 3d core-electron and ligand excitations. This research provides important theoretical insights into the spectral characteristics of heavy-element complexes. Furthermore, it establishes the foundation for utilizing M4,5-edge spectroscopy as a means to investigate the chemical activities of such complexes. By leveraging this technique, we can gain a deeper understanding of the bonding behavior and reactivity of heavy-element compounds.

The Role of the Lowest Excited Triplet State in Defining the Rate of Photoaquation of Hexacyanometalates

Photosolvation is a type of ligand substitution reaction started by irradiation of a solution with light, triggering the replacement of a ligand with a molecule from the solvent. The excited state is created through many possible pathways. For the class of hexacyanides of groups 8 and 9 of the periodic table, irradiation in the ligand field band is followed by intersystem crossing to the lowest excited triplet state, which we propose to mediate the photoaquation reaction in this class of complexes. In this study, we present time-resolved X-ray absorption data showing indications of the triplet intermediate state in the cobalt(III) hexacyanide complex and we discuss general aspects of the photoaquation reaction in comparison with reported data on the isoelectronic iron(II) hexacyanide. Quantum chemical calculations are analyzed and suggest that the nature of the lowest excited triplet state in each complex can explain the drastically different rate of reactions observed.

Interpreting the Cu-O2 Antibonding Nature in Two Cu-O2 Complexes from Cu L-Edge X-ray Absorption Spectra

Cu-O2 structures play important roles in bioinorganic chemistry and enzyme catalysis, where the bonding between the Cu and O2 parts serves as a fundamental research concern. Here, we performed a multiconfigurational study on the copper L2,3-edge X-ray absorption spectra (XAS) of two copper enzyme model complexes to gain a better understanding of the antibonding nature from the clearly interpreted structure-spectroscopy relation. We obtained spectra in good agreement with the experiments by using the restricted active space second-order perturbation theory (RASPT2) method, which facilitated reliable chemical analysis. Spectral feature interpretations were supported by computing the spin-orbit natural transition orbitals. All major features were assigned to be mainly from Cu 2p to antibonding orbitals between Cu 3d and O2 π*, Cu 3d-πO-O* (type A), and a few also to mixed antibonding/bonding orbitals between Cu 3d and O2 π, Cu 3d ± πO-O (type M). Our calculations provided a clear illustration of the interactions between Cu 3d and O2 π*/π orbitals that are carried in the metal L-edge XAS.

X-ray absorption spectra of f-element complexes: insight from relativistic multiconfigurational wavefunction theory

X-ray absorption near edge structure (XANES) spectroscopy, coupled with ab initio calculations, has emerged as the state-of-the-art tool for elucidating the metal-ligand bonding in f-element complexes. This highlight presents recent efforts in calculating XANES spectra of lanthanide and actinide compounds with relativistic multiconfiguration wavefunction approaches that account for differences in donation bonding in the ground state (GS) versus a core-excited state (ES), multiplet effects, and spin-orbit-coupling. With the GS and ES wavefunctions available, including spin-orbit effects, an arsenal of chemical bonding tools that are popular among chemists can be applied to rationalize the observed intensities in terms of covalent bonding.

Soft x-ray signatures of ionic manganese-oxo systems, including a high-spin manganese(V) complex

Manganese-oxo species catalyze key reactions, including C–H bond activation or dioxygen formation in natural photosynthesis. To better understand relevant reaction intermediates, we characterize electronic states and geometric structures of [MnOn]+...

Covalency in Actinide(IV) Hexachlorides in Relation to Chlorine K­-Edge X­-ray Absorption Structure

