Prospects of high-resolution resonant X-ray inelastic scattering studies on solid materials, liquids and gases at diffraction-limited storage rings

New Implementation of an Equation-of-Motion Coupled-Cluster Damped-Response Framework with Illustrative Applications to Resonant Inelastic X-ray Scattering

We present an implementation of a damped response framework for calculating resonant inelastic X-ray scattering (RIXS) at the equation-of-motion coupled-cluster singles and doubles (CCSD) and second-order approximate coupled-cluster singles and doubles (CC2) levels of theory in the open-source program e^T. This framework lays the foundation for future extension to higher excitation methods (notably, the coupled-cluster singles and doubles with perturbative triples, CC3) and to multilevel approaches. Our implementation adopts a fully relaxed ground state and different variants of the core-valence separation projection technique to address convergence issues. Illustrative results are compared with those obtained within the frozen-core core-valence separated approach, available in Q-Chem, as well as with experiment. The performance of the CC2 method is evaluated in comparison with that of CCSD. It is found that, while the CC2 method is noticeably inferior to CCSD for X-ray absorption spectra, the quality of the CC2 RIXS spectra is often comparable to that of the CCSD level of theory, when the same valence excited states are probed. Finally, we present preliminary RIXS results for a solvated molecule in aqueous solution.

The meV XUV-RIXS facility at UE112-PGM1 of BESSY II

Resonant inelastic X-ray scattering in the XUV-regime has been implemented at BESSY II, pushing for a few-meV bandwidth in inelastic X-ray scattering at transition metal M-edges, rare earth N-edges and the K-edges of light elements up to carbon with full polarization control. The new dedicated low-energy beamline UE112-PGM1 has been designed to provide 1 µm vertical and 20 µm horizontal beam dimensions that serve together with sub-micrometre solid-state sample positioning as the source point for a high-resolution plane grating spectrometer and a high-transmission Rowland spectrometer for rapid overview spectra. The design and commissioning results of the beamline and high-resolution spectrometer are presented. Helium autoionization spectra demonstrate a resolving power of the beamline better than 10 000 at 64 eV with a 300 lines mm-1 grating while the measured resolving power of the spectrometer in the relevant energy range is 3000 to 6000.

An ultra-high-stability four-axis ultra-high-vacuum sample manipulator

A report on a four-axis ultra-high-stability manipulator developed for use at the Veritas and Species RIXS beamlines at MAX IV Laboratory, Lund, Sweden, is presented. The manipulator consists of a compact, light-weight X-Y table with a stiffened Z tower carrying a platform with a rotary seal to which a manipulator rod holding the sample can be attached. Its design parameters have been optimized to achieve high eigen-frequencies via a light-weight yet stiff construction, to absorb forces without deformations, provide a low center of gravity, and have a compact footprint without compromising access to the manipulator rod. The manipulator system can house a multitude of different, easily exchangeable, manipulator rods that can be tailor-made for specific experimental requirements without having to rebuild the entire sample positioning system. It is shown that the manipulator has its lowest eigen-frequency at 48.5 Hz and that long-term stability is in the few tens of nanometres. Position accuracy is shown to be better than 100 nm. Angular accuracy is in the 500 nrad range with a long-term stability of a few hundred nanoradians.

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.

A design of resonant inelastic X-ray scattering (RIXS) spectrometer for spatial- and time-resolved spectroscopy

The optical design of a Hettrick-Underwood-style soft X-ray spectrometer with Wolter type 1 mirrors is presented. The spectrometer with a nominal length of 3.1 m can achieve a high resolving power (resolving power higher than 10000) in the soft X-ray regime when a small source beam (<3 µm in the grating dispersion direction) and small pixel detector (5 µm effective pixel size) are used. Adding Wolter mirrors to the spectrometer before its dispersive elements can realize the spatial imaging capability, which finds applications in the spectroscopic studies of spatially dependent electronic structures in tandem catalysts, heterostructures, etc. In the pump-probe experiments where the pump beam perturbs the materials followed by the time-delayed probe beam to reveal the transient evolution of electronic structures, the imaging capability of the Wolter mirrors can offer the pixel-equivalent femtosecond time delay between the pump and probe beams when their wavefronts are not collinear. In combination with some special sample handing systems, such as liquid jets and droplets, the imaging capability can also be used to study the time-dependent electronic structure of chemical transformation spanning multiple time domains from microseconds to nanoseconds. The proposed Wolter mirrors can also be adopted to the existing soft X-ray spectrometers that use the Hettrick-Underwood optical scheme, expanding their capabilities in materials research.

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.

