Photoinduced Structural Dynamics of Molecular Systems Mapped by Time-Resolved X-ray Methods

Electronic structure of light-induced nitrosyl linkage isomers revealed by X-ray absorption spectroscopy at Ru L3,2-edges

X-ray absorption spectroscopy (XAS) is a powerful tool for examining changes of the electronic and molecular structure following light-induced excitation of a molecule. Specifically, this method can be applied to investigate the ground (GS, RuNO) and metastable states (MS1, RuON and MS2, Ruη2(NO)) of the nitrosyl ligand (NO), which differ in their coordination mode to the metal. In this work, we report for the first time experimental and theoretical (DFT) Ru L3,2-edge XA spectra for the octahedral complex trans-[RuNOPy4F](ClO4)2 (1, Py = pyridine) in both ground and metastable states. The transition from GS to MS1 using 420 nm light excitation leads to a significant downshift of the 2p → LUMO(+1) peaks by about 0.5-0.8 eV, attributed to the destabilisation of 2p orbitals and stabilization of LUMO(+1). Subsequent irradiation of MS1 at 920 nm produces isomer MS2, for which even greater stabilization of LUMO occurs, though without a significant change in 2p energy. The change in 2p energy is attributed to a variation in the charge on the Ru atom after NO isomerization, while LUMO(+1) stabilization is related to changes in the Ru(NO) bond length and the composition of this orbital.

Femtosecond Spin-State Switching Dynamics of Fe(II) Complexes Condensed in Thin Films

The tailoring of spin-crossover films has made significant progress over the past decade, mostly motivated by the prospect in technological applications. In contrast to spin-crossover complexes in solution, the investigation of the ultrafast switching in spin-crossover films has remained scarce. Combining the progress in molecule synthesis and film growth with the opportunities at X-ray free-electron lasers, we study the photoinduced spin-state switching dynamics of a molecular film at room temperature. The subpicosecond switching from the S = 0 low-spin ground state to the S = 2 high-spin state is monitored by analyzing the transient evolution of the Fe L3 X-ray absorption edge fine structure, i.e. element-specifically at the switching center of the Fe(II) complex. Our measurements show the involvement of an intermediate state in the switching. At large excitation fluences, the fraction of high-spin molecules saturates at ≈50%, which is likely due to molecule-molecule interaction within the film.

Time-resolved Coulomb explosion imaging of vibrational wave packets in alkali dimers on helium nanodroplets

Vibrational wave packets are created in the lowest triplet state 13Σu+ of K2 and Rb2 residing on the surface of helium nanodroplets, through non-resonant stimulated impulsive Raman scattering induced by a moderately intense near-infrared laser pulse. A delayed, intense 50-fs laser pulse doubly ionizes the alkali dimers via multiphoton absorption and thereby causes them to Coulomb explode into a pair of alkali ions Ak+. From the kinetic energy distribution P(Ekin) of the Ak+ fragment ions, measured at a large number of delays, we determine the time-dependent internuclear distribution P(R, t), which represents the modulus square of the wave packet within the accuracy of the experiment. For both K2 and Rb2, P(R, t) exhibits a periodic oscillatory structure throughout the respective 300 and 100 ps observation times. The oscillatory structure is reflected in the time-dependent mean value of R, ⟨R⟩(t). The Fourier transformation of ⟨R⟩(t) shows that the wave packets are composed mainly of the vibrational ground state and the first excited vibrational state, in agreement with numerical simulations. In the case of K2, the oscillations are observed for 300 ps, corresponding to more than 180 vibrational periods with an amplitude that decreases gradually from 0.035 to 0.020 Å. Using time-resolved spectral analysis, we find that the decay time of the amplitude is ∼260 ps. The decrease is ascribed to the weak coupling between the vibrating dimers and the droplet.

Structural Bifurcation in the High→Low-Spin and Low→High-Spin Phase Transitions Explains the Asymmetric Spin-Crossover in [FeL2][BF4]2 (L=2,6-Di{pyrazol-1-yl}isonicotinonitrile)

Polycrystalline [FeL2][BF4]2 (L=2,6-di(pyrazol-1-yl)isonicotinonitrile) exhibits an abrupt hysteretic spin transition near 240 K, with a shoulder on the warming branch whose appearance depends on the sample history. The freshly isolated material is a ca 60 : 40 mixture of triclinic (HS1) and tetragonal (HS2) high-spin polymorphs, which are structurally closely related. Both HS1 and HS2 undergo a high→low-spin transition on cooling at 230±10 K. HS1 transforms to a new triclinic low-spin phase with a doubled unit cell volume (LS3), while HS2 forms a monoclinic low-spin phase (LS4) with similar unit cell dimensions to HS2. Single crystals of LS3 and LS4 both convert to HS1 on rewarming. The low→high-spin transition for LS4 is ca 10 K higher in temperature than for LS3, explaining the asymmetric thermal hysteresis. Powder diffraction, calorimetry and magnetic data show that multiple cycling about the spin-transition leads to slow enrichment of the HS1 and LS3 phases at the expense of HS2 and LS4. That is consistent with the HS2/LS4 fraction of the polycrystalline sample undergoing rare, bifurcated HS2→(LS3+LS4) and LS4→(HS1+HS2) phase transitions. The rate of enrichment of HS1/LS3 differed between these experiments, implying it is sample and/or measurement-dependent. Three other salts of this iron(II) complex and the coordination polymer [Ag(μ-L)]BF4 are also briefly described.