Chlorine K-edge X-ray absorption near edge structure (XANES) in actinide^IV hexachlorides, [AnCl₆]²⁻ (An = Th–Pu), is calculated with relativistic multiconfiguration wavefunction theory (WFT). Of particular focus is a 3-peak feature emerging from U toward Pu, and its assignment in terms of donation bonding to the An 5f vs. 6d shells. With or without spin–orbit coupling, the calculated and previously measured XANES spectra are in excellent agreement with respect to relative peak positions, relative peak intensities, and peak assignments. Metal–ligand bonding analyses from WFT and Kohn–Sham theory (KST) predict comparable An 5f and 6d covalency from U to Np and Pu. Although some frontier molecular orbitals in the KST calculations display increasing An 5f–Cl 3p mixing from Th to Pu, because of energetic stabilization of 5f relative to the Cl 3p combinations of the matching symmetry, increasing hybridization is neither seen in the WFT natural orbitals, nor is it reflected in the calculated bond orders. The appearance of the pre-edge peaks from U to Pu and their relative intensities are rationalized simply by the energetic separation of transitions to 6d t_2gversus transitions to weakly-bonded and strongly stabilized a_2u, t_2u and t_1u orbitals with 5f character. The study highlights potential pitfalls when interpreting XANES spectra based on ground state Kohn–Sham molecular orbitals.

Chlorine K-edge XANES of An(iv) hexachlorides, calculated with multiconfiguration wavefunction theory, is interpreted in terms of similar metal–ligand covalency along the An = Th–Pu series.

Two-Component Multireference Restricted Active Space Configuration Interaction for the Computation of L-Edge X-ray Absorption Spectra

X-ray absorption spectroscopy is a powerful probe of local electronic and nuclear structures, providing insights into chemical processes. The theoretical prediction and interpretation of metal L-edge X-ray absorption spectra are complicated by both relativistic effects, including spin-orbit coupling and the multiconfigurational nature of the states involved. This work details an exact two-component multireference restricted active space (RAS) configuration interaction scheme that uses an exact two-component state-averaged complete active space self-consistent-field method, which includes the spin-orbit coupling in a variational manner, for the accurate description of the electronic structure before using a RAS configuration interaction method to describe the core excited states of the X-ray spectrum. Benchmark calculations are presented for a series of iron-containing complexes, with results showing key features of the spectrum being reproduced, including ligand-to-metal charge transfer and shake-up excitations.

Resonant X-ray photo-oxidation of light-harvesting iron (II/III) N-heterocyclic carbene complexes

Two photoactive iron N-heterocyclic carbene complexes \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${[\hbox {Fe}^{{{\rm{II}}}}(\hbox {btz})_2(\hbox {bpy})]^{2+}}$$\end{document}[FeII(btz)2(bpy)]2+ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${[\hbox {Fe}^{{\rm{III}}}(\hbox {btz})_3]^{3+}}$$\end{document}[FeIII(btz)3]3+, where btz is 3,3’-dimethyl-1,1’-bis(p-tolyl)-4,4’-bis(1,2,3-triazol-5-ylidene) and bpy is 2,2’-bipyridine, have been investigated by Resonant Photoelectron Spectroscopy (RPES). Tuning the incident X-ray photon energy to match core-valence excitations provides a site specific probe of the electronic structure properties and ligand-field interactions, as well as information about the resonantly photo-oxidised final states. Comparing measurements of the Fe centre and the surrounding ligands demonstrate strong mixing of the Fe \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hbox {t}_{{\rm{2g}}}}$$\end{document}t2g levels with occupied ligand \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi$$\end{document}π orbitals but weak mixing with the corresponding unoccupied ligand orbitals. This highlights the importance of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi$$\end{document}π-accepting and -donating considerations in ligand design strategies for photofunctional iron carbene complexes. Spin-propensity is also observed as a final-state effect in the RPES measurements of the open-shell \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Fe}^{{\rm{III}}}$$\end{document}FeIII complex. Vibronic coupling is evident in both complexes, where the energy dispersion hints at a vibrationally hot final state. The results demonstrate the significant impact of the iron oxidation state on the frontier electronic structure and highlights the differences between the emerging class of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Fe}^{{\rm{III}}}$$\end{document}FeIII photosensitizers from those of more traditional \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Fe}^{{\rm{II}}}$$\end{document}FeII complexes.

