Spatial quantum beats in vibrational resonant inelastic soft x-ray scattering at dissociating states in oxygen

A fully dynamical description of time-resolved resonant inelastic X-ray scattering of pyrazine

Recent advancements in ultrashort and intense X-ray sources have enabled the utilisation of resonant inelastic X-ray scattering (RIXS) as a probing technique for monitoring photoinduced dynamics in molecular systems. To account for dynamic phenomena like non-adiabatic transitions across the relevant electronic state manifold, a time-dependent framework is crucial. Here, we introduce a fully time-dependent approach for calculating transient RIXS spectra using wavepacket dynamics simulations, alongside an explicit treatment of the X-ray probe pulse that surpasses Kramers-Heisenberg-Dirac constraints. Our analysis of pyrazine at the nitrogen K-edge underscores the importance of considering nuclear motion effects in all electronic states involved in the transient RIXS process. As a result, we propose a numerically exact approach to computationally support and predict cutting-edge time-resolved RIXS experiments.

Quantifying vibronic coupling with resonant inelastic X-ray scattering

Electron–phonon interactions are fundamental to the behavior of chemical and physical systems.

Observation of Double Excitations in the Resonant Inelastic X-ray Scattering of Nitric Oxide

The nitrogen K-edge resonant inelastic X-ray scattering (RIXS) map of nitric oxide (NO) has been measured and simulated to provide a detailed analysis of the observed features. High-resolution experimental RIXS maps were collected using an in situ gas flow cell and a high-transmission soft X-ray spectrometer. Accurate descriptions of the ground, excited, and core-excited states are based upon restricted active space self-consistent-field calculations using second order multiconfigurational perturbation theory. The nitrogen K-edge RIXS map of NO shows a range of features that can be assigned to intermediate states arising from 1s → π* and 1s → Rydberg excitations; additional bands are attributed to doubly excited intermediate states comprising 1s → π* and π → π* excitations. These results provide a detailed picture of RIXS for an open-shell molecule and an extensive description of the core-excited electronic structure of NO, an important molecule in many chemical and biological processes.

Towards an extremely high resolution broad-band flat-field spectrometer in the `water window'

The optical design of a novel spectrometer is presented, combining a cylindrically convex pre-mirror with a cylindrically concave varied-line-spacing grating (both in the meridional) to deliver a resolving power of 100000-200000 in the `water window' (2-5 nm). Most remarkably, the extremely high spectral resolution is achieved for an effective meridional source size of 50 µm (r.m.s.); this property could potentially be applied to diagnose SASE-FEL and well resolve individual single spikes in its radiation spectrum. The overall optical aberrations of the system are well analysed and compensated, providing an excellent flat-field at the detector domain throughout the whole spectral range. Also, a machine-learning scheme - SVM - is introduced to explore and reconstruct the optimal system with high efficiency.

Electronic decay of core-excited HCl molecules probed by THz streaking

The ultrafast electronic decay of HCl molecules in the time domain after resonant core excitation was measured. Here, a Cl-2p core electron was promoted to the antibonding σ^* orbital initiating molecular dissociation, and simultaneously, the electronic excitation relaxes via an Auger decay. For HCl, both processes compete on similar ultrashort femtosecond time scales. In order to measure the lifetime of the core hole excitation, we collinearly superimposed 40 fs soft x-ray pulses with intense terahertz (THz) radiation from the free-electron laser in Hamburg (FLASH). Electrons emitted from the molecules are accelerated (streaked) by the THz electric field where the resulting momentum change depends on the field's phase at the instant of ionization. Evaluation of a time-shift between the delay-dependent streaking spectra of photo- and Auger electrons yields a decay constant of (11 ± 2) fs for LMM Auger electrons. For further validation, the method was also applied to the MNN Auger decay of krypton. Reproduction of the value already published in the literature confirms that a temporal resolution much below the duration of the exciting x-ray pulses can be reached.

Compatibility of quantitative X-ray spectroscopy with continuous distribution models of water at ambient conditions

The phase diagram of water harbors controversial views on underlying structural properties of its constituting molecular moieties, its fluctuating hydrogen-bonding network, as well as pair-correlation functions. In this work, long energy-range detection of the X-ray absorption allows us to unambiguously calibrate the spectra for water gas, liquid, and ice by the experimental atomic ionization cross-section. In liquid water, we extract the mean value of 1.74 ± 2.1% donated and accepted hydrogen bonds per molecule, pointing to a continuous-distribution model. In addition, resonant inelastic X-ray scattering with unprecedented energy resolution also supports continuous distribution of molecular neighborhoods within liquid water, as do X-ray emission spectra once the femtosecond scattering duration and proton dynamics in resonant X-ray-matter interaction are taken into account. Thus, X-ray spectra of liquid water in ambient conditions can be understood without a two-structure model, whereas the occurrence of nanoscale-length correlations within the continuous distribution remains open.

