From Ligand Fields to Molecular Orbitals: Probing the Local Valence Electronic Structure of Ni2+ in Aqueous Solution with Resonant Inelastic X-ray Scattering

Orbital Magnetic Moment and Single-Ion Magnetic Anisotropy of the S = 1/2 K3[Fe(CN)6] Compound: A Case Where the Orbital Magnetic Moment Dominates the Spin Magnetic Moment

The potassium hexacyanoferrate(III), K3[FeIII(CN)6], is known for its exceptional magnetic anisotropy among the 3d transition metal series. The Fe(III) ions are in the S = 1/2 low spin state imposed by the strong crystal field of the cyanido ligands. A large orbital magnetic moment is expected from previous publications. In the present work, X-ray magnetic circular dichroism was recorded for a powder sample, allowing direct measurement of the Fe(III) orbital magnetic moment. A combination of molecular multiconfigurational ab initio and atomic ligand field multiplets calculations provides the spin and orbital magnetic moments for the [FeIII(CN)6]3- isolated cluster, the crystallographic unit cell, and the powder sample. The calculations of the angular dependencies of the spin and orbital magnetic moments with the external magnetic induction direction reveal easy magnetization axes for each S = 1/2 molecular entity and the crystal. It also shows that the orbital magnetic moment dominates the spin magnetic moment for all directions. Our measurements confirm that the orbital magnetic moment contributes to 60% of the total magnetization for the powder, which is in excellent agreement with our theoretical predictions. An orbital magnetic moment greater than the spin magnetic moment is exceptional for 3d transition metal ions. The impact of crystal field strength and distortion, π back-bonding, spin-orbit coupling, and external magnetic induction was analyzed, leading to a deeper understanding of the spin and orbital magnetic anisotropies.

Computational approaches for XANES, VtC-XES, and RIXS using linear-response time-dependent density functional theory based methods

The emergence of state-of-the-art X-ray light sources has paved the way for novel spectroscopies that take advantage of their atomic specificity to shed light on fundamental physical, chemical, and biological processes both in the static and time domains. The success of these experiments hinges on the ability to interpret and predict core-level spectra, which has opened avenues for theory to play a key role. Over the last two decades, linear-response time-dependent density functional theory (LR-TDDFT), despite various theoretical challenges, has become a computationally attractive and versatile framework to study excited-state spectra including X-ray spectroscopies. In this context, we focus our discussion on LR-TDDFT approaches for the computation of X-ray Near-Edge Structure (XANES), Valence-to-Core X-ray Emission (VtC-XES), and Resonant Inelastic X-ray Scattering (RIXS) spectroscopies in molecular systems with an emphasis on Gaussian basis set implementations. We illustrate these approaches with applications and provide a brief outlook of possible new directions.

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.

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.

Resonant Inelastic X-ray Scattering Calculations of Transition Metal Complexes Within a Simplified Time-Dependent Density Functional Theory Framework

We present a time-dependent density functional theory (TDDFT) approach to compute the light-matter couplings between two different manifolds of excited states relative to a common ground state in the context of 4d transition metal systems. These quantities are the necessary ingredients to solve the Kramers-Heisenberg (KH) equation for resonant inelastic X-ray scattering (RIXS) and several other types of two-photon spectroscopies. The procedure is based on the pseudo-wavefunction approach, where the solutions of a TDDFT calculation can be used to construct excited-state wavefunctions, and on the restricted energy window approach, where a manifold of excited states can be rigorously defined based on the energies of the occupied molecular orbitals involved in the excitation process. Thus, the present approach bypasses the need to solve the costly TDDFT quadratic-response equations. We illustrate the applicability of the method to 4d transition metal molecular complexes by calculating the 2p4d RIXS maps of three representative ruthenium complexes and comparing them to experimental results. The method can capture all the experimental features in all three complexes to allow the assignment of the experimental peaks, with relative energies correct to within ∼0.6 eV at the cost of two independent TDDFT calculations.

Mechanism of L2,3-edge x-ray magnetic circular dichroism intensity from quantum chemical calculations and experiment-A case study on V(IV)/V(III) complexes