Ultrafast strong-field dissociation of vinyl bromide: An attosecond transient absorption spectroscopy and non-adiabatic molecular dynamics study

Attosecond extreme ultraviolet (XUV) and soft x-ray sources provide powerful new tools for studying ultrafast molecular dynamics with atomic, state, and charge specificity. In this report, we employ attosecond transient absorption spectroscopy (ATAS) to follow strong-field-initiated dynamics in vinyl bromide. Probing the Br M edge allows one to assess the competing processes in neutral and ionized molecular species. Using ab initio non-adiabatic molecular dynamics, we simulate the neutral and cationic dynamics resulting from the interaction of the molecule with the strong field. Based on the dynamics results, the corresponding time-dependent XUV transient absorption spectra are calculated by applying high-level multi-reference methods. The state-resolved analysis obtained through the simulated dynamics and related spectral contributions enables a detailed and quantitative comparison with the experimental data. The main outcome of the interaction with the strong field is unambiguously the population of the first three cationic states, D ₁, D ₂, and D ₃. The first two show exclusively vibrational dynamics while the D ₃ state is characterized by an ultrafast dissociation of the molecule via C-Br bond rupture within 100 fs in 50% of the analyzed trajectories. The combination of the three simulated ionic transient absorption spectra is in excellent agreement with the experimental results. This work establishes ATAS in combination with high-level multi-reference simulations as a spectroscopic technique capable of resolving coupled non-adiabatic electronic-nuclear dynamics in photoexcited molecules with sub-femtosecond resolution.

Role of Dopants on the Local Electronic Structure of Polymeric Carbon Nitride Photocatalysts

Polymeric carbon nitride (PCN) is a promising class of materials for solar-to-chemical energy conversion. The increase of the photocatalytic activity of PCN is often achieved by the incorporation of heteroatoms, whose impact on the electronic structure of PCN remains poorly explored. This work reveals that the local electronic structure of PCN is strongly altered by doping with sulfur and iron using X-ray absorption spectroscopy (XAS) and resonant inelastic X-ray scattering (RIXS). From XAS at the carbon and nitrogen K-edges, sulfur atoms are found to mostly affect carbon atoms, in contrast to iron doping mostly altering nitrogen sites. In RIXS at the nitrogen K-edge, a vibrational progression, affected by iron doping, is evidenced, which is attributed to a vibronic coupling between excited electrons in nitrogen atoms and C-N stretching modes in PCN heterocycling rings. This work opens new perspectives for the characterization of vibronic coupling in polymeric photocatalysts.

Solution XANES and EXAFS analysis of active species of titanium, vanadium complex catalysts in ethylene polymerisation/dimerisation and syndiospecific styrene polymerisation

Mechanistic studies in homogeneous catalysis through the solution transition metal K Edge XANES (X-ray absorption near-edge structure) and EXAFS (Extended X-ray absorption fine structure) analysis for vanadium and titanium complex catalysts for ethylene polymerisation/dimerization, and syndiospecific styrene polymerisation, including interpretation of the XANES spectra, have been introduced. The core excitation spectra of the complexes based on the time-dependent density functional theory (TD-DFT) can be used to interpret the Ti and V K-edge features and to extract information on the electronic structure from the XANES spectra. Theoretical calculations and experimental XAS analysis should have great potential for analysing the active species.

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.

Restricted active space simulations of the metal L-edge X-ray absorption spectra and resonant inelastic X-ray scattering: revisiting [CoII/III(bpy)3]2+/3+complexes

The metal L-edge spectra of cobalt compounds have been interpreted through restricted active space calculations.

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.

Ab Initio Study of Covalency in the Ground versus Core-Excited States and X-ray Absorption Spectra of Actinide Complexes

Relativistic multireference ab initio wave function calculations within the restricted active space (RAS) framework were performed to calculate metal and ligand X-ray absorption (XAS) near-edge spectroscopy (XANES) intensities for the metal M_4,5 edges of [PuO₂(H₂O)₅]²⁺, [An^VIO₂]²⁺ (An = U, Np, Pu), and [AmCl₆]^3- and the Cl K edge of the Am complex. The extent of An(5f)-ligand bonding was determined via natural localized molecular orbital analyses of the relevant spin-orbit coupled multireference states. The calculated spectra are in good agreement with experiments and allow a detailed assignment of the observed spectral features. The XANES M_4,5-edge spectra are representative of the actinide orbital covalency in the probed core-excited states, which may be different from the ground-state covalency. An assignment of ground-state An orbital covalency based on XAS spectra should therefore be made with caution.

