Femtosecond x-ray spectroscopy of an electrocyclic ring-opening reaction

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.

Laser Control of Electronic Exchange Interaction within a Molecule

Electronic interactions play a fundamental role in atoms, molecular structure and reactivity. We introduce a general concept to control the effective electronic exchange interaction with intense laser fields via coupling to excited states. As an experimental proof of principle, we study the SF_{6} molecule using a combination of soft x-ray and infrared (IR) laser pulses. Increasing the IR intensity increases the effective exchange energy of the core hole with the excited electron by 50%, as observed by a characteristic spin-orbit branching ratio change. This work demonstrates altering electronic interactions by targeting many-particle quantum properties.

Conformer-Specific Dissociation Dynamics in Dimethyl Methylphosphonate Radical Cation

The dynamics of the dimethyl methylphosphonate (DMMP) radical cation after production by strong field adiabatic ionization have been investigated. Pump-probe experiments using strong field 1300 nm pulses to adiabatically ionize DMMP and a 800 nm non-ionizing probe induce coherent oscillations of the parent ion yield with a period of about 45 fs. The yields of two fragments, PO2C2H7+ and PO2CH4+, oscillate approximately out of phase with the parent ion, but with a slight phase shift relative to each other. We use electronic structure theory and nonadiabatic surface hopping dynamics to understand the underlying dynamics. The results show that while the cation oscillates on the ground state along the P=O bond stretch coordinate, the probe excites population to higher electronic states that can lead to fragments PO2C2H7+ and PO2CH4+. The computational results combined with the experimental observations indicate that the two conformers of DMMP that are populated under experimental conditions exhibit different dynamics after being excited to the higher electronic states of the cation leading to different dissociation products. These results highlight the potential usefulness of these pump-probe measurements as a tool to study conformer-specific dynamics in molecules of biological interest.

Extreme Ultraviolet Reflection-Absorption Spectroscopy: Probing Dynamics at Surfaces from a Molecular Perspective

Extreme ultraviolet light sources based on high harmonic generation are enabling the development of novel spectroscopic methods to help advance the frontiers of ultrafast science and technology. In this Account, we discuss the development of extreme ultraviolet reflection-absorption (XUV-RA) spectroscopy at near grazing incident reflection geometry and highlight recent applications of this method to study ultrafast electron dynamics at surfaces. Measuring core-to-valence transitions with broadband, femtosecond pulses of XUV light extends the benefits of X-ray absorption spectroscopy to a laboratory tabletop by providing a chemical fingerprint of materials, including the ability to resolve individual elements with sensitivity to oxidation state, spin state, carrier polarity, and coordination geometry. Combining this chemical state sensitivity with femtosecond time resolution provides new insight into the material properties that govern charge carrier dynamics in complex materials. It is well-known that surface dynamics differ significantly from equivalent processes in bulk materials and that charge separation, trapping, transport, and recombination occurring uniquely at surfaces govern the efficiency of numerous technologically relevant processes spanning photocatalysis, photovoltaics, and information storage and processing. Importantly, XUV-RA spectroscopy at near grazing angle is also surface sensitive with a probe depth of ∼3 nm, providing a new window into electronic and structural dynamics at surfaces and interfaces. Here we highlight the unique capabilities and recent applications of XUV-RA spectroscopy to study photoinduced surface dynamics in metal oxide semiconductors, including photocatalytic oxides (Fe₂O₃, Co₃O₄ NiO, and CuFeO₂) as well as photoswitchable magnetic oxide (CoFe₂O₄). We first compare the ultrafast electron self-trapping rates via small polaron formation at the surface and bulk of Fe₂O₃ where we note that the energetics and kinetics of this process differ significantly at the surface. Additionally, we demonstrate the ability to systematically tune this kinetics by molecular functionalization, thereby providing a route to control carrier transport at surfaces. We also measure the spectral signatures of charge transfer excitons with site specific localization of both electrons and holes in a series of transition metal oxide semiconductors (Fe₂O₃, NiO, Co₃O₄). The presence of valence band holes probed at the oxygen L₁-edge confirms a direct relationship between the metal-oxygen bond covalency and water oxidation efficiency. For a mixed metal oxide CuFeO₂ in the layered delafossite structure, XUV-RA reveals that the sub-picosecond hole thermalization from O 2p to Cu 3d states of CuFeO₂ leads to the spatial separation of electrons and holes, resulting in exceptional photocatalytic performance for H₂ evolution and CO₂ reduction of this material. Finally, we provide an example to show the ability of XUV-RA to probe spin state specific dynamics in a photoswitchable ferrimagnet, cobalt ferrite (CoFe₂O₄). This study provides a detailed understating of ultrafast spin switching in a complex magnetic material with site-specific resolution. In summary, the applications of XUV-RA spectroscopy demonstrated here illustrate the current abilities and future promise of this method to extend molecule-level understanding from well-defined photochemical complexes to complex materials so that charge and spin dynamics at surfaces can be tuned with the precision of molecular photochemistry.

