Recent experimental and theoretical developments in time-resolved X-ray spectroscopies

Development of a portable and cost-effective femtosecond fibre laser synchronizable with synchrotron X-ray pulses

This study introduces a compact, portable femtosecond fibre laser system designed for synchronization with SPring-8 synchrotron X-ray pulses in a uniform filling mode. Unlike traditional titanium-sapphire mode-locked lasers, which are fixed installations, our system utilizes fibre laser technology to provide a practical alternative for time-resolved spectroscopy, striking a balance between usability, portability and cost-efficiency. Comprehensive evaluations, including pulse characterization, timing jitter and frequency stability tests revealed a centre wavelength of 1600 nm, a pulse energy of 4.5 nJ, a pulse duration of 35 fs with a timing jitter of less than 9 ps, confirming the suitability of the system for time-resolved spectroscopic studies. This development enhances the feasibility of experiments that combine synchrotron X-rays and laser pulses, offering significant scientific contributions by enabling more flexible and diverse research applications.

Mapping Hydrogen Positions along the Proton Transfer Pathway in an Organic Crystal by Computational X-ray Spectra

Understanding proton transfer (PT) dynamics in condensed phases is crucial in chemistry. We computed a 2D map of N 1s X-ray photoelectron/absorption spectroscopy (XPS/XAS) for an organic donor-acceptor salt crystal against two varying N-H distances to track proton motions. Our results provide a continuous spectroscopic mapping of O-H···N↔O-··· H+-N processes via hydrogen bonds at both nitrogens, demonstrating the sensitivity of N 1s transient XPS/XAS to hydrogen positions and PT. By reducing the O-H length at N1 by only 0.2 Å, we achieved excellent theory-experiment agreement in both XPS and XAS. Our study highlights the challenge in refining proton positions in experimental crystal structures by periodic geometry optimizations and proposes an alternative scaled snapshot protocol as a more effective approach. This work provides valuable insights into X-ray spectra for correlated PT dynamics in complex crystals, benefiting future experimental studies.

Tracking nuclear motion in single-molecule magnets using femtosecond X-ray absorption spectroscopy

The development of new data storage solutions is crucial for emerging digital technologies. Recently, all-optical magnetic switching has been achieved in dielectrics, proving to be faster than traditional methods. Despite this, single-molecule magnets (SMMs), which are an important class of magnetic materials due to their nanometre size, remain underexplored for ultrafast photomagnetic switching. Herein, we report femtosecond time-resolved K-edge X-ray absorption spectroscopy (TR-XAS) on a Mn(III)-based trinuclear SMM. Exploiting the elemental specificity of XAS, we directly track nuclear dynamics around the metal ions and show that the ultrafast dynamics upon excitation of a crystal-field transition are dominated by a magnetically active Jahn-Teller mode. Our results, supported by simulations, reveal minute bond length changes from 0.01 to 0.05 Å demonstrating the sensitivity of the method. These geometrical changes are discussed in terms of magneto-structural relationships and consequently our results illustrate the importance of TR-XAS for the emerging area of ultrafast molecular magnetism.

Deciphering Photoinduced Catalytic Reaction Mechanisms in Natural and Artificial Photosynthetic Systems on Multiple Temporal and Spatial Scales Using X-ray Probes

Utilization of renewable energies for catalytically generating value-added chemicals is highly desirable in this era of rising energy demands and climate change impacts. Artificial photosynthetic systems or photocatalysts utilize light to convert abundant CO2, H2O, and O2 to fuels, such as carbohydrates and hydrogen, thus converting light energy to storable chemical resources. The emergence of intense X-ray pulses from synchrotrons, ultrafast X-ray pulses from X-ray free electron lasers, and table-top laser-driven sources over the past decades opens new frontiers in deciphering photoinduced catalytic reaction mechanisms on the multiple temporal and spatial scales. Operando X-ray spectroscopic methods offer a new set of electronic transitions in probing the oxidation states, coordinating geometry, and spin states of the metal catalytic center and photosensitizers with unprecedented energy and time resolution. Operando X-ray scattering methods enable previously elusive reaction steps to be characterized on different length scales and time scales. The methodological progress and their application examples collected in this review will offer a glimpse into the accomplishments and current state in deciphering reaction mechanisms for both natural and synthetic systems. Looking forward, there are still many challenges and opportunities at the frontier of catalytic research that will require further advancement of the characterization techniques.

GUGA-based MRCI approach with core-valence separation approximation (CVS) for the calculation of the core-excited states of molecules

We develop and demonstrate how to use the Graphical Unitary Group Approach (GUGA)-based MRCISD with Core-Valence Separation (CVS) approximation to compute the core-excited states. First, perform a normal Self-Consistent-Field (SCF) or valence MCSCF calculation to optimize the molecular orbitals. Second, rotate the optimized target core orbitals and append to the active space, form an extended CVS active space, and perform a CVS-MCSCF calculation for core-excited states. Finally, construct the CVS-MRCISD expansion space and perform a CVS-MRCISD calculation to optimize the CI coefficients based on the variational method. The CVS approximation with GUGA-based methods can be implemented by flexible truncation of the Distinct Row Table. Eliminating the valence-excited configurations from the CVS-MRCISD expansion space can prevent variational collapse in the Davidson iteration diagonalization. The accuracy of the CVS-MRCISD scheme was investigated for excitation energies and compared with that of the CVS-MCSCF and CVS-CASPT2 methods using the same active space. The results show that CVS-MRCISD is capable of reproducing well-matched vertical core excitation energies that are consistent with experiments by combining large basis sets and a rational reference space. The calculation results also highlight the fact that the dynamic correlation between electrons makes an undeniable contribution in core-excited states.