Partial density of states representation for accurate deep neural network predictions of X-ray spectra

The performance of a machine learning (ML) algorithm for chemistry is highly contingent upon the architect's choice of input representation. This work introduces the partial density of states (p-DOS) descriptor: a novel, quantum-inspired structural representation which encodes relevant electronic information for machine learning models seeking to simulate X-ray spectroscopy. p-DOS uses a minimal basis set in conjunction with a guess (non-optimised) electronic configuration to extract and then discretise the density of states (DOS) of the absorbing atom to form the input vector. We demonstrate that while the electronically-focused p-DOS performs well in isolation, optimal performance is achieved when supplemented with nuclear structural information imparted via a geometric representation. p-DOS provides a description of the key electronic properties of a system which is not only concise and computationally efficient, but also independent of molecular size or choice of basis set. It can be rapidly generated, facilitating its application with large training sets. Its performance is demonstrated using a wide variety of examples at the sulphur K-edge, including the prediction of ultrafast X-ray spectroscopic signal associated with photoexcited 2(5H)-thiophenone. These results highlight the potential for ML models developed using p-DOS to contribute to the interpretation and prediction of experimental results e.g. in operando measurements of batteries and/or catalysts and femtosecond time-resolved studies, especially those made possible by emergent cutting-edge technologies, especially X-ray free electron lasers.

MP2-Based Composite Extrapolation Schemes Can Predict Core-Ionization Energies for First-Row Elements with Coupled-Cluster Level Accuracy

X-ray photoelectron spectroscopy (XPS) measures core-electron binding energies (CEBEs) to reveal element-specific insights into the chemical environment and bonding. Accurate theoretical CEBE prediction aids XPS interpretation but requires proper modeling of orbital relaxation and electron correlation upon core-ionization. This work systematically investigates basis set selection for extrapolation to the complete basis set limit of CEBEs from ΔMP2 and ΔCC energies across 94 K-edges in diverse organic molecules. We demonstrate that an alternative composite scheme using ΔMP2 in a large basis corrected by ΔCC-ΔMP2 difference in a small basis can quantitatively recover optimally extrapolated ΔCC CEBEs within 0.02 eV. Unlike ΔCC, MP2 calculations do not suffer from convergence issues and are computationally cheaper, and thus, the composite ΔMP2/ΔCC scheme balances accuracy and cost, overcoming limitations of solely using either method. We conclude by providing a comprehensive analysis of the choice of small and large basis sets for the composite schemes and provide practical recommendations for highly accurate (within 0.10-0.15 eV MAE) ab initio prediction of XPS data.

Probing the Dynamic Landscape: From Static to Time-Resolved X-Ray Absorption Spectroscopy to Investigate Copper Redox Chemistry in Neurodegenerative Disorders

Copper (Cu), with its ability to exist in various oxidation states, notably Cu(I) and Cu(II), plays a crucial role in diverse biological redox reactions. This includes its involvement in pathways associated with oxidative stress in neurodegenerative disorders such as Alzheimer's disease, Parkinson's disease, and Transmissible Spongiform Encephalopathies. This paper offers an overview of X-ray Absorption Spectroscopy (XAS) studies designed to elucidate the interactions between Cu ions and proteins or peptides associated with these neurodegenerative diseases. The emphasis lies on XAS specificity, revealing the local coordination environment, and on its sensitivity to Cu oxidation states. Furthermore, the paper focuses on XAS applications targeting the characterization of intermediate reaction states and explores the opportunities arising from recent advancements in time-resolved XAS at ultrabright synchrotron and Free Electron Laser radiation sources.

Core Binding Energy Calculations: A Scalable Approach with the Quantum Embedding-Based Equation-of-Motion Coupled-Cluster Method

We investigated the use of density matrix embedding theory to facilitate the computation of core ionization energies (IPs) of large molecules at the equation-of-motion coupled-cluster singles doubles with perturbative triples (EOM-CCSD*) level in combination with the core-valence separation (CVS) approximation. The unembedded IP-CVS-EOM-CCSD* method with a triple-ζ basis set produced ionization energies within 1 eV of experiment with a standard deviation of ∼0.2 eV for the core65 data set. The embedded variant contributed very little systematic error relative to the unembedded method, with a mean unsigned error of 0.07 eV and a standard deviation of ∼0.1 eV, in exchange for accelerating the calculations by many orders of magnitude. By employing embedded EOM-CC methods, we computed the core ionization energies of the uracil hexamer, doped fullerene, and chlorophyll molecule, utilizing up to ∼4000 basis functions within 1 eV from experimental values. Such calculations are not currently possible with the unembedded EOM-CC method.

Simulating transient X-ray photoelectron spectra of Fe(CO)5 and its photodissociation products with multireference algebraic diagrammatic construction theory

Accurate simulations of transient X-ray photoelectron spectra (XPS) provide unique opportunities to bridge the gap between theory and experiment in understanding the photoactivated dynamics in molecules and materials. However, simulating X-ray photoelectron spectra along a photochemical reaction pathway is challenging as it requires accurate description of electronic structure incorporating core-hole screening, orbital relaxation, electron correlation, and spin-orbit coupling in excited states or at nonequilibrium ground-state geometries. In this work, we employ the recently developed multireference algebraic diagrammatic construction theory (MR-ADC) to investigate the core-ionized states and X-ray photoelectron spectra of Fe(CO)5 and its photodissociation products (Fe(CO)4, Fe(CO)3) following excitation with 266 nm light. The simulated transient Fe 3p and CO 3σ XPS spectra incorporating spin-orbit coupling and high-order electron correlation effects are shown to be in a good agreement with the experimental measurements by Leitner et al. [J. Chem. Phys., 2018, 149, 044307]. Our calculations suggest that core-hole screening, spin-orbit coupling, and ligand-field splitting effects are similarly important in reproducing the experimentally observed chemical shifts in transient Fe 3p XPS spectra of iron carbonyl complexes. Our results also demonstrate that the MR-ADC methods can be very useful in interpreting the transient XPS spectra of transition metal compounds.