Resonant inelastic X-ray scattering of a Ru photosensitizer: Insights from individual ligands to the electronic structure of the complete molecule

N 1s Resonant Inelastic X-ray Scattering (RIXS) was used to probe the molecular electronic structure of the ruthenium photosensitizer complex cis-bis(isothiocyanato) bis(2,2'-bipyridyl-4,4'-dicarboxylato) ruthenium(II), known as "N3." In order to interpret these data, crystalline powder samples of the bipyridine-dicarboxylic acid ligand ("bi-isonicotinic acid") and the single ring analog "isonicotinic acid" were studied separately using the same method. Clear evidence for intermolecular hydrogen bonding is observed for each of these crystalline powders, along with clear vibronic coupling features. For bi-isonicotinic acid, these results are compared to those of a physisorbed multilayer, where no hydrogen bonding is observed. The RIXS of the "N3" dye, again prepared as a bulk powder sample, is interpreted in terms of the orbital contributions of the bi-isonicotinic acid and thiocyanate ligands by considering the two different nitrogen species. This allows direct comparison with the isolated ligand molecules where we highlight the impact of the central Ru atom on the electronic structure of the ligand. Further interpretation is provided through complementary resonant photoemission spectroscopy and density functional theory calculations. This combination of techniques allows us to confirm the localization and relative coupling of the frontier orbitals and associated vibrational losses.

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.

Modular soft x-ray spectrometer for applications in energy sciences and quantum materials

Over the past decade, the advances in grating-based soft X-ray spectrometers have revolutionized the soft X-ray spectroscopies in materials research. However, these novel spectrometers are mostly dedicated designs, which cannot be easily adopted for applications with diverging demands. Here we present a versatile spectrometer design concept based on the Hettrick-Underwood optical scheme that uses modular mechanical components. The spectrometer's optics chamber can be used with gratings operated in either inside or outside orders, and the detector assembly can be reconfigured accordingly. The spectrometer can be designed to have high spectral resolution, exceeding 10 000 resolving power when using small source (∼1μm) and detector pixels (∼5μm) with high line density gratings (∼3000 lines/mm), or high throughput at moderate resolution. We report two such spectrometers with slightly different design goals and optical parameters in this paper. We show that the spectrometer with high throughput and large energy window is particularly useful for studying the sustainable energy materials. We demonstrate that the extensive resonant inelastic X-ray scattering (RIXS) map of battery cathode material LiNi_1/3Co_1/3Mn_1/3O₂ can be produced in few hours using such a spectrometer. Unlike analyzing only a handful of RIXS spectra taken at selected excitation photon energies across the elemental absorption edges to determine various spectral features like the localized dd excitations and non-resonant fluorescence emissions, these features can be easily identified in the RIXS maps. Studying such RIXS maps could reveal novel transition metal redox in battery compounds that are sometimes hard to be unambiguously identified in X-ray absorption and emission spectra. We propose that this modular spectrometer design can serve as the platform for further customization to meet specific scientific demands.

Extreme ultraviolet resonant inelastic X-ray scattering (RIXS) at a seeded free-electron laser

In the past few years, we have been witnessing an increased interest for studying materials properties under non-equilibrium conditions. Several well established spectroscopies for experiments in the energy domain have been successfully adapted to the time domain with sub-picosecond time resolution. Here we show the realization of high resolution resonant inelastic X-ray scattering (RIXS) with a stable ultrashort X-ray source such as an externally seeded free electron laser (FEL). We have designed and constructed a RIXS experimental endstation that allowed us to successfully measure the d-d excitations in KCoF₃ single crystals at the cobalt M_2,3-edge at FERMI FEL (Elettra-Sincrotrone Trieste, Italy). The FEL-RIXS spectra show an excellent agreement with the ones obtained from the same samples at the MERIXS endstation of the MERLIN beamline at the Advanced Light Source storage ring (Berkeley, USA). We established experimental protocols for performing time resolved RIXS experiments at a FEL source to avoid X ray-induced sample damage, while retaining comparable acquisition time to the synchrotron based measurements. Finally, we measured and modelled the influence of the FEL mixed electromagnetic modes, also present in externally seeded FELs, and the beam transport with ~120 meV experimental resolution achieved in the presented RIXS setup.

Towards 10 meV resolution: The design of an ultrahigh resolution soft X-ray RIXS spectrometer

We present the optical design of the Centurion soft X-ray resonant inelastic X-ray scattering (RIXS) spectrometer to be located on the SIX beamline at NSLS-II. The spectrometer is designed to reach a resolving power of 100 000 at 1000 eV at its best resolution. It is also designed to have continuously variable 2θ motion over a range of 112° using a custom triple rotating flange. We have analyzed several possible spectrometer designs capable of reaching the target resolution. After careful analysis, we have adopted a Hettrick-Underwood spectrometer design, with an additional plane mirror to maintain a fixed direction for the outgoing beam. The spectrometer can cancel defocus and coma aberrations at all energies, has an erect focal plane, and minimizes mechanical motions of the detector. When the beamline resolution is accounted for, the net spectral resolution will be 14 meV at 1000 eV. This will open up many low energy excitations to study and will expand greatly the power of soft X-ray RIXS.