Correlation of refractive index based and THz streaking arrival time tools for a hard X-ray free-electron laser

To fully exploit ultra-short X-ray pulse durations routinely available at X-ray free-electron lasers to follow out-of-equilibrium dynamics, inherent arrival time fluctuations of the X-ray pulse with an external perturbing laser pulse need to be measured. In this work, two methods of arrival time measurement were compared to measure the arrival time jitter of hard X-ray pulses. The methods were photoelectron streaking by a THz field and a transient refractive index change of a semiconductor. The methods were validated by shot-to-shot correction of a pump-probe transient reflectivity measurement. An ultimate shot-to-shot full width at half-maximum error between the devices of 19.2 ± 0.1 fs was measured.

Time-Resolved X-ray Absorption Spectroscopy: An MCTDH Quantum Dynamics Protocol

Expressions for linear and nonlinear spectroscopy simulation in the X-ray window in which the time evolution of a photoexcited molecular system is treated via quantum dynamics are derived. By leveraging on the peculiar properties of core-excited/ionized states, first- and third-order response functions are recast in the limit of time-scale separation between the extremely short core-state lifetime and the (comparably longer) electronic-state transfer and nuclear vibrational motion. This work is a natural extension of Segatta et al. (J. Chem. Theory Comput. 2023, 19, 2075-2091), in which some of the present authors coupled MCTDH quantum dynamics to spectroscopy simulation at different levels of sophistication. Full quantum dynamics and approximate expressions are compared by simulating X-ray transient absorption spectroscopy at the carbon K-edge in the pyrene molecule.

Calibrating TDDFT Calculations of the X-ray Emission Spectrum of Liquid Water: The Effects of Hartree-Fock Exchange

The structure and dynamics of liquid water continue to be debated, with insight provided by, among others, X-ray emission spectroscopy (XES), which shows a split in the high-energy 1b1 feature. This split is yet to be reproduced by theory, and it remains unclear if these difficulties are related to inaccuracies in dynamics simulations, spectrum calculations, or both. We investigate the performance of different methods for calculating XES of liquid water, focusing on the ability of time-dependent density functional theory (TDDFT) to reproduce reference spectra obtained by high-level coupled cluster and algebraic-diagrammatic construction scheme calculations. A metric for evaluating the agreement between theoretical spectra termed the integrated absolute difference (IAD), which considers the integral of shifted difference spectra, is introduced and used to investigate the performance of different exchange-correlation functionals. We find that computed spectra of symmetric and asymmetric model water structures are strongly and differently influenced by the amount of Hartree-Fock exchange, with best agreement to reference spectra for ∼40-50%. Lower percentages tend to yield high density of contributing states, resulting in too broad features. The method introduced here is useful also for other spectrum calculations, in particular where the performance for ensembles of structures are evaluated.

Operando time-resolved soft x-ray absorption spectroscopy for photoexcitation processes of metal complexes in solutions

Operando time-resolved soft x-ray absorption spectroscopy (TR-SXAS) is an effective method to reveal the photochemical processes of metal complexes in solutions. In this study, we have developed the TR-SXAS measurement system for observing various photochemical reactions in solutions by the combination of laser pump pulses with soft x-ray probe pulses from the synchrotron radiation. For the evaluation of the developed TR-SXAS system, we have measured nitrogen K-edge x-ray absorption spectroscopy (XAS) spectra of aqueous iron phenanthroline solutions during a photoinduced spin transition process. The decay process of the high spin state to the low spin state in the iron complex has been obtained from the ligand side by N K-edge XAS, and the time constant is close to that obtained from the central metal side by time-resolved Fe K-edge XAS in the previous studies.

Jahn-Teller effects in initial and final states: high-resolution X-ray absorption, photoelectron and Auger spectroscopy of allene

Carbon K-edge resonant Auger spectra of gas-phase allene following excitation of the pre-edge 1s → π* transitions are presented and analysed with the support of EOM-CCSD/cc-pVTZ calculations. X-Ray absorption (XAS), X-ray photoelectron (XPS), valence band and non-resonant Auger spectra are also reanalysed with a series of computational approaches. The results presented demonstrate the importance of including nuclear ensemble effects for simulating X-ray observables and as an effective strategy for capturing Jahn-Teller effects in spectra.

Energy-dependent timescales in the dissociation of diiodothiophene dication

Photodissociation molecular dynamics of gas-phase 2,5-diiodothiophene molecules was studied in an electron-energy-resolved electron-multi-ion coincidence experiment performed at the FinEstBeAMS beamline of MAX IV synchrotron. Following the photoionization of the iodine 4d subshell and the Auger decay, the dissociation landscape of the molecular dication was investigated as a function of the Auger electron energy. Concentrating on an major dissociation pathway, C₄H₂I₂S²⁺ → C₄H₂S⁺ + I⁺ + I, and accessing the timescales of the process via ion momentum correlation analysis, it was revealed how this three-body process changes depending on the available internal energy. Using a generalized secondary dissociation model, the process was shown to evolve from secondary dissociation regime towards concerted dissociation as the available energy increased, with the secondary dissociation time constant changing from 1.5 ps to 129 fs. The experimental results were compared with simulations using a stochastic charge-hopping molecular mechanics model. It represented the observed trend and also gave a fair quantitative agreement with the experiment.