Water Solvent Reorganization upon Ultrafast Resonant Stimulated X-ray Raman Excitation of a Metalloporphyrin Dimer

We propose an X-ray Raman pump-X-ray diffraction probe scheme to follow solvation dynamics upon charge migration in a solute molecule. The X-ray Raman pump selectively prepares a valence electronic wavepacket in the solute, while the probe provides information about the entire molecular ensemble. A combination of molecular dynamics and ab initio quantum chemistry simulations is applied to a Zn-Ni porphyrin dimer in water. Using time-resolved X-ray diffraction and pair distribution functions, we extracted solvation shell dynamics.

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.

A sub-100 nm thickness flat jet for extreme ultraviolet to soft X-ray absorption spectroscopy

Experimental characterization of the structural, electronic and dynamic properties of dilute systems in aqueous solvents, such as nanoparticles, molecules and proteins, are nowadays an open challenge. X-ray absorption spectroscopy (XAS) is probably one of the most established approaches to this aim as it is element-specific. However, typical dilute systems of interest are often composed of light elements that require extreme-ultraviolet to soft X-ray photons. In this spectral regime, water and other solvents are rather opaque, thus demanding radical reduction of the solvent volume and removal of the liquid to minimize background absorption. Here, we present an experimental endstation designed to operate a liquid flat jet of sub-micrometre thickness in a vacuum environment compatible with extreme ultraviolet/soft XAS measurements in transmission geometry. The apparatus developed can be easily connected to synchrotron and free-electron-laser user-facility beamlines dedicated to XAS experiments. The conditions for stable generation and control of the liquid flat jet are analyzed and discussed. Preliminary soft XAS measurements on some test solutions are shown.

Activating a high-spin iron(II) complex to thermal spin-crossover with an inert non-isomorphous molecular dopant

[Fe(bpp)2][ClO4]2 (bpp = 2,6-bis{pyrazol-1-yl}pyridine; monoclinic, C2/c) is high-spin between 5-300 K, and crystallises with a highly distorted molecular geometry that lies along the octahedral-trigonal prismatic distortion pathway. In contrast, [Ni(bpp)2][ClO4]2 (monoclinic, P21) adopts a more regular, near-octahedral coordination geometry. Gas phase DFT minimisations (ω-B97X-D/6-311G**) of [M(bpp)2]2+ complexes show the energy penalty associated with that coordination geometry distortion runs as M2+ = Fe2+ (HS) ≈ Mn2+ (HS) < Zn2+ ≈ Co2+ (HS) ≲ Cu2+ ≪ Ni2+ ≪ Ru2+ (LS; HS = high-spin, LS = low-spin). Slowly crystallised solid solutions [FexNi1-x(bpp)2][ClO4]2 with x = 0.53 (1a) and 0.74 (2a) adopt the P21 lattice, while x = 0.87 (3a) and 0.94 (4a) are mixed-phase materials with the high-spin C2/c phase as the major component. These materials exhibit thermal spin-transitions at T½ = 250 ± 1 K which occurs gradually in 1a, and abruptly and with narrow thermal hysteresis in 2a-4a. The transition proceeds to 100% completeness in 1a and 2a; that is, the 26% Ni doping in 2a is enough to convert high-spin [Fe(bpp)2][ClO4]2 into a cooperative, fully SCO-active material. These results were confirmed crystallographically for 1a and 2a, which revealed similarities and differences between these materials and the previously published [FexNi1-x(bpp)2][BF4]2 series. Rapidly precipitated powders with the same compositions (1b-4b) mostly resemble 1a-4a, except that 2b is a mixed-phase material; 2b-4b also contain a fraction of amorphous solid in addition to the two crystal phases. The largest iron fraction that can be accommodated by the P21 phase in this system is 0.7 ± 0.1.

A Survey of the Angular Distortion Landscape in the Coordination Geometries of High-Spin Iron(II) 2,6-Bis(pyrazolyl)pyridine Complexes

Reaction of 2,4,6-trifluoropyridine with sodium 3,4-dimethoxybenzenethiolate and 2 equiv of sodium pyrazolate in tetrahydrofuran at room temperature affords 4-(3,4-dimethoxyphenylsulfanyl)-2,6-di(pyrazol-1-yl)pyridine (L), in 30% yield. The iron(II) complexes [FeL2][BF4]2 (1a) and [FeL2][ClO4]2 (1b) are high-spin with a highly distorted six-coordinate geometry. This structural deviation from ideal D2d symmetry is common in high-spin [Fe(bpp)2]2+ (bpp = di{pyrazol-1-yl}pyridine) derivatives, which are important in spin-crossover materials research. The magnitude of the distortion in 1a and 1b is the largest yet discovered for a mononuclear complex. Gas-phase DFT calculations at the ω-B97X-D/6-311G** level of theory identified four minimum or local minimum structural pathways across the distortion landscape, all of which are observed experimentally in different complexes. Small distortions from D2d symmetry are energetically favorable in complexes with electron-donating ligand substituents, including sulfanyl groups, which also have smaller energy penalties associated with the lowest energy distortion pathway. Natural population analysis showed that these differences reflect greater changes to the Fe-N{pyridyl} σ-bonding as the distortion proceeds, in the presence of more electron-rich pyridyl donors. The results imply that [Fe(bpp)2]2+ derivatives with electron-donating pyridyl substituents are more likely to undergo cooperative spin transitions in the solid state. The high-spin salt [Fe(bpp)2][CF3SO3]2, which also has a strong angular distortion, is also briefly described and included in the analysis.

Ultrafast and persistent photoinduced phase transition at room temperature monitored by streaming powder diffraction

Ultrafast photoinduced phase transitions at room temperature, driven by a single laser shot and persisting long after stimuli, represent emerging routes for ultrafast control over materials' properties. Time-resolved studies provide fundamental mechanistic insight into far-from-equilibrium electronic and structural dynamics. Here we study the photoinduced phase transformation of the Rb0.94Mn0.94Co0.06[Fe(CN)6]0.98 material, designed to exhibit a 75 K wide thermal hysteresis around room temperature between MnIIIFeII tetragonal and MnIIFeIII cubic phases. We developed a specific powder sample streaming technique to monitor by ultrafast X-ray diffraction the structural and symmetry changes. We show that the photoinduced polarons expand the lattice, while the tetragonal-to-cubic photoinduced phase transition occurs within 100 ps above threshold fluence. These results are rationalized within the framework of the Landau theory of phase transition as an elastically-driven and cooperative process. We foresee broad applications of the streaming powder technique to study non-reversible and ultrafast dynamics.

