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

PINK: a tender X-ray beamline for X-ray emission spectroscopy

A high-flux beamline optimized for non-resonant X-ray emission spectroscopy (XES) in the tender X-ray energy range has been constructed at the BESSY II synchrotron source. The beamline utilizes a cryogenically cooled undulator that provides X-rays over the energy range 2.1 keV to 9.5 keV. This energy range provides access to XES [and in the future X-ray absorption spectroscopy (XAS)] studies of transition metals ranging from Ti to Cu (Kα, Kβ lines) and Zr to Ag (Lα, Lβ), as well as light elements including P, S, Cl, K and Ca (Kα, Kβ). The beamline can be operated in two modes. In PINK mode, a multilayer monochromator (E/ΔE ≃ 30-80) provides a high photon flux (1014 photons s-1 at 6 keV and 300 mA ring current), allowing non-resonant XES measurements of dilute substances. This mode is currently available for general user operation. X-ray absorption near-edge structure and resonant XAS techniques will be available after the second stage of the PINK commissioning, when a high monochromatic mode (E/ΔE ≃ 10000-40000) will be facilitated by a double-crystal monochromator. At present, the beamline incorporates two von Hamos spectrometers, enabling time-resolved XES experiments with time scales down to 0.1 s and the possibility of two-color XES experiments. This paper describes the optical scheme of the PINK beamline and the endstation. The design of the two von Hamos dispersive spectrometers and sample environment are discussed here in detail. To illustrate, XES spectra of phosphorus complexes, KCl, TiO2 and Co3O4 measured using the PINK setup are presented.

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.

Resonant Excitation Unlocks Chemical Selectivity of Platinum Lβ Valence-to-Core X-ray Emission Spectra

Valence-to-core X-ray emission spectroscopy (VtC XES) is an emerging technique that uses hard X-rays to probe the valence electronic structure of an absorbing atom. Despite finding varied applications for light elements and first row transition metals, little work has been done on heavier elements such as second and third row transition metals. This lack of application is at least partially due to the relatively low resolution of the data at the high energies required to measure these elements, which obscures the useful chemical information that can be extracted from the lower energy, higher resolution spectra of lighter elements. Herein, we collect data on a set of platinum-containing compounds and demonstrate that the VtC XES resolution can be dramatically enhanced by exciting the platinum atom in resonance with its L3-edge white line absorption. Whereas spectra excited using standard nonresonant absorption well above the Pt L3-edge display broad, unfeatured VtC regions, resonant XES (RXES) spectra have more than twofold improved resolution and are revealed to be rich in chemical information with the ability to distinguish between even closely related species. We further demonstrate that these RXES spectra may be used to selectively probe individual components of a mixture of Pt-containing compounds, establishing this technique as a viable probe for chemically complex samples. Lastly, it is shown that the spectra are interpretable using a molecular orbital framework and may be calculated using density functional theory, thus suggesting resonant excitation as a general strategy for extracting chemically useful information from heavy element VtC spectra.

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.

Relativistic Multiconfigurational Ab Initio Calculation of Uranyl 3d4f Resonant Inelastic X-ray Scattering

We applied relativistic multiconfigurational all-electron ab initio calculations including the spin-orbit interaction to calculate the 3d4f resonant inelastic X-ray scattering (RIXS) map (3d3/2 → 5f5/2 U M4 absorption edge and 4f5/2 → 3d3/2 U Mβ emission) of uranyl (UO22+). The calculated data are in excellent agreement with experimental results and allow a detailed understanding of the observed features and an unambiguous assignment of all involved intermediate and final states. The energies corresponding to the maxima of the resonant emission and the non-resonant (normal) emission were determined with high accuracy, and the corresponding X-ray absorption near edge structure spectra extracted at these two positions were simulated and agree well with the measured data. With the high quality of our theoretical data, we show that the cause of the splitting of the three main peaks in emission is due to the fine structure splitting of the 4f orbitals induced through the trans di-oxo bonds in uranyl and that we are able to obtain direct information about the energy differences between the 5f and 4f orbitals: Δ5f δ/ϕ - 4f δ/ϕ, Δ5f π* - 4f π, and Δ5f σ* - 4f σ from the 3d4f RIXS map. RIXS maps contain a wealth of information, and ab initio calculations facilitate an understanding of their complex structure in a clear and transparent way. With these calculations, we show that the multiconfigurational protocol, which is nowadays applied as a standard tool to study the X-ray spectra of transition metal complexes, can be extended to the calculation of RIXS maps of systems containing actinides.

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.