Element- and enantiomer-selective visualization of molecular motion in real-time

Ultrafast optical-domain spectroscopies allow to monitor in real time the motion of nuclei in molecules. Achieving element-selectivity had to await the advent of time resolved X-ray spectroscopy, which is now commonly carried at X-ray free electron lasers. However, detecting light element that are commonly encountered in organic molecules, remained elusive due to the need to work under vacuum. Here, we present an impulsive stimulated Raman scattering (ISRS) pump/carbon K-edge absorption probe investigation, which allowed observation of the low-frequency vibrational modes involving specific selected carbon atoms in the Ibuprofen RS dimer. Remarkably, by controlling the probe light polarization we can preferentially access the enantiomer of the dimer to which the carbon atoms belong.

Modeling Nonresonant X-ray Emission of Second- and Third-Period Elements without Core-Hole Reference States and Empirical Parameters

Nonresonant X-ray emission (XE) energies and oscillator strengths are obtained using the effective potential of the generalized Kohn-Sham semi-canonical projected random phase approximation (GKS-spRPA) method. XE energies are estimated as a difference between the valence and core ionization eigenvalues, while the oscillator strengths are obtained within a frozen orbital approximation. This straightforward approach provides accurate XE energies without any need for core-hole reference states, empirical shifting parameters, or tuning of density functionals. To account for relativistic corrections to the core orbitals, we have formulated a scalar relativistic (sr) GKS-spRPA approach based on the spin-free X2C one-electron Hamiltonian. The sr-GKS-spRPA method provides highly reliable XE energies using uncontracted basis-sets on atoms where the core-hole is created prior to emission. For the largest basis-sets used in our study, using completely uncontracted polarized core-valence Dunning basis-sets, the mean absolute errors (MAEs) are within 0.7 eV compared to experimental reference values for a test-set consisting of 27 valence-to-core XE energies of molecules with second- and third-period elements. Considering a balance of accuracy and computational effort, we recommend the use of s-uncontracted def2-TZVP for second-period and all-uncontracted def2-TZVP for third-period elements. For this recommended basis-set, the MAE is 0.2 eV. The analytically continued sr-GKS-spRPA approach, with an O(N4) computational cost, enables efficient computation of XE spectra of molecules such as S₈ and C₆₀ with several core-hole states.

Ultrafast Charge Relocation Dynamics in Enol-Keto Tautomerization Monitored with a Local Soft-X-ray Probe

Proton-coupled electron transfer (PCET) is the underlying mechanism governing important reactions ranging from water splitting in photosynthesis to oxygen reduction in hydrogen fuel cells. The interplay of proton and electronic charge distribution motions can vary from sequential to concerted schemes, with elementary steps occurring on ultrafast time scales. We demonstrate with a simulation study that femtosecond soft-X-ray spectroscopy provides key insights into the PCET mechanism of a photoinduced intramolecular enol* → keto* tautomerization reaction. A full quantum treatment of the electronic and nuclear dynamics of 2-(2'-hydroxyphenyl)benzothiazole upon electronic excitation reveals how spectral signatures of local excitations from core to frontier orbitals display the distinctly different stages of charge relocation for the H atom, donating, and accepting sites. Our findings indicate that ultraviolet/X-ray pump-probe spectroscopy provides a unique way to probe ultrafast electronic structure rearrangements in photoinduced chemical reactions essential to understanding the mechanism of PCET.

Basis Set Selection for Molecular Core-Level GW Calculations

The GW approximation has been recently gaining popularity among the methods for simulating molecular core-level X-ray photoemission spectra. Traditionally, Gaussian-type orbital GW core-level binding energies have been computed using either the cc-pVnZ or def2-nZVP basis set families, extrapolating the obtained results to the complete basis set limit, followed by an element-specific relativistic correction. Despite achieving rather good accuracy, it has been previously stated that these binding energies are chronically underestimated. In the present work, we show that those previous studies obtained results that were not well-converged with respect to the basis set size and that, once basis set convergence is achieved, there seems to be no such underestimation. Standard techniques known to offer a good cost-accuracy ratio in other theories demonstrate that the cc-pVnZ and def2-nZVP families exhibit contraction errors and might lead to unreliable complete basis set extrapolations for absolute binding energies, often deviating about 200-500 meV from the putative basis set limit found in this work. On the other hand, uncontracted versions of these basis sets offer vastly improved convergence. Even faster convergence can be obtained using core-rich property-optimized basis set families like pcSseg-n, pcJ-n, and ccX-nZ. Finally, we also show that the improvement observed for core properties using these specialized basis sets does not degrade their description of valence excitations: vertical ionization potentials and electron affinities computed with these basis sets converge as fast as the ones obtained with the aug-cc-pVnZ family, thus offering a balanced description of both core and valence regions.