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.

Toward ultrafast soft x-ray spectroscopy of organic photovoltaic devices

Novel ultrafast x-ray sources based on high harmonic generation and at x-ray free electron lasers are opening up new opportunities to resolve complex ultrafast processes in condensed phase systems with exceptional temporal resolution and atomic site specificity. In this perspective, we present techniques for resolving charge localization, transfer, and separation processes in organic semiconductors and organic photovoltaic devices with time-resolved soft x-ray spectroscopy. We review recent results in ultrafast soft x-ray spectroscopy of these systems and discuss routes to overcome the technical challenges in performing time-resolved x-ray experiments on photosensitive materials with poor thermal conductivity and low pump intensity thresholds for nonlinear effects.

Vibrational Coherences of the Photoinduced Mixed-Valent Creutz-Taube Ion Revealed by Excited State Dynamics

A recent study of photoinduced mixed-valency in the one-electron reduced form (μ-pz)[RuII(NH3)5]24+ of the Creutz-Taube ion used transient absorption spectroscopy with vis-NIR broadband detection to uncover a mixed-valent excited state with a typical intervalence charge transfer band and a nanosecond lifetime [Pieslinger et al. Angew. Chem., Int. Ed. 2022, 61, e202211747]. Herein, we use excited state dynamics simulations with implicit solvation to elucidate the electronic and vibrational evolution in the first 10 ps after the optical excitation. A manifold of excited states with weak interaction between the metal centers is populated already at time zero due to the breakdown of the Condon approximation and dominates the population of electronic states at short time scales (<0.5 ps). A long-lived vibrational wave packet mostly confined to oscillations of the metal center-bridge distances is observed. The oscillations are traced to the electronic structure properties of states with weak metal-metal coupling. The long-lived mixed-valent excited state of the Creutz-Taube ion analogue is formed vibrationally cold and has a more compact geometry. While experimentally, intersystem crossing and vibrational relaxation were deduced to be completed within 1 ps, our analysis indicates that both processes might persist at longer times.

A Δ-learning strategy for interpretation of spectroscopic observables

Accurate computations of experimental observables are essential for interpreting the high information content held within x-ray spectra. However, for complicated systems this can be difficult, a challenge compounded when dynamics becomes important owing to the large number of calculations required to capture the time-evolving observable. While machine learning architectures have been shown to represent a promising approach for rapidly predicting spectral lineshapes, achieving simultaneously accurate and sufficiently comprehensive training data is challenging. Herein, we introduce Δ-learning for x-ray spectroscopy. Instead of directly learning the structure-spectrum relationship, the Δ-model learns the structure dependent difference between a higher and lower level of theory. Consequently, once developed these models can be used to translate spectral shapes obtained from lower levels of theory to mimic those corresponding to higher levels of theory. Ultimately, this achieves accurate simulations with a much reduced computational burden as only the lower level of theory is computed, while the model can instantaneously transform this to a spectrum equivalent to a higher level of theory. Our present model, demonstrated herein, learns the difference between TDDFT(BLYP) and TDDFT(B3LYP) spectra. Its effectiveness is illustrated using simulations of Rh L3-edge spectra tracking the C-H activation of octane by a cyclopentadienyl rhodium carbonyl complex.

Iron(II) complexes of 2,6-bis(imidazo[1,2-a]pyridin-2-yl)pyridine and related ligands with annelated distal heterocyclic donors

Following a published synthesis of 2,6-bis(imidazo[1,2-a]pyridin-2-yl)pyridine (L1), treatment of α,α'-dibromo-2,6-diacetylpyridine with 2 equiv. 2-aminopyrimidine or 2-aminoquinoline in refluxing acetonitrile respectively gives 2,6-bis(imidazo[1,2-a]pyrimidin-2-yl)pyridine (L2) and 2,6-bis(imidazo[1,2-a]quinolin-2-yl)pyridine (L3). Solvated crystals of [Fe(L1)2][BF4]2 (1[BF4]2) and [Fe(L2)2][BF4]2 (2[BF4]2) are mostly high-spin, although one solvate of 1[BF4]2 undergoes thermal spin-crossover on cooling. The iron coordination geometry is consistently distorted in crystals of 2[BF4]2 which may reflect the influence of intramolecular, inter-ligand N⋯π interactions on the molecular conformation. Only 1 : 1 Fe : L3 complexes were observed in solution, or isolated in the solid state; a crystal structure of [FeBr(py)2L3]Br·0.5H2O (py = pyridine) is presented. A solvate crystal structure of high-spin [Fe(L4)2][BF4]2 (L4 = 2,6-di{quinolin-2-yl}pyridine; 4[BF4]2) is also described, which exhibits a highly distorted six-coordinate geometry with a helical ligand conformation. The iron(II) complexes are high-spin in solution at room temperature, but 1[BF4]2 and 2[BF4]2 undergo thermal spin-crossover equilibria on cooling. All the compounds exhibit a ligand-based emission in solution at room temperature. Gas phase DFT calculations mostly reproduce the spin state properties of the complexes, but show small anomalies attributed to intramolecular, inter-ligand dispersion interactions in the sterically crowded molecules.