Resonant inelastic x-ray incarnation of Young's double-slit experiment

Young's archetypal double-slit experiment forms the basis for modern diffraction techniques: The elastic scattering of waves yields an interference pattern that captures the real-space structure. Here, we report on an inelastic incarnation of Young's experiment and demonstrate that resonant inelastic x-ray scattering (RIXS) measures interference patterns, which reveal the symmetry and character of electronic excited states in the same way as elastic scattering does for the ground state. A prototypical example is provided by the quasi-molecular electronic structure of insulating Ba₃CeIr₂O₉ with structural Ir dimers and strong spin-orbit coupling. The double "slits" in this resonant experiment are the highly localized core levels of the two Ir atoms within a dimer. The clear double-slit-type sinusoidal interference patterns that we observe allow us to characterize the electronic excitations, demonstrating the power of RIXS interferometry to unravel the electronic structure of solids containing, e.g., dimers, trimers, ladders, or other superstructures.

Ultrafast dissociation features in RIXS spectra of the water molecule

The “pseudo-atomic” peak is formed significantly faster than the atomic-like peak in water RIXS.

L-edge spectroscopy of dilute, radiation-sensitive systems using a transition-edge-sensor array

We present X-ray absorption spectroscopy and resonant inelastic X-ray scattering (RIXS) measurements on the iron L-edge of 0.5 mM aqueous ferricyanide. These measurements demonstrate the ability of high-throughput transition-edge-sensor (TES) spectrometers to access the rich soft X-ray (100-2000 eV) spectroscopy regime for dilute and radiation-sensitive samples. Our low-concentration data are in agreement with high-concentration measurements recorded by grating spectrometers. These results show that soft-X-ray RIXS spectroscopy acquired by high-throughput TES spectrometers can be used to study the local electronic structure of dilute metal-centered complexes relevant to biology, chemistry, and catalysis. In particular, TES spectrometers have a unique ability to characterize frozen solutions of radiation- and temperature-sensitive samples.

Ultrafast Independent N-H and N-C Bond Deformation Investigated with Resonant Inelastic X-Ray Scattering

The femtosecond excited-state dynamics following resonant photoexcitation enable the selective deformation of N-H and N-C chemical bonds in 2-thiopyridone in aqueous solution with optical or X-ray pulses. In combination with multiconfigurational quantum-chemical calculations, the orbital-specific electronic structure and its ultrafast dynamics accessed with resonant inelastic X-ray scattering at the N 1s level using synchrotron radiation and the soft X-ray free-electron laser LCLS provide direct evidence for this controlled photoinduced molecular deformation and its ultrashort timescale.

Nuclear Dynamical Correlation Effects in X-ray Spectroscopy from a Theoretical Time-Domain Perspective

To date X-ray spectroscopy has become a routine tool that can reveal highly local and element-specific information on the electronic structure of atoms in complex environments. Here, we focus on nuclear dynamical correlation effects in X-ray spectra and develop a rigorous time-correlation function method employing ground state classical molecular dynamics simulations. The importance of nuclear correlation phenomena is demonstrated by comparison against the results from the conventional sampling approach performed on the same data set for gas phase water. In contrast to the first-order absorption, second-order resonant inelastic scattering spectra exhibit pronounced fingerprints of nuclear motions. The developed methodology is not biased to a particular electronic structure method and, owing to its generality, can be applied to, e.g., X-ray photoelectron and Auger spectroscopies.

A study of the water molecule using frequency control over nuclear dynamics in resonant X-ray scattering

We report a full analysis of the resonant inelastic X-ray scattering spectra of H₂O, D₂O and HDO.

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.

Stochastic stimulated electronic x-ray Raman spectroscopy

Resonant inelastic x-ray scattering (RIXS) is a well-established tool for studying electronic, nuclear, and collective dynamics of excited atoms, molecules, and solids. An extension of this powerful method to a time-resolved probe technique at x-ray free electron lasers (XFELs) to ultimately unravel ultrafast chemical and structural changes on a femtosecond time scale is often challenging, due to the small signal rate in conventional implementations at XFELs that rely on the usage of a monochromator setup to select a small frequency band of the broadband, spectrally incoherent XFEL radiation. Here, we suggest an alternative approach, based on stochastic spectroscopy, which uses the full bandwidth of the incoming XFEL pulses. Our proposed method is relying on stimulated resonant inelastic x-ray scattering, where in addition to a pump pulse that resonantly excites the system a probe pulse on a specific electronic inelastic transition is provided, which serves as a seed in the stimulated scattering process. The limited spectral coherence of the XFEL radiation defines the energy resolution in this process and stimulated RIXS spectra of high resolution can be obtained by covariance analysis of the transmitted spectra. We present a detailed feasibility study and predict signal strengths for realistic XFEL parameters for the CO molecule resonantly pumped at the [Formula: see text] transition. Our theoretical model describes the evolution of the spectral and temporal characteristics of the transmitted x-ray radiation, by solving the equation of motion for the electronic and vibrational degrees of freedom of the system self consistently with the propagation by Maxwell equations.

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.