Structural Characterization of Titanium-Silica Oxide Using Synchrotron Radiation X-ray Absorption Spectroscopy

In this study, titania−silica oxides (TixSiy oxides) were successfully prepared via the sol−gel technique. The Ti and Si precursors were titanium (IV), isopropoxide (TTIP), and tetraethylorthosilicate (TEOS), respectively. In this work, the effects of pH and the Ti/Si atomic ratio of titanium−silicon binary oxide (TixSiy) on the structural characteristics of TixSiy oxide are reported. 29Si solid-state NMR and FTIR were used to validate the chemical structure of TixSiy oxide. The structural characteristics of TixSiy oxide were investigated using X-ray diffraction, XRF, Fe-SEM, diffraction particle size analysis, and nitrogen adsorption measurements. By applying X-ray absorption spectroscopy (XAS) obtained from synchrotron light sources, the qualitative characterization of the Ti−O−Si and Ti−O−Ti bonds in Ti−Si oxides was proposed. Some Si atoms in the SiO2 network were replaced by Ti atoms, suggesting that Si−O−Ti bonds were formed as a result of the synthesis accomplished using the sol−gel technique described in this article. Upon increasing the pH to alkaline conditions (pH 9.0 and 10.0), the nanoparticles acquired a more spherical shape, and their size distribution became more uniform, resulting in an acceptable nanostructure. TixSiy oxide nanoparticles were largely spherical in shape, and agglomeration was minimized. However, the Ti50Si50 oxide particles at pH 10.0 become nano-sized and agglomerated. The presence of a significant pre-edge feature in the spectra of Ti50Si50 oxide samples implied that a higher fraction of Ti atoms occupied tetrahedral symmetry locations, as predicted in samples where Ti directly substituted Si. The proportion of Ti atoms in a tetrahedral environment agreed with the value of 1.83 given for the Ti−O bond distance in TixSiy oxides produced at pH 9.0 using extended X-ray absorption fine structure (EXAFS) analysis. Photocatalysis was improved by adding 3% wt TiO2, SiO2, and TixSiy oxide to the PLA film matrix. TiO2 was more effective than Ti50Si50 pH 9.0, Ti50Si50 pH 10.0, Ti50Si50 pH 8.0, and SiO2 in degrading methylene blue (MB). The most effective method to degrade MB was TiO2 > Ti70Si30 > Ti50Si50 > Ti40Si60 > SiO2. Under these conditions, PLA/Ti70Si30 improved the effectiveness of the photocatalytic activity of PLA.

Beyond structural insight: a deep neural network for the prediction of Pt L2/3-edge X-ray absorption spectra

X-ray absorption spectroscopy at the L_2/3 edge can be used to obtain detailed information about the local electronic and geometric structure of transition metal complexes. By virtue of the dipole selection rules, the transition metal L_2/3 edge usually exhibits two distinct spectral regions: (i) the "white line", which is dominated by bound electronic transitions from metal-centred 2p orbitals into unoccupied orbitals with d character; the intensity and shape of this band consequently reflects the d density of states (d-DOS), which is strongly modulated by mixing with ligand orbitals involved in chemical bonding, and (ii) the post-edge, where oscillations encode the local geometric structure around the X-ray absorption site. In this Article, we extend our recently-developed XANESNET deep neural network (DNN) beyond the K-edge to predict X-ray absorption spectra at the Pt L_2/3 edge. We demonstrate that XANESNET is able to predict Pt L_2/3 -edge X-ray absorption spectra, including both the parts containing electronic and geometric structural information. The performance of our DNN in practical situations is demonstrated by application to two Pt complexes, and by simulating the transient spectrum of a photoexcited dimeric Pt complex. Our discussion includes an analysis of the feature importance in our DNN which demonstrates the role of key features and assists with interpreting the performance of the network.

First experiments with a water-jet plasma X-ray source driven by the novel high-power-high-repetition rate L1 Allegra laser at ELI Beamlines

ELI Beamlines is a rapidly progressing pillar of the pan-European Extreme Light Infrastructure (ELI) project focusing on the development and deployment of science driven by high-power lasers for user operations. This work reports the results of a commissioning run of a water-jet plasma X-ray source driven by the L1 Allegra laser, outlining the current capabilities and future potential of the system. The L1 Allegra is one of the lasers developed in-house at ELI Beamlines, designed to be able to reach a pulse energy of 100 mJ at a 1 kHz repetition rate with excellent beam properties. The water-jet plasma X-ray source driven by this laser opens opportunities for new pump-probe experiments with sub-picosecond temporal resolution and inherent synchronization between pump and probe pulses.

Multi-reference approach to the computation of double core-hole spectra

Double Core-Hole (DCH) states of small molecules are assessed with the restricted active space self-consistent field and multi-state restricted active space perturbation theory of second order approximations. To ensure an unbiased description of the relaxation and correlation effects on the DCH states, the neutral ground-state and DCH wave functions are optimized separately, whereas the spectral intensities are computed with a biorthonormalized set of molecular orbitals within the state-interaction approximation. Accurate shake-up satellite binding energies and intensities of double-core-ionized states (K^-2) are obtained for H₂O, N₂, CO, and C₂H_2n (n = 1-3). The results are analyzed in detail and show excellent agreement with recent theoretical and experimental data. The K^-2 shake-up spectra of H₂O and C₂H_2n molecules are here completely characterized for the first time.