Exploring fingerprints of ultrafast structural dynamics in molecular solutions with an X-ray laser

We apply ultrashort X-ray laser pulses to track optically excited structural dynamics of [Ir2(dimen)4]2+ molecules in solution. In our exploratory study we determine angular correlations in the scattered X-rays, which comprise a complex fingerprint of the ultrafast dynamics. Model-assisted analysis of the experimental correlation data allows us to elucidate various aspects of the photoinduced changes in the excited molecular ensembles. We unambiguously identify that in our experiment the photoinduced transition dipole moments in [Ir2(dimen)4]2+ molecules are oriented perpendicular to the Ir-Ir bond. The analysis also shows that the ground state conformer of [Ir2(dimen)4]2+ with a larger Ir-Ir distance is mostly responsible for the formation of the excited state. We also reveal that the ensemble of solute molecules can be characterized with a substantial structural heterogeneity due to solvent influence. The proposed X-ray correlation approach offers an alternative path for studies of ultrafast structural dynamics of molecular ensembles in the liquid and gas phases.

Laser-Driven Transient Phase Oscillations in Individual Spin Crossover Particles

An unusual expansion dynamics of individual spin crossover nanoparticles is studied by ultrafast transmission electron microscopy. After exposure to nanosecond laser pulses, the particles exhibit considerable length oscillations during and after their expansion. The vibration period of 50-100 ns is of the same order of magnitude as the time that the particles need for a transition from the low-spin to the high-spin state. The observations are explained in Monte Carlo calculations using a model where elastic and thermal coupling between the molecules within a crystalline spin crossover particle govern the phase transition between the two spin states. The experimentally observed length oscillations are in agreement with the calculations, and it is shown that the system undergoes repeated transitions between the two spin states until relaxation in the high-spin state occurs due to energy dissipation. Spin crossover particles are therefore a unique system where a resonant transition between two phases occurs in a phase transformation of first order.

Implication of the double-gating mode in a hybrid photon counting detector for measurements of transient heat conduction in GaAs/AlAs superlattice structures

Understanding and control of thermal transport in solids at the nanoscale are crucial in engineering and enhance the properties of a new generation of optoelectronic, thermoelectric and photonic devices. In this regard, semiconductor superlattice structures provide a unique platform to study phenomena associated with phonon propagations in solids such as heat conduction. Transient X-ray diffraction can directly probe atomic motions and therefore is among the rare techniques sensitive to phonon dynamics in condensed matter. Here, optically induced transient heat conduction in GaAs/AlAs superlattice structures is studied using the EIGER2 detector. Benchmark experiments have been performed at the Austrian SAXS beamline at Elettra-Sincrotrone Trieste operated in the hybrid filling mode. This work demonstrates that drifts of experimental conditions, such as synchrotron beam fluctuations, become less essential when utilizing the EIGER2 double-gating mode which results in a faster acquisition of high-quality data and facilitates data analysis and data interpretation.

Ultrafast Jahn-Teller Photoswitching in Cobalt Single-Ion Magnets

Single-ion magnets (SIMs) constitute the ultimate size limit in the quest for miniaturizing magnetic materials. Several bottlenecks currently hindering breakthroughs in quantum information and communication technologies could be alleviated by new generations of SIMs displaying multifunctionality. Here, ultrafast optical absorption spectroscopy and X-ray emission spectroscopy are employed to track the photoinduced spin-state switching of the prototypical complex [Co(terpy)2 ]2+ (terpy = 2,2':6',2″-terpyridine) in solution phase. The combined measurements and their analysis supported by density functional theory (DFT), time-dependent-DFT (TD-DFT) and multireference quantum chemistry calculations reveal that the complex undergoes a spin-state transition from a tetragonally elongated doublet state to a tetragonally compressed quartet state on the femtosecond timescale, i.e., it sustains ultrafast Jahn-Teller (JT) photoswitching between two different spin multiplicities. Adding new Co-based complexes as possible contenders in the search for JT photoswitching SIMs will greatly widen the possibilities for implementing magnetic multifunctionality and eventually controlling ultrafast magnetization with optical photons.

Solvent-Dependent Structural Dynamics in the Ultrafast Photodissociation Reaction of Triiodide Observed with Time-Resolved X-ray Solution Scattering

Resolving the structural dynamics of bond breaking, bond formation, and solvation is required for a deeper understanding of solution-phase chemical reactions. In this work, we investigate the photodissociation of triiodide in four solvents using femtosecond time-resolved X-ray solution scattering following 400 nm photoexcitation. Structural analysis of the scattering data resolves the solvent-dependent structural evolution during the bond cleavage, internal rearrangements, solvent-cage escape, and bond reformation in real time. The nature and structure of the reaction intermediates during the recombination are determined, elucidating the full mechanism of photodissociation and recombination on ultrafast time scales. We resolve the structure of the precursor state for recombination as a geminate pair. Further, we determine the size of the solvent cages from the refined structures of the radical pair. The observed structural dynamics present a comprehensive picture of the solvent influence on structure and dynamics of dissociation reactions.

Ultrafast X-Ray Probes of Elementary Molecular Events

Elementary events that determine photochemical outcomes and molecular functionalities happen on the femtosecond and subfemtosecond timescales. Among the most ubiquitous events are the nonadiabatic dynamics taking place at conical intersections. These facilitate ultrafast, nonradiative transitions between electronic states in molecules that can outcompete slower relaxation mechanisms such as fluorescence. The rise of ultrafast X-ray sources, which provide intense light pulses with ever-shorter durations and larger observation bandwidths, has fundamentally revolutionized our spectroscopic capabilities to detect conical intersections. Recent theoretical studies have demonstrated an entirely new signature emerging once a molecule traverses a conical intersection, giving detailed insights into the coupled nuclear and electronic motions that underlie, facilitate, and ultimately determine the ultrafast molecular dynamics. Following a summary of current sources and experiments, we survey these techniques and provide a unified overview of their capabilities. We discuss their potential to dramatically increase our understanding of ultrafast photochemistry.