Ground state potential energy surfaces around selected atoms from resonant inelastic x-ray scattering

Thermally driven chemistry as well as materials’ functionality are determined by the potential energy surface of a systems electronic ground state. This makes the potential energy surface a central and powerful concept in physics, chemistry and materials science. However, direct experimental access to the potential energy surface locally around atomic centers and to its long-range structure are lacking. Here we demonstrate how sub-natural linewidth resonant inelastic soft x-ray scattering at vibrational resolution is utilized to determine ground state potential energy surfaces locally and detect long-range changes of the potentials that are driven by local modifications. We show how the general concept is applicable not only to small isolated molecules such as O₂ but also to strongly interacting systems such as the hydrogen bond network in liquid water. The weak perturbation to the potential energy surface through hydrogen bonding is observed as a trend towards softening of the ground state potential around the coordinating atom. The instrumental developments in high resolution resonant inelastic soft x-ray scattering are currently accelerating and will enable broad application of the presented approach. With this multidimensional potential energy surfaces that characterize collective phenomena such as (bio)molecular function or high-temperature superconductivity will become accessible in near future.

High-energy resolution X-ray absorption and emission spectroscopy reveals insight into unique selectivity of La-based nanoparticles for CO₂

The lanthanum-based materials, due to their layered structure and f-electron configuration, are relevant for electrochemical application. Particularly, La2O2CO3 shows a prominent chemoresistive response to CO2. However, surprisingly less is known about its atomic and electronic structure and electrochemically significant sites and therefore, its structure-functions relationships have yet to be established. Here we determine the position of the different constituents within the unit cell of monoclinic La2O2CO3 and use this information to interpret in situ high-energy resolution fluorescence-detected (HERFD) X-ray absorption near-edge structure (XANES) and valence-to-core X-ray emission spectroscopy (vtc XES). Compared with La(OH)3 or previously known hexagonal La2O2CO3 structures, La in the monoclinic unit cell has a much lower number of neighboring oxygen atoms, which is manifested in the whiteline broadening in XANES spectra. Such a superior sensitivity to subtle changes is given by HERFD method, which is essential for in situ studying of the interaction with CO2. Here, we study La2O2CO3-based sensors in real operando conditions at 250 °C in the presence of oxygen and water vapors. We identify that the distribution of unoccupied La d-states and occupied O p- and La d-states changes during CO2 chemoresistive sensing of La2O2CO3. The correlation between these spectroscopic findings with electrical resistance measurements leads to a more comprehensive understanding of the selective adsorption at La site and may enable the design of new materials for CO2 electrochemical applications.

Rydberg-resolved resonant inelastic soft x-ray scattering: dynamics at core ionization thresholds

Resonant inelastic x-ray scattering spectra excited in the immediate vicinity of the core-level ionization thresholds of N2 have been recorded. Final states of well-resolved symmetry-selected Rydberg series converging to valence-level ionization thresholds with vibrational excitations are observed. The results are well described by a quasi-two-step model which assumes that the excited electron is unaffected by the radiative decay. This threshold dynamics simplifies the interpretation of resonant inelastic x-ray scattering spectra considerably and facilitates characterization of low-energy excited final states in molecular systems.

Diffraction-limited storage rings - a window to the science of tomorrow

This article summarizes the contributions in this special issue on Diffraction-Limited Storage Rings. It analyses the progress in accelerator technology enabling a significant increase in brightness and coherent fraction of the X-ray light provided by storage rings. With MAX IV and Sirius there are two facilities under construction that already exploit these advantages. Several other projects are in the design stage and these will probably enhance the performance further. To translate the progress in light source quality into new science requires similar progress in aspects such as optics, beamline technology, detectors and data analysis. The quality of new science will be limited by the weakest component in this value chain. Breakthroughs can be expected in high-resolution imaging, microscopy and spectroscopy. These techniques are relevant for many fields of science; for example, for the fundamental understanding of the properties of correlated electron materials, the development and characterization of materials for data and energy storage, environmental applications and bio-medicine.

X-ray spectroscopy for chemical and energy sciences: the case of heterogeneous catalysis

Heterogeneous catalysis is the enabling technology for much of the current and future processes relevant for energy conversion and chemicals synthesis. The development of new materials and processes is greatly helped by the understanding of the catalytic process at the molecular level on the macro/micro-kinetic time scale and on that of the actual bond breaking and bond making. The performance of heterogeneous catalysts is inherently the average over the ensemble of active sites. Much development aims at unravelling the structure of the active site; however, in general, these methods yield the ensemble-average structure. A benefit of X-ray-based methods is the large penetration depth of the X-rays, enabling in situ and operando measurements. The potential of X-ray absorption and emission spectroscopy methods (XANES, EXAFS, HERFD, RIXS and HEROS) to directly measure the structure of the catalytically active site at the single nanoparticle level using nanometer beams at diffraction-limited storage ring sources is highlighted. The use of pump-probe schemes coupled with single-shot experiments will extend the time range from the micro/macro-kinetic time domain to the time scale of bond breaking and making.