In this work, we present a combined experimental and theoretical study on the V L_2,3-edge x-ray absorption (XAS) and x-ray magnetic circular dichroism (XMCD) spectra of V^IVO(acac)₂ and V^III(acac)₃ prototype complexes. The recorded V L_2,3-edge XAS and XMCD spectra are richly featured in both V L₃ and L₂ spectral regions. In an effort to predict and interpret the nature of the experimentally observed spectral features, a first-principles approach for the simultaneous prediction of XAS and XMCD spectra in the framework of wavefunction based ab initio methods is presented. The theory used here has previously been formulated for predicting optical absorption and MCD spectra. In the present context, it is applied to the prediction of the V L_2,3-edge XAS and XMCD spectra of the V^IVO(acac)₂ and V^III(acac)₃ complexes. In this approach, the spin-free Hamiltonian is computed on the basis of the complete active space configuration interaction (CASCI) in conjunction with second order N-electron valence state perturbation theory (NEVPT2) as well as the density functional theory (DFT)/restricted open configuration interaction with singles configuration state functions based on a ground state Kohn-Sham determinant (ROCIS/DFT). Quasi-degenerate perturbation theory is then used to treat the spin-orbit coupling (SOC) operator variationally at the many particle level. The XAS and XMCD transitions are computed between the relativistic many particle states, considering their respective Boltzmann populations. These states are obtained from the diagonalization of the SOC operator along with the spin and orbital Zeeman operators. Upon averaging over all possible magnetic field orientations, the XAS and XMCD spectra of randomly oriented samples are obtained. This approach does not rely on the validity of low-order perturbation theory and provides simultaneous access to the calculation of XMCD A, B, and C terms. The ability of the method to predict the XMCD C-term signs and provide access to the XMCD intensity mechanism is demonstrated on the basis of a generalized state coupling mechanism based on the type of the excitations dominating the relativistically corrected states. In the second step, the performance of CASCI, CASCI/NEVPT2, and ROCIS/DFT is evaluated. The very good agreement between theory and experiment has allowed us to unravel the complicated XMCD C-term mechanism on the basis of the SOC interaction between the various multiplets with spin S' = S, S ± 1. In the last step, it is shown that the commonly used spin and orbital sum rules are inadequate in interpreting the intensity mechanism of the XAS and XMCD spectra of the V^IVO(acac)₂ and V^III(acac)₃ complexes as they breakdown when they are employed to predict their magneto-optical properties. This conclusion is expected to hold more generally.

Modeling core-level excitations with variationally optimized reduced-density matrices and the extended random phase approximation

The information contained within ground-state one- and two-electron reduced-density matrices (RDMs) can be used to compute wave functions and energies for electronically excited states through the extended random phase approximation (ERPA). The ERPA is an appealing framework for describing excitations out of states obtained via the variational optimization of the two-electron RDM (2-RDM), as the variational 2-RDM (v2RDM) approach itself can only be used to describe the lowest-energy state of a given spin symmetry. The utility of the ERPA for predicting near-edge features relevant to x-ray absorption spectroscopy is assessed for the case that the 2-RDM is obtained from a ground-state v2RDM-driven complete active space self-consistent field (CASSCF) computation. A class of killer conditions for the CASSCF-specific ERPA excitation operator is derived, and it is demonstrated that a reliable description of core-level excitations requires an excitation operator that fulfills these conditions; the core-valence separation (CVS) scheme yields such an operator. Absolute excitation energies evaluated within the CASSCF/CVS-ERPA framework are slightly more accurate than those obtained from the usual random phase approximation (RPA), but the CVS-ERPA is not more accurate than RPA for predicting the relative positions of near-edge features. Nonetheless, CVS-ERPA is established as a reasonable starting point for the treatment of core-level excitations using variationally optimized 2-RDMs.

The nature of frontier orbitals under systematic ligand exchange in (pseudo-)octahedral Fe(ii) complexes

The impact of ligand substitution on metal-ligand covalency and the valence excited state landscape is investigated using resonant inelastic soft X-ray scattering.

Understanding and controlling properties of transition metal complexes is a crucial step towards tailoring materials for sustainable energy applications. In a systematic approach, we use resonant inelastic X-ray scattering to study the influence of ligand substitution on the valence electronic structure around an aqueous iron(ii) center. Exchanging cyanide with 2-2′-bipyridine ligands reshapes frontier orbitals in a way that reduces metal 3d charge delocalization onto the ligands. This net decrease of metal–ligand covalency results in lower metal-centered excited state energies in agreement with previously reported excited state dynamics. Furthermore, traces of solvent-effects were found indicating a varying interaction strength of the solvent with ligands of different character. Our results demonstrate how ligand exchange can be exploited to shape frontier orbitals of transition metal complexes in solution-phase chemistry; insights upon which future efforts can built when tailoring the functionality of photoactive systems for light-harvesting applications.

A Restricted Open Configuration Interaction with Singles Method To Calculate Valence-to-Core Resonant X-ray Emission Spectra: A Case Study

In this work, a new protocol for the calculation of valence-to-core resonant X-ray emission (VtC RXES) spectra is introduced. The approach is based on the previously developed restricted open configuration interaction with singles (ROCIS) method and its parametrized version, based on a ground-state Kohn-Sham determinant (DFT/ROCIS) method. The ROCIS approach has the following features: (1) In the first step approximation, many-particle eigenstates are calculated in which the total spin is retained as a good quantum number. (2) The ground state with total spin S and excited states with spin S' = S, S ± 1, are obtained. (3) These states have a qualitatively correct multiplet structure. (4) Quasi-degenerate perturbation theory is used to treat the spin-orbit coupling operator variationally at the many-particle level. (5) Transition moments are obtained between the relativistic many-particle states. The method has shown great potential in the field of X-ray spectroscopy, in particular in the field of transition-metal L-edge, which cannot be described correctly with particle-hole theories. In this work, the method is extended to the calculation of resonant VtC RXES [alternatively referred to as 1s-VtC resonant inelastic X-ray scattering (RIXS)] spectra. The complete Kramers-Dirac-Heisenerg equation is taken into account. Thus, state interference effects are treated naturally within this protocol. As a first application of this protocol, a computational study on the previously reported VtC RXES plane on a molecular managanese(V) complex is performed. Starting from conventional X-ray absorption spectra (XAS), we present a systematic study that involves calculations and electronic structure analysis of both the XAS and non-resonant and resonant VtC XES spectra. The very good agreement between theory and experiment, observed in all cases, allows us to unravel the complicated intensity mechanism of these spectroscopic techniques as a synergic function of state polarization and interference effects. In general, intense features in the RIXS spectra originate from absorption and emission processes that involve nonorthogonal transition moments. We also present a graphical method to determine the sign of the interference contributions.