Sleeping Beauties in Chemistry. Oosterhoff, Havinga and Schlatmann: Four Years Before "The Woodward-Hoffmann Rules"†

Several forerunners to the Woodward-Hoffmann rules appear in the chemical literature in the early 1960s. While these precedents refer to orbital symmetry and explain either electrocyclic reactions (Luitzen Oosterhoff, cited by Egbert Havinga and Jos Schlatmann in Tetrahedron in 1961) or some cycloaddition reactions (Kenichi Fukui, in a book chapter published in 1964), they did not attract any attention and did not serve to initiate any research prior to the publication of the five Woodward and Hoffmann communications in 1965. Even Woodward and Hoffmann were unaware of these precedents (though Hoffmann knew of Fukui's frontier orbital theory) until after they had completed the relevant portions of their work. The Oosterhoff-Havinga-Schlatmann story will be told in this paper; the Fukui story will be told in the next paper in this series on the history of the development of the Woodward-Hoffmann rules. Explanations for these precedents not being productive in solving the no-mechanism problem are discussed.

Soft X-ray Spectroscopy Simulations with Multiconfigurational Wave Function Theory: Spectrum Completeness, Sub-eV Accuracy, and Quantitative Reproduction of Line Shapes

Multireference methods are known for their ability to accurately treat states of very different nature in many molecular systems, facilitating high-quality simulations of a large variety of spectroscopic techniques. Here, we couple the multiconfigurational restricted active space self-consistent field RASSCF/RASPT2 method (of the CASSCF/CASPT2 methods family) to the displaced harmonic oscillator (DHO) model, to simulate soft X-ray spectroscopy. We applied such an RASSCF/RASPT2+DHO approach at the K-edges of various second-row elements for a set of small organic molecules that have been recently investigated at other levels of theory. X-ray absorption near-edge structure (XANES) and X-ray photoelectron spectroscopy (XPS) are simulated with a sub-eV accuracy and a correct description of the spectral line shapes. The method is extremely sensitive to the observed spectral shifts on a series of differently fluorinated ethylene systems, provides spectral fingerprints to distinguish between stable conformers of the glycine molecule, and accurately captures the vibrationally resolved carbon K-edge spectrum of formaldehyde. Differences with other theoretical methods are demonstrated, which show the advantages of employing a multireference/multiconfigurational approach. A protocol to systematically increase the number of core-excited states considered while maintaining a contained computational cost is presented. Insight is eventually provided for the effects caused by removing core-electrons from a given atom in terms of bond rearrangement and influence on the resulting spectral shapes within a unitary orbital-based framework for both XPS and XANES spectra.

Following excited-state chemical shifts in molecular ultrafast x-ray photoelectron spectroscopy

The conversion of photon energy into other energetic forms in molecules is accompanied by charge moving on ultrafast timescales. We directly observe the charge motion at a specific site in an electronically excited molecule using time-resolved x-ray photoelectron spectroscopy (TR-XPS). We extend the concept of static chemical shift from conventional XPS by the excited-state chemical shift (ESCS), which is connected to the charge in the framework of a potential model. This allows us to invert TR-XPS spectra to the dynamic charge at a specific atom. We demonstrate the power of TR-XPS by using sulphur 2p-core-electron-emission probing to study the UV-excited dynamics of 2-thiouracil. The method allows us to discover that a major part of the population relaxes to the molecular ground state within 220–250 fs. In addition, a 250-fs oscillation, visible in the kinetic energy of the TR-XPS, reveals a coherent exchange of population among electronic states.

Imaging the charge flow in photoexcited molecules would provide key information on photophysical and photochemical processes. Here the authors demonstrate tracking in real time after photoexcitation the change in charge density at a specific site of 2-thiouracil using time-resolved X-ray photoelectron spectroscopy.