Probing the Valence Electronic Structure of Low-Spin Ferrous and Ferric Complexes Using 2p3d Resonant Inelastic X-ray Scattering (RIXS)

Understanding the detailed electronic structure of transition metal ions is essential in numerous areas of inorganic chemistry. In particular, the ability to map out the many particle d-d spectrum of a transition metal catalyst is key to understanding and predicting reactivity. However, from a practical perspective, there are often experimental limitations on the ability to determine the energetic ordering, and multiplicity of all the excited states. These limitations derive in part from parity and spin-selection rules, as well as from the limited energy range of many standard laboratory instruments. Herein, we demonstrate the ability of 2p3d resonant inelastic X-ray scattering (RIXS) to obtain detailed insights into the many particle spectrum of simple inorganic molecular iron complexes. The present study focuses on low-spin ferrous and ferric iron complexes, including [Fe^III/II(tacn)₂]^3+/2+ and [Fe^III/II(CN)₆]^3-/4-. This series thus allows us to assess the contribution of d-count and ligand donor type, by comparing the purely σ-donating tacn ligand to the π-accepting cyanide. In order to highlight the conceptual difference between RIXS and traditional optical spectroscopy, we compare first RIXS results with UV-vis and magnetic circular dichroism spectroscopy. We then highlight the ability of 2p3d RIXS to (1) separate d-d transitions from charge transfer transitions and (2) to determine the many particle d-d spectrum over a much wider energy range than is possible by optical spectroscopy. Our experimental results are correlated with semiempirical multiplet simulations and ab initio complete active space self-consistent field calculations in order to obtain detailed assignments of the excited states. These results show that Δ S = 1, and possibly Δ S = 2, transitions may be observed in 2p3d RIXS spectra. Hence, this methodology has great promise for future applications in all areas of transition metal inorganic chemistry.

Comprehensive Experimental and Computational Spectroscopic Study of Hexacyanoferrate Complexes in Water: From Infrared to X-ray Wavelengths

We present a joint experimental and computational study of the hexacyanoferrate aqueous complexes at equilibrium in the 250 meV to 7.15 keV regime. The experiments and the computations include the vibrational spectroscopy of the cyanide ligands, the valence electronic absorption spectra, and Fe 1s core hole spectra using element-specific-resonant X-ray absorption and emission techniques. Density functional theory-based quantum mechanics/molecular mechanics molecular dynamics simulations are performed to generate explicit solute-solvent configurations, which serve as inputs for the spectroscopy calculations of the experiments spanning the IR to X-ray wavelengths. The spectroscopy simulations are performed at the same level of theory across this large energy window, which allows for a systematic comparison of the effects of explicit solute-solvent interactions in the vibrational, valence electronic, and core-level spectra of hexacyanoferrate complexes in water. Although the spectroscopy of hexacyanoferrate complexes in solution has been the subject of several studies, most of the previous works have focused on a narrow energy window and have not accounted for explicit solute-solvent interactions in their spectroscopy simulations. In this work, we focus our analysis on identifying how the local solvation environment around the hexacyanoferrate complexes influences the intensity and line shape of specific spectroscopic features in the UV/vis, X-ray absorption, and valence-to-core X-ray emission spectra. The identification of these features and their relationship to solute-solvent interactions is important because hexacyanoferrate complexes serve as model systems for understanding the photochemistry and photophysics of a large class of Fe(II) and Fe(III) complexes in solution.

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.