Relativistic EOM-CCSD for Core-Excited and Core-Ionized State Energies Based on the Four-Component Dirac-Coulomb(-Gaunt) Hamiltonian

We report an implementation of the core-valence separation approach to the four-component relativistic Hamiltonian-based equation-of-motion coupled-cluster with singles and doubles theory (CVS-EOM-CCSD) for the calculation of relativistic core-ionization potentials and core-excitation energies. With this implementation, which is capable of exploiting double group symmetry, we investigate the effects of the different CVS-EOM-CCSD variants and the use of different Hamiltonians based on the exact two-component (X2C) framework on the energies of different core-ionized and -excited states in halogen- (CH₃I, HX, and X^-, X = Cl-At) and xenon-containing (Xe, XeF₂) species. Our results show that the X2C molecular mean-field approach [Sikkema, J.; J. Chem. Phys. 2009, 131, 124116], based on four-component Dirac-Coulomb mean-field calculations (²DC^M), is capable of providing core excitations and ionization energies that are nearly indistinguishable from the reference four-component energies for up to and including fifth-row elements. We observe that two-electron integrals over the small-component basis sets lead to non-negligible contributions to core binding energies for the K and L edges for atoms such as iodine or astatine and that the approach based on Dirac-Coulomb-Gaunt mean-field calculations (²DCG^M) are significantly more accurate than X2C calculations for which screened two-electron spin-orbit interactions are included via atomic mean-field integrals.

Density Functional Theory Calculations of Core-Electron Binding Energies at the K-Edge of Heavier Elements

The capability to determine core-electron binding energies (CEBEs) is vital in the analysis of X-ray photoelectron spectroscopy, and the continued development of light sources has made inner shell spectroscopy of heavier elements increasingly accessible. Density functional theory is widely used to determine CEBEs of lighter elements (boron-fluorine). It is shown that good performance of exchange-correlation functionals for these elements does not necessarily translate to the calculation of CEBEs for the heavier elements from the next row of the periodic table, and in general, larger errors are observed. Two strategies are explored that improve the accuracy of the calculated CEBEs. The first is to apply element and functional dependent energy corrections, and the second is a reparametrization of a short-range corrected functional. This functional is able to reproduce experimental phosphorus and sulfur K-edge CEBEs with an average error of 0.15 eV demonstrating the importance of reducing the self-interaction error associated with the core electrons and represents progress toward a density functional theory calculation that performs equally well for ionization at the K-edge of all elements.

Determining Excited-State Structures and Photophysical Properties in Phenylphosphine Rhenium(I) Diimine Biscarbonyl Complexes Using Time-Resolved Infrared and X-ray Absorption Spectroscopies

We have explored the structural factors on the photophysical properties in two rhenium(I) diimine complexes in acetonitrile solution, cis,trans-[Re(dmb)(CO)₂(PPh₂Et)₂]⁺ (Et(2,2)) and cis,trans-[Re(dmb)(CO)₂(PPh₃)₂]⁺ ((3,3)) (dmb = 4,4'-dimethyl-2,2'-bipyridine, Ph = phenyl, Et = ethyl) using the combination method of time-resolved infrared spectroscopy, time-resolved extended X-ray absorption fine structure, and quantum chemical calculations. The difference between these complexes is the number of phenyl groups in the phosphine ligand, and this only indirectly affects the central Re(I). Despite this minor difference, the complexes exhibit large differences in emission wavelength and excited-state lifetime. Upon photoexcitation, the bond length of Re-P and angle of P-Re-P are significantly changed in both complexes, while the phenyl groups are largely rotated by ∼20° only in (3,3). In contrast, there is little change in charge distribution on the phenyl groups when Re to dmb charge transfer occurs upon photoexcitation. We concluded that the instability from steric effects of phenyl groups and diimine leads to a smaller Stokes shift of the lowest excited triplet state (T₁) in (3,3). The large structural change between the ground and excited states causes the longer lifetime of T₁ in (3,3).

Capturing photochemical and photophysical transformations in iron complexes with ultrafast X-ray spectroscopy and scattering

Light-driven chemical transformations provide a compelling approach to understanding chemical reactivity with the potential to use this understanding to advance solar energy and catalysis applications. Capturing the non-equilibrium trajectories of electronic excited states with precision, particularly for transition metal complexes, would provide a foundation for advancing both of these objectives. Of particular importance for 3d metal compounds is characterizing the population dynamics of charge-transfer (CT) and metal-centered (MC) electronic excited states and understanding how the inner coordination sphere structural dynamics mediate the interaction between these states. Recent advances in ultrafast X-ray laser science has enabled the electronic excited state dynamics in 3d metal complexes to be followed with unprecedented detail. This review will focus on simultaneous X-ray emission spectroscopy (XES) and X-ray solution scattering (XSS) studies of iron coordination and organometallic complexes. These simultaneous XES-XSS studies have provided detailed insight into the mechanism of light-induced spin crossover in iron coordination compounds, the interaction of CT and MC excited states in iron carbene photosensitizers, and the mechanism of Fe-S bond dissociation in cytochrome c.