Development of an experimental apparatus to observe ultrafast phenomena by tender X-ray absorption spectroscopy at PAL-XFEL

Understanding the ultrafast dynamics of molecules is of fundamental importance. Time-resolved X-ray absorption spectroscopy (TR-XAS) is a powerful spectroscopic technique for unveiling the time-dependent structural and electronic information of molecules that has been widely applied in various fields. Herein, the design and technical achievement of a newly developed experimental apparatus for TR-XAS measurements in the tender X-ray range with X-ray free-electron lasers (XFELs) at the Pohang Accelerator Laboratory XFEL (PAL-XFEL) are described. Femtosecond TR-XAS measurements were conducted at the Ru L3-edge of well known photosensitizer tris(bipyridine)ruthenium(II) chloride ([Ru(bpy)3]2+) in water. The results indicate ultrafast photoinduced electron transfer from the Ru center to the ligand, which demonstrates that the newly designed setup is applicable for monitoring ultrafast reactions in the femtosecond domain.

Jahn-Teller Distortion and Dissociation of CCl4+ by Transient X-ray Spectroscopy Simultaneously at the Carbon K- and Chlorine L-Edge

X-ray Transient Absorption Spectroscopy (XTAS) and theoretical calculations are used to study CCl₄⁺ prepared by 800 nm strong-field ionization. XTAS simultaneously probes atoms at the carbon K-edge (280–300 eV) and chlorine L-edge (195–220 eV). Comparison of experiment to X-ray spectra computed by orbital-optimized density functional theory (OO-DFT) indicates that after ionization, CCl₄⁺ undergoes symmetry breaking driven by Jahn–Teller distortion away from the initial tetrahedral structure (T_d) in 6 ± 2 fs. The resultant symmetry-broken covalently bonded form subsequently separates to a noncovalently bound complex between CCl₃⁺ and Cl over 90 ± 10 fs, which is again predicted by theory. Finally, after more than 800 fs, L-edge signals for atomic Cl are observed, indicating dissociation to free CCl₃⁺ and Cl. The results for Jahn–Teller distortion to the symmetry-broken form of CCl₄⁺ and formation of the Cl–CCl⁺₃ complex characterize previously unobserved new species along the route to dissociation.

Dynamics of CCl₄⁺ prepared by 800 nm strong-field ionization, as studied with X-ray transient absorption spectroscopy (XTAS) and quantum chemical calculations.

Theoretical Calculation of Core-Excited States along Dissociative Pathways beyond Second-Order Perturbation Theory

We extend the multireference driven similarity renormalization (MR-DSRG) method to compute core-excited states by combining it with a GASSCF treatment of orbital relaxation and static electron correlation effects. We consider MR-DSRG treatments of dynamical correlation truncated at the level of perturbation theory (DSRG-MRPT2/3) and iterative linearized approximations with one- and two-body operators [MR-LDSRG(2)] in combination with a spin-free exact-two-component (X2C) one-electron treatment of scalar relativistic effects. This approach is calibrated and tested on a series of 16 core-excited states of five closed- and open-shell diatomic molecules containing first-row elements (C, N, and O). All GASSCF-MR-DSRG theories show excellent agreement with experimental adiabatic transitions energies, with mean absolute errors ranging between 0.17 and 0.35 eV, even for the challenging partially doubly excited states of the N₂⁺ molecule. The vibrational structure of all these transitions, obtained from using a full potential energy scan, shows a mean absolute error as low as 25 meV for DSRG-MRPT2 and 12/13 meV for DSRG-MRPT3 and MR-LDSRG(2). We generally find that a treatment of dynamical correlation that goes beyond the second-order level in perturbation theory improves the accuracy of the potential energy surface, especially in the bond-dissociation region.

On Electron Pair Rearrangements in Photochemical Reactions: 1,3-Cyclohexadiene Ring Opening

1,3-Cyclohexadiene ring opening has been studied within the bonding evolution theory (BET) framework. We have focused on describing for the first time the electron pair rearrangements leading to the cis-1,3,5-hexatriene (HT) product from CHD. The nature of bonding in this process begins with the weakening of the double bonds in the Franck-Condon region. Along the 1¹B surface, the C-C sigma bond weakens. Meanwhile, its density redistributes toward the whole CHD ring, mainly over double bonds. Breaking of this bond occurs on the 2¹A surface due to the symmetrical splitting of pair density from this region. This density redistributes toward the reaction center once the pericyclic minimum is reached. The formation of the double bonds that characterize HT occurs gradually in the ground state. However, near the 2¹A/1¹A intersection, these bonds are partially established.