Basics and applications of ELNES calculations

The electron energy loss near edge structures (ELNES) appearing in an electron energy loss spectrum obtained through transmission electron microscopy (TEM) have the potential to unravel atomic and electronic structures with sub-nano meter resolution. For this reason, TEM-ELNES has become one of the most powerful analytical methods in materials research. On the other hand, theoretical calculations are indispensable in interpreting the ELNES spectrum. Here, the basics and applications of one-particle, two-particle and multi-particle ELNES calculations are reviewed. A key point for the ELNES calculation is the proper introduction of the core-hole effect. Some applications of one-particle ELNES calculations to huge systems of more than 1000 atoms, and complex systems, such as liquids, are reported. In the two-particle calculations, the importance of the correct treatment of the excitonic interaction is demonstrated in calculating the low-energy ELNES, for example at the Li-K edge. In addition, an unusually strong excitonic interactions in the O-K edge of perovskite oxides is identified. The multi-particle calculations are necessary to reproduce the multiplet structures appearing at the transition metal L2,3-edges and rare-earth M4,5-edges. Applications to dilute magnetic semiconductors and Li-ion battery materials are presented. Furthermore, beyond the 'conventional' ELNES calculations, theoretical calculations of electron/X-ray magnetic circular dichroism (MCD) and the vibrational information in ELNES, are reported.

Time-resolved soft X-ray absorption spectroscopy in transmission mode on liquids at MHz repetition rates

We present a setup combining a liquid flatjet sample delivery and a MHz laser system for time-resolved soft X-ray absorption measurements of liquid samples at the high brilliance undulator beamline UE52-SGM at Bessy II yielding unprecedented statistics in this spectral range. We demonstrate that the efficient detection of transient absorption changes in transmission mode enables the identification of photoexcited species in dilute samples. With iron(II)-trisbipyridine in aqueous solution as a benchmark system, we present absorption measurements at various edges in the soft X-ray regime. In combination with the wavelength tunability of the laser system, the set-up opens up opportunities to study the photochemistry of many systems at low concentrations, relevant to materials sciences, chemistry, and biology.

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.

Orbital breathing effects in the computation of x-ray d-ion spectra in solids by ab initio wave-function-based methods

In existing theoretical approaches to core-level excitations of transition-metal ions in solids relaxation and polarization effects due to the inner core hole are often ignored or described phenomenologically. Here we set up an ab initio computational scheme that explicitly accounts for such physics in the calculation of x-ray absorption and resonant inelastic x-ray scattering spectra. Good agreement is found with experimental transition-metal L-edge data for the strongly correlated d ⁹ cuprate Li₂CuO₂, for which we determine the absolute scattering intensities. The newly developed methodology opens the way for the investigation of even more complex d ⁿ electronic structures of group VI B to VIII B correlated oxide compounds.

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.

A liquid flatjet system for solution phase soft-x-ray spectroscopy

We present a liquid flatjet system for solution phase soft-x-ray spectroscopy. The flatjet set-up utilises the phenomenon of formation of stable liquid sheets upon collision of two identical laminar jets. Colliding the two single water jets, coming out of the nozzles with 50 μm orifices, under an impact angle of 48° leads to double sheet formation, of which the first sheet is 4.6 mm long and 1.0 mm wide. The liquid flatjet operates fully functional under vacuum conditions (<10(-3) mbar), allowing soft-x-ray spectroscopy of aqueous solutions in transmission mode. We analyse the liquid water flatjet thickness under atmospheric pressure using interferomeric or mid-infrared transmission measurements and under vacuum conditions by measuring the absorbance of the O K-edge of water in transmission, and comparing our results with previously published data obtained with standing cells with Si3N4 membrane windows. The thickness of the first liquid sheet is found to vary between 1.4-3 μm, depending on the transverse and longitudinal position in the liquid sheet. We observe that the derived thickness is of similar magnitude under 1 bar and under vacuum conditions. A catcher unit facilitates the recycling of the solutions, allowing measurements on small sample volumes (∼10 ml). We demonstrate the applicability of this approach by presenting measurements on the N K-edge of aqueous NH4 (+). Our results suggest the high potential of using liquid flatjets in steady-state and time-resolved studies in the soft-x-ray regime.