Terahertz Magneto-Optical Excitations of the sd-Hybrid States of Lithium Nitridocobaltate Li2(Li1-xCox)N

We report the results of the experimental and theoretical study of the magnetic anisotropy of single crystals of the Co-doped lithium nitride Li₂(Li_1-xCo_x)N with x = 0.005, 0.01, and 0.02. It was shown recently that doping of the Li₃N crystalline matrix with 3d transition metal (TM) ions yields superior magnetic properties comparable with the strongly anisotropic single-molecule magnetism of rare-earth complexes. Our combined electron spin resonance (ESR) and THz spectroscopic investigations of Li₂(Li_1-xCo_x)N in a very broad frequency range up to 1.7 THz and in magnetic fields up to 16 T enable an accurate determination of the energies of the spin levels of the ground state multiplet Ŝ = 1 of the paramagnetic Co(I) ion. In particular, we find a very large zero field splitting (ZFS) of almost 1 THz (∼4 meV or 33 cm^-1) between the ground-state singlet and the first excited doublet state. On the computational side, ab initio many-body quantum chemistry calculations reveal a ZFS gap consistent with the experimental value. Such a large ZFS energy yields a very strong single-ion magnetic anisotropy of easy-plane type resembling that of rare-earth ions. Its microscopic origin is the unusual linear coordination of the Co(I) ions in Li₂(Li_1-xCo_x)N with two nitrogen ligands. Our calculations also evidence a strong 3d-4s hybridization of the electronic shells resulting in significant electron spin density at the ⁵⁹Co nuclei, which may be responsible for the experimentally observed extraordinary large hyperfine structure of the ESR signals. Altogether, our experimental spectroscopic and computational results enable comprehensive insights into the remarkable properties of the Li₂[Li_1-x(TM)_x]N magnets on the microscopic level.

TD-DFT simulations of K-edge resonant inelastic X-ray scattering within the restricted subspace approximation

Truncation of orbital subspaces in TD-DFT yields an accurate description of RIXS spectra for soft X-ray K-edges.

Probing Sulfur Chemical and Electronic Structure with Experimental Observation and Quantitative Theoretical Prediction of Kα and Valence-to-Core Kβ X-ray Emission Spectroscopy

An extensive experimental and theoretical study of the Kα and Kβ high-resolution X-ray emission spectroscopy (XES) of sulfur-bearing systems is presented. This study encompasses a wide range of organic and inorganic compounds, including numerous experimental spectra from both prior published work and new measurements. Employing a linear-response time-dependent density functional theory (LR-TDDFT) approach, strong quantitative agreement is found in the calculation of energy shifts of the core-to-core Kα as well as the full range of spectral features in the valence-to-core Kβ spectrum. The ability to accurately calculate the sulfur Kα energy shift supports the use of sulfur Kα XES as a bulk-sensitive tool for assessing sulfur speciation. The fine structure of the sulfur Kβ spectrum, in conjunction with the theoretical results, is shown to be sensitive to the local electronic structure including effects of symmetry, ligand type and number, and, in the case of organosulfur compounds, to the nature of the bonded organic moiety. This agreement between theory and experiment, augmented by the potential for high-access XES measurements with the latest generation of laboratory-based spectrometers, demonstrates the possibility of broad analytical use of XES for sulfur and nearby third-row elements. The effective solution of the forward problem, i.e., successful prediction of detailed spectra from known molecular structure, also suggests future use of supervised machine learning approaches to experimental inference, as has seen recent interest for interpretation of X-ray absorption near-edge structure (XANES).

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.

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.

Stimulated X-ray Raman and Absorption Spectroscopy of Iron-Sulfur Dimers

Iron-sulfur complexes play an important role in biological processes such as metabolic electron transport. A detailed understanding of the mechanism of long-range electron transfer requires knowledge of the electronic structure of the complexes, which has traditionally been challenging to obtain, either by theory or by experiment, but the situation has begun to change with advances in quantum chemical methods and intense free electron laser light sources. We compute the spectra for stimulated X-ray Raman spectroscopy (SXRS) and absorption spectroscopy of homovalent and mixed-valence [2Fe-2S] complexes, using the ab initio density matrix renormalization group algorithm. The simulated spectra show clear signatures of the theoretically predicted dense low-lying excited states within the d-d manifold. Furthermore, the difference in spectral intensity between the absorption-active and Raman-active states provides a potential mechanism to selectively excite states by a proper tuning of the excitation pump, to access the electronic dynamics within this manifold.

Electronic Structure of Aqueous [Co(bpy)3]2+/3+ Electron Mediators

We report on the electronic structure of cobalt(II) tris-2,2'-bipyridine and cobalt(III) tris-2,2'-bipyridine in aqueous solution using resonant inelastic X-ray scattering (RIXS) spectroscopy at the Co L-edge and N K-edge resonances. Partial fluorescence yield X-ray absorption spectra at both edges were obtained by signal integration of the respective RIXS spectra. Experiments are complemented by calculations of the X-ray absorption spectra for high- and low-spin configurations using density functional theory/restricted open-shell configuration interaction singles and time-dependent density functional theory methods. We find that linear combinations of the simulated X-ray absorption spectra for different spin states reproduce the experimental spectra. Best agreement is obtained for measurements at the Co L-edge, for both samples. For cobalt(II) tris-2,2'-bipyridine, our combined experimental and computational study reveals ∼40% low-spin and ∼60% high-spin state components. Much stronger low-spin character is found for cobalt(III) tris-2,2'-bipyridine, ∼80% low spin and ∼20% high spin. Prominent energy-loss features in the Co RIXS spectra are indicative of d-d excitations and charge-transfer excitations due to strong mixing between metal and ligand orbitals in both complexes. Analysis of N 1s RIXS data reveals the emission from metal dominated orbitals in the valence region, supporting the strong metal-ligand mixing.