Direct detection of photo-induced reactions by IR: from Brook rearrangement to photo-catalysis

In situ IR detection of photoreactions induced by the light of LEDs at appropriate wavelengths provides a simple, cost-effective, and versatile method to get insight into mechanistic details. In particular, conversions of functional groups can be selectively followed. Overlapping UV-Vis bands or fluorescence from the reactants and products and the incident light do not obstruct IR detection. Compared with in situ photo-NMR, our setup does not require tedious sample preparation (optical fibers) and offers a selective detection of reactions, even at positions where ¹H-NMR lines overlap or ¹H resonances are not clear-cut. We illustrate the applicability of our setup following the photo-Brook rearrangement of (adamant-1-yl-carbonyl)-tris(trimethylsilyl)silane, address photo-induced α-bond cleavage (1-hydroxycyclohexyl phenyl ketone), study photoreduction using tris(bipyridine)ruthenium(II), investigate photo-oxygenation of double bonds with molecular oxygen and the fluorescent 2,4,6-triphenylpyrylium photocatalyst, and address photo-polymerization. With the LED/FT-IR combination, reactions can be qualitatively followed in fluid solution, (highly) viscous environments, and in the solid state. Viscosity changes during the reaction (e.g., during a polymerization) do not obstruct the method.

Target State Optimized Density Functional Theory for Electronic Excited and Diabatic States

A flexible self-consistent field method, called target state optimization (TSO), is presented for exploring electronic excited configurations and localized diabatic states. The key idea is to partition molecular orbitals into different subspaces according to the excitation or localization pattern for a target state. Because of the orbital-subspace constraint, orbitals belonging to different subspaces do not mix. Furthermore, the determinant wave function for such excited or diabatic configurations can be variationally optimized as a ground state procedure, unlike conventional ΔSCF methods, without the possibility of collapsing back to the ground state or other lower-energy configurations. The TSO method can be applied both in Hartree-Fock theory and in Kohn-Sham density functional theory (DFT). The density projection procedure and the working equations for implementing the TSO method are described along with several illustrative applications. For valence excited states of organic compounds, it was found that the computed excitation energies from TSO-DFT and time-dependent density functional theory (TD-DFT) are of similar quality with average errors of 0.5 and 0.4 eV, respectively. For core excitation, doubly excited states and charge-transfer states, the performance of TSO-DFT is clearly superior to that from conventional TD-DFT calculations. It is shown that variationally optimized charge-localized diabatic states can be defined using TSO-DFT in energy decomposition analysis to gain both qualitative and quantitative insights on intermolecular interactions. Alternatively, the variational diabatic states may be used in molecular dynamics simulation of charge transfer processes. The TSO method can also be used to define basis states in multistate density functional theory for excited states through nonorthogonal state interaction calculations. The software implementing TSO-DFT can be accessed from the authors.

Femtosecond-resolved imaging of a single-particle phase transition in energy-filtered ultrafast electron microscopy

Using an energy filter in transmission electron microscopy has enabled elemental mapping at the atomic scale and improved the precision of structural determination by gating inelastic and elastic imaging electrons, respectively. Here, we use an energy filter in ultrafast electron microscopy to enhance the temporal resolution toward the domain of atomic motion. Visualizing transient structures with femtosecond temporal precision was achieved by selecting imaging electrons in a narrow energy distribution from dense chirped photoelectron packets with broad longitudinal momentum distributions and thus typically exhibiting picosecond durations. In this study, the heterogeneous ultrafast phase transitions of vanadium dioxide (VO₂) nanoparticles, a representative strongly correlated system, were filmed and attributed to the emergence of a transient, low-symmetry metallic phase caused by different local strains. Our approach enables electron microscopy to access the time scale of elementary nuclear motion to visualize the onset of the structural dynamics of matter at the nanoscale.

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.

Nature of the Ultrafast Interligands Electron Transfers in Dye-Sensitized Solar Cells

Charge-transfer dynamics and interligand electron transfer (ILET) phenomena play a pivotal role in dye-sensitizers, mostly represented by the Ru-based polypyridyl complexes, for TiO2 and ZnO-based solar cells. Starting from metal-to-ligand charge-transfer (MLCT) excited states, charge dynamics and ILET can influence the overall device efficiency. In this letter, we focus on N34- dye ( [Ru(dcbpy)2(NCS)2]4-, dcbpy = 4,4'-dicarboxy-2,2'-bipyridine) to provide a first direct observation with high time resolution (<20 fs) of the ultrafast electron exchange between bpy-like ligands. ILET is observed in water solution after photoexcitation in the ∼400 nm MLCT band, and assessment of its ultrafast time-scale is here given through a real-time electronic dynamics simulation on the basis of state-of-the-art electronic structure methods. Indirect effects of water at finite temperature are also disentangled by investigating the system in a symmetric gas-phase structure. As main result, remarkably, the ILET mechanism appears to be based upon a purely electronic evolution among the dense, experimentally accessible, MLCT excited states manifold at ∼400 nm, which rules out nuclear-electronic couplings and proves further the importance of the dense electronic manifold in improving the efficiency of dye sensitizers in solar cell devices.

Flow cell for operando X-ray photon-in-photon-out studies on photo-electrochemical thin film devices