Snapshots of the fluctuating hydrogen bond network in liquid water on the sub-femtosecond timescale with vibrational resonant inelastic x-ray scattering

Liquid water molecules interact strongly with each other, forming a fluctuating hydrogen bond network and thereby giving rise to the anomalous phase diagram of liquid water. Consequently, symmetric and asymmetric water molecules have been found in the picosecond time average with IR and optical Raman spectroscopy. With subnatural linewidth resonant inelastic x-ray scattering (RIXS) at vibrational resolution, we take sub-femtosecond snapshots of the electronic and structural properties of water molecules in the hydrogen bond network. We derive a strong dominance of nonsymmetric molecules in liquid water in contrast to the gas phase on the sub-femtosecond timescale of RIXS and determine the fraction of highly asymmetrically distorted molecules.

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

The spectroscopic technique of resonant inelastic X-ray scattering (RIXS) will particularly profit from immensely improved brilliance of diffraction-limited storage rings (DLSRs). In RIXS one measures the intensities of excitations as a function of energy and momentum transfer. DLSRs will allow for pushing the achievable energy resolution, signal intensity and the sampled spot size to new limits. With RIXS one nowadays probes a broad range of electronic systems reaching from simple molecules to complex materials displaying phenomena like peculiar magnetism, two-dimensional electron gases, superconductivity, photovoltaic energy conversion and heterogeneous catalysis. In this article the types of improved RIXS studies that will become possible with X-ray beams from DLSRs are envisioned.

Femtosecond dynamics of momentum-dependent magnetic excitations from resonant inelastic X-ray scattering in CaCu2O3

Taking spinon excitations in the quantum antiferromagnet CaCu2O3 as an example, we demonstrate that femtosecond dynamics of magnetic electronic excitations can be probed by direct resonant inelastic x-ray scattering (RIXS). To this end, we isolate the contributions of single and double spin-flip excitations in experimental RIXS spectra, identify the physical mechanisms that cause them, and determine their respective time scales. By comparing theory and experiment, we find that double spin flips need a finite amount of time to be generated, rendering them sensitive to the core-hole lifetime, whereas single spin flips are, to a very good approximation, independent of it. This shows that RIXS can grant access to time-domain dynamics of excitations and illustrates how RIXS experiments can distinguish between excitations in correlated electron systems based on their different time dependence.

Interference between resonant and nonresonant inelastic x-ray scattering

A detailed study of inelastic x-ray scattering from the ground state to the 3Σg(3σ(g)(-1)3s(g)1) state of the O2 molecule is presented. The observed angular anisotropy shows that the vibrational excitations within this final state are strongly dependent on the polarization of the incident radiation. The analysis demonstrates that this is a manifestation of interference between resonant and direct nonresonant inelastic x-ray scattering. This interference provides a new tool to monitor nuclear dynamics by relative rotation of the polarization vectors of the incident and scattered photons.

Transition-Metal Nanoparticle Oxidation in a Chemically Nonhomogenous Environment Revealed by 2p3d Resonant X-ray Emission

X-ray absorption spectroscopy (XAS) is often employed in fields such as catalysis to determine whether transition-metal nanoparticles are oxidized. Here we show 2p3/2 XAS and 2p3d resonant X-ray emission spectroscopy (RXES) data of oleate-coated cobalt nanoparticles with average diameters of 4.0, 4.2, 5.0, 8.4, and 15.2 nm. Two particle batches were exposed to air for different periods of time, whereas the others were measured as synthesized. In the colloidal nanoparticles, the cobalt sites can have different chemical environments (metallic/oxidized/surface-coordinated), and it is shown that most XAS data cannot distinguish whether the nanoparticles are oxidized or surface-coated. In contrast, the high-energy resolution RXES spectra reveal whether more than the first metal layer is oxidized based on the unique energetic separation of spectral features related to the formal metal (X-ray fluorescence) or to a metal oxide (d-d excitations). This is the first demonstration of metal 2p3d RXES as a novel surface science tool.

Dissociative x-ray lasing

X-ray lasing is predicted to ensue when molecules are pumped into dissociative core-excited states by a free-electron-laser pulse. The lasing is due to the population inversion created in the neutral dissociation product, and the process features self-trapping of the x-ray pulse at the gain ridge. Simulations performed for the HCl molecule pumped at the 2p(1/2)→6σ resonance demonstrate that the scheme can be used to create ultrashort coherent x-ray pulses.

A setup for resonant inelastic soft x-ray scattering on liquids at free electron laser light sources

We present a flexible and compact experimental setup that combines an in vacuum liquid jet with an x-ray emission spectrometer to enable static and femtosecond time-resolved resonant inelastic soft x-ray scattering (RIXS) measurements from liquids at free electron laser (FEL) light sources. We demonstrate the feasibility of this type of experiments with the measurements performed at the Linac Coherent Light Source FEL facility. At the FEL we observed changes in the RIXS spectra at high peak fluences which currently sets a limit to maximum attainable count rate at FELs. The setup presented here opens up new possibilities to study the structure and dynamics in liquids.