XUV pump-XUV probe transient absorption spectroscopy at FELs

The emergence of ultra-intense extreme-ultraviolet (XUV) and X-ray free-electron lasers (FELs) has opened the door for the experimental realization of non-linear XUV and X-ray spectroscopy techniques. Here we demonstrate an experimental setup for an all-XUV transient absorption spectroscopy method for gas-phase targets at the FEL. The setup combines a high spectral resolving power of E/ΔE ≈ 1500 with sub-femtosecond interferometric resolution, and covers a broad XUV photon-energy range between approximately 20 and 110 eV. We demonstrate the feasibility of this setup firstly on a neon target. Here, we intensity- and time-resolve key aspects of non-linear XUV-FEL light-matter interactions, namely the non-resonant ionization dynamics and resonant coupling dynamics of bound states, including XUV-induced Stark shifts of energy levels. Secondly, we show that this setup is capable of tracking the XUV-initiated dissociation dynamics of small molecular targets (oxygen and diiodomethane) with site-specific resolution, by measuring the XUV transient absorption spectrum. In general, benefitting from a single-shot detection capability, we show that the setup and method provides single-shot phase-locked XUV pulse pairs. This lays the foundation to perform, in the future, experiments as a function of the XUV interferometric time delay and the relative phase, which enables advanced coherent non-linear spectroscopy schemes in the XUV and X-ray spectral range.

Femtosecond X-ray spectroscopy of haem proteins

We discuss our recently reported femtosecond (fs) X-ray emission spectroscopy results on the ligand dissociation and recombination in nitrosylmyoglobin (MbNO) in the context of previous studies on ferrous haem proteins. We also present a preliminary account of femtosecond X-ray absorption studies on MbNO, pointing to the presence of more than one species formed upon photolysis.

Reduction Mechanisms of Anticancer Osmium(VI) Complexes Revealed by Atomic Telemetry and Theoretical Calculations

Resonant X-ray emission spectroscopy (RXES) has developed in the past decade as a powerful tool to probe the chemical state of a metal center and in situ study chemical reactions. We have used it to monitor spectral changes associated with the reduction of osmium(VI) nitrido complexes to the osmium(III) ammine state by the biologically relevant reducing agent, glutathione. RXES difference maps are consistent with the proposed DFT mechanism and the formation of two stable osmium(IV) intermediates, thereby supporting the overall pathway for the reduction of these high-valent anticancer metal complexes for which reduction by thiols within cells may be essential to the antiproliferative activity.

Femtosecond Charge Density Modulations in Photoexcited CuWO4

Copper tungstate (CuWO4) is an important semiconductor with a sophisticated and debatable electronic structure that has a direct impact on its chemistry. Using the PAL-XFEL source, we study the electronic dynamics of photoexcited CuWO4. The Cu L3 X-ray absorption spectrum shifts to lower energy upon photoexcitation, which implies that the photoexcitation process from the oxygen valence band to the tungsten conduction band effectively increases the charge density on the Cu atoms. The decay time of this spectral change is 400 fs indicating that the increased charge density exists only for a very short time and relaxes electronically. The initial increased charge density gives rise to a structural change on a time scale longer than 200 ps.

Using X-ray free-electron lasers for spectroscopy of molecular catalysts and metalloenzymes

The metal centres in metalloenzymes and molecular catalysts are responsible for the rearrangement of atoms and electrons during complex chemical reactions, and they enable selective pathways of charge and spin transfer, bond breaking/making and the formation of new molecules. Mapping the electronic structural changes at the metal sites during the reactions gives a unique mechanistic insight that has been difficult to obtain to date. The development of X-ray free-electron lasers (XFELs) enables powerful new probes of electronic structure dynamics to advance our understanding of metalloenzymes. The ultrashort, intense and tunable XFEL pulses enable X-ray spectroscopic studies of metalloenzymes, molecular catalysts and chemical reactions, under functional conditions and in real time. In this Technical Review, we describe the current state of the art of X-ray spectroscopy studies at XFELs and highlight some new techniques currently under development. With more XFEL facilities starting operation and more in the planning or construction phase, new capabilities are expected, including high repetition rate, better XFEL pulse control and advanced instrumentation. For the first time, it will be possible to make real-time molecular movies of metalloenzymes and catalysts in solution, while chemical reactions are taking place.

Toward Quantum Computing for High-Energy Excited States in Molecular Systems: Quantum Phase Estimations of Core-Level States

This paper explores the utility of the quantum phase estimation (QPE) algorithm in calculating high-energy excited states characterized by the promotion of electrons occupying core-level shells. These states have been intensively studied over the last few decades, especially in supporting the experimental effort at light sources. Results obtained with QPE are compared with various high-accuracy many-body techniques developed to describe core-level states. The feasibility of the quantum phase estimator in identifying classes of challenging shake-up states characterized by the presence of higher-order excitation effects is discussed. We also demonstrate the utility of the QPE algorithm in targeting excitations from specific centers in a molecule. Lastly, we discuss how the lowest-order Trotter formula can be applied to reducing the complexity of the ansatz without affecting the error.

Ultrafast Spectroscopy of Photoactive Molecular Systems from First Principles: Where We Stand Today and Where We Are Going

Computational spectroscopy is becoming a mandatory tool for the interpretation of the complex, and often congested, spectral maps delivered by modern non-linear multi-pulse techniques. The fields of Electronic Structure Methods, Non-Adiabatic Molecular Dynamics, and Theoretical Spectroscopy represent the three pillars of the virtual ultrafast optical spectrometer, able to deliver transient spectra in silico from first principles. A successful simulation strategy requires a synergistic approach that balances between the three fields, each one having its very own challenges and bottlenecks. The aim of this Perspective is to demonstrate that, despite these challenges, an impressive agreement between theory and experiment is achievable now regarding the modeling of ultrafast photoinduced processes in complex molecular architectures. Beyond that, some key recent developments in the three fields are presented that we believe will have major impacts on spectroscopic simulations in the very near future. Potential directions of development, pending challenges, and rising opportunities are illustrated.