Background: Photo-electro-chemical (PEC) water splitting represents a promising technology towards an artificial photosynthetic device but many fundamental electronic processes, which govern long-term stability and energetics, are not yet fully understood. X-ray absorption spectroscopy (XAS), and particularly its high energy resolution fluorescence-detected (HERFD) mode, emerges as a powerful tool to study photo-excited charge carrier behavior under operating conditions. The established thin film device architecture of PEC cells provides a well-defined measurement geometry, but it puts many constraints on conducting operando XAS experiments. It remains a challenge to establish a standardized thin film exchange procedure and concurrently record high-quality photoelectrochemical and X‑ray absorption spectroscopy data that is unperturbed by bubble formation. Here we address and overcome these instrumental limitations for photoelectrochemical operando HERFD-XAS. Methods: We constructed a novel operando photo-electro-chemical cell by computer numerical control milling, guided by the materials' X‑ray and visible light absorption properties to optimize signal detection. To test the cell's functionality, semiconducting thin film photoelectrodes have been fabricated via solution deposition and their photoelectrochemical responses under simulated solar light were studied using a commercial potentiostat in a three-electrode configuration during HERFD-XAS experiments at a synchrotron. Results: We demonstrate the cell's capabilities to measure and control potentiostatically and in open‑circuit, to detect X‑ray signals unperturbed by bubbles and to fluently exchange different thin film samples by collecting high-resolution Fe K-edge spectra of hematite ( α -Fe 2O 3) and ferrite thin film ( MFe 2O 4, M= Zn, Ni) photoelectrodes during water oxidation. Conclusions: Our cell establishes a measurement routine that will provide experimental access of photo-electro-chemical operando HERFD-XAS experiments to a broader scientific community, particularly due to the ease of sample exchange. We believe to enable a broad range of experiments which acquired fundamental insights will spur further photoelectrochemical research and commercialization of water splitting technologies.

Molecular Chirality and Its Monitoring by Ultrafast X-ray Pulses

Major advances in X-ray sources including the development of circularly polarized and orbital angular momentum pulses make it possible to probe matter chirality at unprecedented energy regimes and with Ångström and femtosecond spatiotemporal resolutions. We survey the theory of stationary and time-resolved nonlinear chiral measurements that can be carried out in the X-ray regime using tabletop X-ray sources or large scale (XFEL, synchrotron) facilities. A variety of possible signals and their information content are discussed.

Characterizing coherences in chemical dynamics with attosecond time-resolved x-ray absorption spectroscopy

Coherence can drive wave-like motion of electrons and nuclei in photoexcited systems, which can yield fast and efficient ways to exert materials’ functionalities beyond the thermodynamic limit. The search for coherent phenomena has been a central topic in chemical physics although their direct characterization is often elusive. Here, we highlight recent advances in time-resolved x-ray absorption spectroscopy (tr-XAS) to investigate coherent phenomena, especially those that utilize the eminent light source of isolated attosecond pulses. The unparalleled time and state sensitivities of tr-XAS in tandem with the unique element specificity render the method suitable to study valence electronic dynamics in a wide variety of materials. The latest studies have demonstrated the capabilities of tr-XAS to characterize coupled electronic–structural coherence in small molecules and coherent light–matter interactions of core-excited excitons in solids. We address current opportunities and challenges in the exploration of coherent phenomena, with potential applications for energy- and bio-related systems, potential crossings, strongly driven solids, and quantum materials. With the ongoing developments in both theory and light sources, tr-XAS holds great promise for revealing the role of coherences in chemical dynamics.

Exact two-component Hamiltonians for relativistic quantum chemistry: Two-electron picture-change corrections made simple

Based on self-consistent field (SCF) atomic mean-field (amf) quantities, we present two simple yet computationally efficient and numerically accurate matrix-algebraic approaches to correct both scalar-relativistic and spin-orbit two-electron picture-change effects (PCEs) arising within an exact two-component (X2C) Hamiltonian framework. Both approaches, dubbed amfX2C and e(xtended)amfX2C, allow us to uniquely tailor PCE corrections to mean-field models, viz. Hartree-Fock or Kohn-Sham DFT, in the latter case also avoiding the need for a point-wise calculation of exchange-correlation PCE corrections. We assess the numerical performance of these PCE correction models on spinor energies of group 18 (closed-shell) and group 16 (open-shell) diatomic molecules, achieving a consistent ≈10^-5 Hartree accuracy compared to reference four-component data. Additional tests include SCF calculations of molecular properties such as absolute contact density and contact density shifts in copernicium fluoride compounds (CnF_n, n = 2,4,6), as well as equation-of-motion coupled-cluster calculations of x-ray core-ionization energies of 5d- and 6d-containing molecules, where we observe an excellent agreement with reference data. To conclude, we are confident that our (e)amfX2C PCE correction models constitute a fundamental milestone toward a universal and reliable relativistic two-component quantum-chemical approach, maintaining the accuracy of the parent four-component one at a fraction of its computational cost.

Development of a Multitimescale Time-Resolved Electron Diffraction Setup: Photoinduced Dynamics of Oxygen Radicals on Graphene Oxide

We developed a multitimescale time-resolved electron diffraction setup by electrically synchronizing a nanosecond laser with our table-top picosecond time-resolved electron diffractometer. The setup covers the photoinduced structural dynamics of target materials at timescales ranging from picoseconds to submilliseconds. Using this setup, we sequentially observed the ultraviolet (UV) photoinduced bond dissociation, radical formation, and relaxation dynamics of the oxygen atoms in the epoxy functional group on the basal plane of graphene oxide (GO). The results show that oxygen radicals formed via UV photoexcitation on the basal plane of GO in several tens of picoseconds and then relaxed back to the initial state on the microsecond timescale. The results of first-principles calculations also support the formation of oxygen radicals in the excited state on an early timescale. These results are essential for the further discussion of the reactivities on the basal plane of GO, such as catalytic reactions and antibacterial and antiviral activities. The results also suggest that the multitimescale time-resolved electron diffraction system is a promising tool for laboratory-based molecular dynamics studies of materials and chemical systems.

Optically Induced Anisotropy in Time-Resolved Scattering: Imaging Molecular-Scale Structure and Dynamics in Disordered Media with Experiment and Theory

Time-resolved scattering experiments enable imaging of materials at the molecular scale with femtosecond time resolution. However, in disordered media they provide access to just one radial dimension thus limiting the study of orientational structure and dynamics. Here we introduce a rigorous and practical theoretical framework for predicting and interpreting experiments combining optically induced anisotropy and time-resolved scattering. Using impulsive nuclear Raman and ultrafast x-ray scattering experiments of chloroform and simulations, we demonstrate that this framework can accurately predict and elucidate both the spatial and temporal features of these experiments.