Monovalent manganese based anodes and co-solvent electrolyte for stable low-cost high-rate sodium-ion batteries

The demand of sustainable power supply requires high-performance cost-effective energy storage technologies. Here we report a high-rate long-life low-cost sodium-ion battery full-cell system by innovating both the anode and the electrolyte. The redox couple of manganese(I/II) in Prussian blue analogs enables a high-rate and stable anode. Soft X-ray absorption spectroscopy and resonant inelastic X-ray scattering provide direct evidence suggesting the existence of monovalent manganese in the charged anode. There is a strong hybridization between cyano ligands and manganese-3d states, which benefits the electronic property for improving rate performance. Additionally, we employ an organic–aqueous cosolvent electrolyte to solve the long-standing solubility issue of Prussian blue analogs. A full-cell sodium-ion battery with low-cost Prussian blue analogs in both electrodes and co-solvent electrolyte retains 95% of its initial discharge capacity after 1000 cycles at 1C and 95% depth of discharge. The revealed manganese(I/II) redox couple inspires conceptual innovations of batteries based on atypical oxidation states.

Sodium ion batteries offer more cost-effective storage than lithium and could be used for grid-scale energy storage. Here, the authors demonstrate a full cell based on a MnHCMn anode and an organic-aqueous cosolvent electrolyte. X-ray spectroscopy evidence further suggests the presence of Mn(I).

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.

Chemical Inhibition Method to Synthesize Highly Crystalline Prussian Blue Analogs for Sodium-Ion Battery Cathodes

The nucleation rate plays a critical role in the synthesis of Prussian blue analogs. Rapid precipitation may lead to a large number of vacancies and a large amount of interstitial water in the material, resulting in poor electrochemical performance in batteries. Hence, sodium citrate is used to compete with [Fe(CN)₆]^4- to slow down the coordination rates of Ni²⁺ and Mn²⁺ ions with ferrous cyanide ions. The feasibility of the experiment is also confirmed by theoretical analysis. Benefiting from stable crystal structure and the removal of interstitial water, the as-prepared Na₂Ni_xMn_yFe(CN)₆ sample exhibits a high reversible capacity of 150 mA h g^-1. In addition, a high rate performance of 77 mA h g^-1 is achieved at a current density of 1600 mA g^-1. Most noteworthy, the Coulombic efficiency and specific capacity gradually increase in the first few cycles, which can be ascribed to the formation of a passivation layer on the surface of the electrode. Continuous testing in an electrolyte solution of 1 M NaPF₆ dissolved in sulfone reveals that the presence of a passivation film is very important for the stability of the electrode.

Towards an ab initio theory for metal L-edge soft X-ray spectroscopy of molecular aggregates

The Frenkel exciton model was adapted to describe X-ray absorption and resonant inelastic scattering spectra of polynuclear transition metal complexes by means of the restricted active space self-consistent field method. The proposed approach allows to substantially decrease the requirements on computational resources if compared to a full supermolecular quantum chemical treatment. This holds true, in particular, in cases where the dipole approximation to the electronic transition charge density can be applied. The computational protocol was applied to the calculation of X-ray spectra of the hemin complex, which forms dimers in aqueous solution. The aggregation effects were found to be comparable to the spectral alterations due to the replacement of the axial ligand by solvent molecules.

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.

Identification of the dominant photochemical pathways and mechanistic insights to the ultrafast ligand exchange of Fe(CO)5 to Fe(CO)4EtOH

We utilized femtosecond time-resolved resonant inelastic X-ray scattering and ab initio theory to study the transient electronic structure and the photoinduced molecular dynamics of a model metal carbonyl photocatalyst Fe(CO)5 in ethanol solution. We propose mechanistic explanation for the parallel ultrafast intra-molecular spin crossover and ligation of the Fe(CO)4 which are observed following a charge transfer photoexcitation of Fe(CO)5 as reported in our previous study [Wernet et al., Nature 520, 78 (2015)]. We find that branching of the reaction pathway likely happens in the (1)A1 state of Fe(CO)4. A sub-picosecond time constant of the spin crossover from (1)B2 to (3)B2 is rationalized by the proposed (1)B2 → (1)A1 → (3)B2 mechanism. Ultrafast ligation of the (1)B2 Fe(CO)4 state is significantly faster than the spin-forbidden and diffusion limited ligation process occurring from the (3)B2 Fe(CO)4 ground state that has been observed in the previous studies. We propose that the ultrafast ligation occurs via (1)B2 → (1)A1 → (1)A' Fe(CO)4EtOH pathway and the time scale of the (1)A1 Fe(CO)4 state ligation is governed by the solute-solvent collision frequency. Our study emphasizes the importance of understanding the interaction of molecular excited states with the surrounding environment to explain the relaxation pathways of photoexcited metal carbonyls in solution.