Spin cascade and doming in ferric hemes: Femtosecond X-ray absorption and X-ray emission studies

The structure-function relationship is at the heart of biology, and major protein deformations are correlated to specific functions. For ferrous heme proteins, doming is associated with the respiratory function in hemoglobin and myoglobins. Cytochrome c (Cyt c) has evolved to become an important electron-transfer protein in humans. In its ferrous form, it undergoes ligand release and doming upon photoexcitation, but its ferric form does not release the distal ligand, while the return to the ground state has been attributed to thermal relaxation. Here, by combining femtosecond Fe Kα and Kβ X-ray emission spectroscopy (XES) with Fe K-edge X-ray absorption near-edge structure (XANES), we demonstrate that the photocycle of ferric Cyt c is entirely due to a cascade among excited spin states of the iron ion, causing the ferric heme to undergo doming, which we identify. We also argue that this pattern is common to a wide diversity of ferric heme proteins, raising the question of the biological relevance of doming in such proteins.

Femtosecond X-ray emission study of the spin cross-over dynamics in haem proteins

In haemoglobin the change from the low-spin (LS) hexacoordinated haem to the high spin (HS, S = 2) pentacoordinated domed deoxy-myoglobin (deoxyMb) form upon ligand detachment from the haem and the reverse process upon ligand binding are what ultimately drives the respiratory function. Here we probe them in the case of Myoglobin-NO (MbNO) using element- and spin-sensitive femtosecond Fe K_α and K_β X-ray emission spectroscopy at an X-ray free-electron laser (FEL). We find that the change from the LS (S = 1/2) MbNO to the HS haem occurs in ~800 fs, and that it proceeds via an intermediate (S = 1) spin state. We also show that upon NO recombination, the return to the planar MbNO ground state is an electronic relaxation from HS to LS taking place in ~30 ps. Thus, the entire ligand dissociation-recombination cycle in MbNO is a spin cross-over followed by a reverse spin cross-over process.

The change from low-spin hexacoordinated to high-spin pentacoordinated domed form in heam upon ligand detachment and the reverse process underlie the respiratory function. The authors, using femtosecond time-resolved X-ray emission spectroscopy, capture the transient states connecting the two forms in myoglobin-NO upon NO photoinduced detachment.

Simulation of time-resolved x-ray absorption spectroscopy of ultrafast dynamics in particle-hole-excited 4-(2-thienyl)-2,1,3-benzothiadiazole

To date, alternating co-polymers based on electron-rich and electron-poor units are the most attractive materials to control functionality of organic semiconductor layers in which ultrafast excited-state processes play a key role. We present a computational study of the photoinduced excited-state dynamics of the 4-(2-thienyl)-2,1,3-benzothiadiazole (BT-1T) molecule, which is a common building block in the backbone of π-conjugated polymers used for organic electronics. In contrast to homo-polymer materials, such as oligothiophene, BT-1T has two non-identical units, namely, thiophene and benzothiadiazole, making it attractive for intramolecular charge transfer studies. To gain a thorough understanding of the coupling of excited-state dynamics with nuclear motion, we consider a scenario based on femtosecond time-resolved x-ray absorption spectroscopy using an x-ray free-electron laser in combination with a synchronized ultraviolet femtosecond laser. Using Tully's fewest switches surface hopping approach in combination with excited-state calculations at the level of configuration interaction singles, we calculate the gas-phase x-ray absorption spectrum at the carbon and nitrogen K edges as a function of time after excitation to the lowest electronically excited state. The results of our time-resolved calculations exhibit the charge transfer driven by non-Born-Oppenheimer physics from the benzothiadiazole to thiophene units during relaxation to the ground state. Furthermore, our ab initio molecular dynamics simulations indicate that the excited-state relaxation processes involve bond elongation in the benzothiadiazole unit as well as thiophene ring puckering at a time scale of 100 fs. We show that these dynamical trends can be identified from the time-dependent x-ray absorption spectrum.

The Role of Structural Representation in the Performance of a Deep Neural Network for X-Ray Spectroscopy

An important consideration when developing a deep neural network (DNN) for the prediction of molecular properties is the representation of the chemical space. Herein we explore the effect of the representation on the performance of our DNN engineered to predict Fe K-edge X-ray absorption near-edge structure (XANES) spectra, and address the question: How important is the choice of representation for the local environment around an arbitrary Fe absorption site? Using two popular representations of chemical space-the Coulomb matrix (CM) and pair-distribution/radial distribution curve (RDC)-we investigate the effect that the choice of representation has on the performance of our DNN. While CM and RDC featurisation are demonstrably robust descriptors, it is possible to obtain a smaller mean squared error (MSE) between the target and estimated XANES spectra when using RDC featurisation, and converge to this state a) faster and b) using fewer data samples. This is advantageous for future extension of our DNN to other X-ray absorption edges, and for reoptimisation of our DNN to reproduce results from higher levels of theory. In the latter case, dataset sizes will be limited more strongly by the resource-intensive nature of the underlying theoretical calculations.