Quantum entanglement control of electron-phonon systems by light irradiation

We numerically study the dynamics of quantum entanglement between interacting electron-phonon and qubit-spin systems under photoirradiation, employing a model of multiple spins and boson modes. The interplay of the antiferromagnetic exchange and electron-phonon interactions provides us with a phase diagram, wherein each phase is characterized by the ground state property of the electron-phonon system. Light irradiation of the electron-phonon system facilitates the generation of quantum entanglement, according to the spin configuration and the phonon state in the ground state. Analyses using the quantum mutual information and the singular values of the reduced density matrix indicate that the quantum mechanical effect of the irradiated light appears in the state of the material.

Hole Dynamics in Photoexcited Hematite Studied with Femtosecond Oxygen K-edge X-ray Absorption Spectroscopy

Hematite (α-Fe₂O₃) is a photoelectrode for the water splitting process because of its relatively narrow bandgap and abundance in the earth's crust. In this study, the photoexcited state of a hematite thin film was investigated with femtosecond oxygen K-edge X-ray absorption spectroscopy (XAS) at the PAL-XFEL in order to follow the dynamics of its photoexcited states. The 200 fs decay time of the hole state in the valence band was observed via its corresponding XAS feature.

Time-Resolved Optical Pump-Resonant X-ray Probe Spectroscopy of 4-Thiouracil: A Simulation Study

We theoretically monitor the photoinduced ππ* → nπ* internal conversion process in 4-thiouracil (4TU), triggered by an optical pump. The element-sensitive spectroscopic signatures are recorded by a resonant X-ray probe tuned to the sulfur, oxygen, or nitrogen K-edge. We employ high-level electronic structure methods optimized for core-excited electronic structure calculation combined with quantum nuclear wavepacket dynamics computed on two relevant nuclear modes, fully accounting for their quantum nature of nuclear motions. We critically discuss the capabilities and limitations of the resonant technique. For sulfur and nitrogen, we document a pre-edge spectral window free from ground-state background and rich with ππ* and nπ* absorption features. The lowest sulfur K-edge shows strong absorption for both ππ* and nπ*. In the lowest nitrogen K-edge window, we resolve a state-specific fingerprint of the ππ* and an approximate timing of the conical intersection via its depletion. A spectral signature of the nπ* transition, not accessible by UV-vis spectroscopy, is identified. The oxygen K-edge is not sensitive to molecular deformations and gives steady transient absorption features without spectral dynamics. The ππ*/nπ* coherence information is masked by more intense contributions from populations. Altogether, element-specific time-resolved resonant X-ray spectroscopy provides a detailed picture of the electronic excited-state dynamics and therefore a sensitive window into the photophysics of thiobases.

Relativistic Orbital-Optimized Density Functional Theory for Accurate Core-Level Spectroscopy

Core-level spectra of 1s electrons of elements heavier than Ne show significant relativistic effects. We combine advances in orbital-optimized density functional theory (OO-DFT) with the spin-free exact two-component (X2C) model for scalar relativistic effects to study K-edge spectra of third period elements. OO-DFT/X2C is found to be quite accurate at predicting energies, yielding a ∼0.5 eV root-mean-square error versus experiment with the modern SCAN (and related) functionals. This marks a significant improvement over the >50 eV deviations that are typical for the popular time-dependent DFT (TDDFT) approach. Consequently, experimental spectra are quite well reproduced by OO-DFT/X2C, sans empirical shifts for alignment. OO-DFT/X2C combines high accuracy with ground state DFT cost and is thus a promising route for computing core-level spectra of third period elements. We also explored K and L edges of 3d transition metals to identify limitations of the OO-DFT/X2C approach in modeling the spectra of heavier atoms.

Theoretical analysis of the role of complex transition dipole phase in XUV transient-absorption probing of charge migration

We theoretically investigate the role of complex dipole phase in the attosecond probing of charge migration. The iodobromoacetylene ion (ICCBr⁺) is considered as an example, in which one can probe charge migration by accessing both the iodine and bromine ends of the molecule with different spectral windows of an extreme-ultraviolet (XUV) pulse. The analytical expression for transient absorption shows that the site-specific information of charge migration is encoded in the complex phase of cross dipole products for XUV transitions between the I-4d and Br-3d spectral windows. Ab-initio quantum chemistry calculations on ICCBr⁺ reveal that there is a constant π phase difference between the I-4d and Br-3d transient-absorption spectral windows, irrespective of the fine-structure energy splittings. Transient absorption spectra are simulated with a multistate model including the complex dipole phase, and the results correctly reconstruct the charge-migration dynamics via the quantum beats in the two element spectral windows, exhibiting out-of-phase oscillations.

Femtosecond X-ray Spectroscopy Directly Quantifies Transient Excited-State Mixed Valency

Quantifying charge delocalization associated with short-lived photoexcited states of molecular complexes in solution remains experimentally challenging, requiring local element specific femtosecond experimental probes of time-evolving electron transfer. In this study, we quantify the evolving valence hole charge distribution in the photoexcited charge transfer state of a prototypical mixed valence bimetallic iron-ruthenium complex, [(CN)₅Fe^IICNRu^III(NH₃)₅]^-, in water by combining femtosecond X-ray spectroscopy measurements with time-dependent density functional theory calculations of the excited-state dynamics. We estimate the valence hole charge that accumulated at the Fe atom to be 0.6 ± 0.2, resulting from excited-state metal-to-metal charge transfer, on an ∼60 fs time scale. Our combined experimental and computational approach provides a spectroscopic ruler for quantifying excited-state valency in solvated complexes.

Simulating X-ray photoelectron spectra with strong electron correlation using multireference algebraic diagrammatic construction theory

A new theoretical approach for the simulations of X-ray photoelectron spectra of strongly correlated molecular systems that combines multireference algebraic diagrammatic construction theory (MR-ADC) with a core–valence separation (CVS) technique.