K- and L-edge X-ray absorption spectrum calculations of closed-shell carbon, silicon, germanium, and sulfur compounds using damped four-component density functional response theory

X-ray absorption spectra of carbon, silicon, germanium, and sulfur compounds have been investigated by means of damped four-component density functional response theory. It is demonstrated that a reliable description of relativistic effects is obtained at both K- and L-edges. Notably, an excellent agreement with experimental results is obtained for L2,3-spectra-with spin-orbit effects well accounted for-also in cases when the experimental intensity ratio deviates from the statistical one of 2 : 1. The theoretical results are consistent with calculations using standard response theory as well as recently reported real-time propagation methods in time-dependent density functional theory, and the virtues of different approaches are discussed. As compared to silane and silicon tetrachloride, an anomalous error in the absolute energy is reported for the L2,3-spectrum of silicon tetrafluoride, amounting to an additional spectral shift of ∼1 eV. This anomaly is also observed for other exchange-correlation functionals, but it is seen neither at other silicon edges nor at the carbon K-edge of fluorine derivatives of ethene. Considering the series of molecules SiH4-XFX with X = 1, 2, 3, 4, a gradual divergence from interpolated experimental ionization potentials is observed at the level of Kohn-Sham density functional theory (DFT), and to a smaller extent with the use of Hartree-Fock. This anomalous error is thus attributed partly to difficulties in correctly emulating the electronic structure effects imposed by the very electronegative fluorines, and partly due to inconsistencies in the spurious electron self-repulsion in DFT. Substitution with one, or possibly two, fluorine atoms is estimated to yield small enough errors to allow for reliable interpretations and predictions of L2,3-spectra of more complex and extended silicon-based systems.

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.

Multi-reference approach to the calculation of photoelectron spectra including spin-orbit coupling

X-ray photoelectron spectra provide a wealth of information on the electronic structure. The extraction of molecular details requires adequate theoretical methods, which in case of transition metal complexes has to account for effects due to the multi-configurational and spin-mixed nature of the many-electron wave function. Here, the restricted active space self-consistent field method including spin-orbit coupling is used to cope with this challenge and to calculate valence- and core-level photoelectron spectra. The intensities are estimated within the frameworks of the Dyson orbital formalism and the sudden approximation. Thereby, we utilize an efficient computational algorithm that is based on a biorthonormal basis transformation. The approach is applied to the valence photoionization of the gas phase water molecule and to the core ionization spectrum of the [Fe(H2O)6](2+) complex. The results show good agreement with the experimental data obtained in this work, whereas the sudden approximation demonstrates distinct deviations from experiments.

Distinguishing between High- and Low-Spin States for Divalent Mn in Mn-Based Prussian Blue Analogue by High-Resolution Soft X-ray Emission Spectroscopy

We combine Mn L2,3-edge X-ray absorption, high resolution Mn 2p-3d-2p resonant X-ray emission, and configuration-interaction full-multiplet (CIFM) calculation to analyze the electronic structure of Mn-based Prussian blue analogue. We clarified the Mn 3d energy diagram for the Mn(2+) low-spin state separately from that of the Mn(2+) high-spin state by tuning the excitation energy for the X-ray emission measurement. The obtained X-ray emission spectra are generally reproduced by the CIFM calculation for the Mn(2+) low spin state having a stronger ligand-to-metal charge-transfer effect between Mn t2g and CN π orbitals than the Mn(2+) high spin state. The d-d-excitation peak nearest to the elastic scattering was ascribed to the Mn(2+) LS state by the CIFM calculation, indicating that the Mn(2+) LS state with a hole on the t2g orbital locates near the Fermi level.