Generalized single excitation configuration interaction: an investigation into the impact of the inclusion of non-orthogonality on the calculation of core-excited states

In this paper, we investigate different non-orthogonal generalizations of the configuration interaction with single substitutions (CIS) method and their impact on the calculation of core-excited states.

Ultrafast nonadiabatic dynamics probed by nitrogen K-edge absorption spectroscopy

Quantum dynamics simulations are used to simulate the ultrafast X-ray Absorption Near-Edge Structure (XANES) spectra of photoexcited pyrazine including two strongly coupled electronically excited states and four normal mode degrees of freedom.

Direct observation of the electronic states of photoexcited hematite with ultrafast 2p3d X-ray absorption spectroscopy and resonant inelastic X-ray scattering

Ultrafast Fe L₃ XAS and 2p3d RIXS elucidate the photoexcitation process of hematite.

Transient X-ray Absorption Spectral Fingerprints of the S1 Dark State in Uracil

Low-lying dark nπ* states play an important role in many photophysical and photochemical processes of organic chromophores. Transient X-ray absorption spectroscopy (TXAS) provides a powerful technique for probing the dynamics of valence states by exciting the electrons into high-lying core excited states. We employ multiconfigurational self-consistent field calculations to investigate the TXAS of uracil along its nonradiative photodecay pathways. An open issue is whether dark nπ* state S₁ (n is the lone pair localized on an oxygen atom) is accessible when bright ππ* state S₂ is selectively excited. Vertical core excitations were calculated along the potential energy surfaces of the three lowest states, S₀-S₂, interpolated between two minima and two minimum-energy conical intersections. Computed TXAS data from the C, N, and O K edges show distinct spectral fingerprints of the dark state in all spectral regimes. At the O 1s edge, the nπ* state has a very strong absorption at 526-527 eV, while at the C (N) 1s edge, by contrast, there is almost zero (very weak) absorption at 279-282 eV (397-398 eV). All K-edge spectra can be used to sensitively detect the dark states. Our proposed O 1s feature has already been observed in a recent TXAS experiment with thymine. Natural transition orbital analysis is used to interpret all dominant features of the three lowest-valence states along the reaction coordinate and reveal some important valence fine-structure information from the core excitation.

Micro-focused MHz pink beam for time-resolved X-ray emission spectroscopy

The full radiation from the first harmonic of a synchrotron undulator (between 5 and 12 keV) at the Advanced Photon Source is microfocused using a stack of beryllium compound refractive lenses onto a fast-moving liquid jet and overlapped with a high-repetition-rate optical laser. This micro-focused geometry is used to perform efficient nonresonant X-ray emission spectroscopy on transient species using a dispersive spectrometer geometry. The overall usable flux achieved on target is above 10¹⁵ photons s^-1 at 8 keV, enabling photoexcited systems in the liquid phase to be tracked with time resolutions from tens of picoseconds to microseconds, and using the full emission spectrum, including the weak valence-to-core signal that is sensitive to chemically relevant electronic properties.

Spin adapted implementation of EOM-CCSD for triplet excited states: Probing intersystem crossings of acetylacetone at the carbon and oxygen K-edges

We present an equation of motion coupled cluster singles and doubles approach for computing transient absorption spectra from a triplet excited state. The implementation determines the left and right excitation vectors by explicitly spin-adapting the triplet excitation space. As an illustrative application, we compute transient state X-ray absorption spectra at the carbon and oxygen K-edges for the acetylacetone molecule.

Ultrafast photoinduced energy and charge transfer

After presenting the basic theoretical models of excitation energy transfer and charge transfer, I describe some of the novel experimental methods used to probe them. Finally, I discuss recent results concerning ultrafast energy and charge transfer in biological systems, in chemical systems and in photovoltaics based on sensitized transition metal oxides.

Hole dynamics in a photovoltaic donor-acceptor couple revealed by simulated time-resolved X-ray absorption spectroscopy

Theoretical and experimental methodologies that can characterize electronic and nuclear dynamics, and the coupling between the two, are needed to understand photoinduced charge transfer in molecular building blocks used in organic photovoltaics. Ongoing developments in ultrafast pump-probe techniques such as time-resolved X-ray absorption spectroscopy, using an X-ray free electron laser in combination with an ultraviolet femtosecond laser, present desirable probes of coupled electronic and nuclear dynamics. In this work, we investigate the charge transfer dynamics of a donor-acceptor pair, which is widely used as a building block in low bandgap block copolymers for organic photovoltaics. We simulate the dynamics of the benzothiadiazole-thiophene molecule upon photoionization with a vacuum ultraviolet (VUV) pulse and study the potential of probing the subsequent charge dynamics using time-resolved X-ray absorption spectroscopy. The photoinduced dynamics are calculated using on-the-fly nonadiabatic molecular dynamics simulations based on Tully's Fewest Switches Surface Hopping approach. We calculate the X-ray absorption spectrum as a function of time after ionization at the Hartree-Fock level. The changes in the time-resolved X-ray absorption spectrum at the sulfur K-edge reveal the ultrafast charge carrier dynamics in the molecule occurring on a femtosecond time scale. These theoretical findings anticipate that ultrafast time-resolved X-ray absorption spectroscopy using an X-ray probe in combination with a VUV pump offers a new approach to investigate the detailed dynamics of organic photovoltaic materials.