Predictions of Pre-edge Features in Time-Resolved Near-Edge X-ray Absorption Fine Structure Spectroscopy from Hole-Hole Tamm-Dancoff-Approximated Density Functional Theory

Time-resolved near-edge X-ray absorption fine structure (TR-NEXAFS) spectroscopy is a powerful technique for studying photochemical reaction dynamics with femtosecond time resolution. In order to avoid ambiguity in TR-NEXAFS spectra from nonadiabatic dynamics simulations, core- and valence-excited states must be evaluated on equal footing and those valence states must also define the potential energy surfaces used in the nonadiabatic dynamics simulation. In this work, we demonstrate that hole-hole Tamm-Dancoff-approximated density functional theory (hh-TDA) is capable of directly simulating TR-NEXAFS spectroscopies. We apply hh-TDA to the excited-state dynamics of acrolein. We identify two pre-edge features in the oxygen K-edge TR-NEXAFS spectrum associated with the S₂ (ππ*) and S₁ (nπ*) excited states. We show that these features can be used to follow the internal conversion dynamics between the lowest three electronic states of acrolein. Due to the low, O(N²) apparent computational complexity of hh-TDA and our GPU-accelerated implementation, this method is promising for the simulation of pre-edge features in TR-NEXAFS spectra of large molecules and molecules in the condensed phase.

All-electron real-time and imaginary-time time-dependent density functional theory within a numeric atom-centered basis function framework

Real-time time-dependent density functional theory (RT-TDDFT) is an attractive tool to model quantum dynamics by real-time propagation without the linear response approximation. Sharing the same technical framework of RT-TDDFT, imaginary-time time-dependent density functional theory (it-TDDFT) is a recently developed robust-convergence ground state method. Presented here are high-precision all-electron RT-TDDFT and it-TDDFT implementations within a numerical atom-centered orbital (NAO) basis function framework in the FHI-aims code. We discuss the theoretical background and technical choices in our implementation. First, RT-TDDFT results are validated against linear-response TDDFT results. Specifically, we analyze the NAO basis sets' convergence for Thiel's test set of small molecules and confirm the importance of the augmentation basis functions for adequate convergence. Adopting a velocity-gauge formalism, we next demonstrate applications for systems with periodic boundary conditions. Taking advantage of the all-electron full-potential implementation, we present applications for core level spectra. For it-TDDFT, we confirm that within the all-electron NAO formalism, it-TDDFT can successfully converge systems that are difficult to converge in the standard self-consistent field method. We finally benchmark our implementation for systems up to ∼500 atoms. The implementation exhibits almost linear weak and strong scaling behavior.

Simulating electronic excitation and dynamics with real-time propagation approach to TDDFT within plane-wave pseudopotential formulation

We give a perspective on simulating electronic excitation and dynamics using the real-time propagation approach to time-dependent density functional theory (RT-TDDFT) in the plane-wave pseudopotential formulation. RT-TDDFT is implemented in various numerical formalisms in recent years, and its practical application often dictates the most appropriate implementation of the theory. We discuss recent developments and challenges, emphasizing numerical aspects of studying real systems. Several applications of RT-TDDFT simulation are discussed to highlight how the approach is used to study interesting electronic excitation and dynamics phenomena in recent years.

Minimizing the Time-Dependent Density Functional Error in Ehrenfest Dynamics

Simulating electron-ion dynamics using time-dependent density functional theory within an Ehrenfest dynamics scheme can be done in two ways that are in principle exact and identical: propagating time-dependent electronic Kohn-Sham equations or propagating electronic coefficients on surfaces obtained from linear-response. We show here that using an approximate functional leads to qualitatively different dynamics in the two approaches. We argue that the latter is more accurate because the functionals are evaluated on domains close to the ground state where currently used approximations perform better. We demonstrate this on an exactly solvable model of charge transfer and discuss implications for time-resolved spectroscopy.

Controlled ultrafast ππ*-πσ* dynamics in tryptophan-based peptides with tailored micro-environment

Ultrafast charge, energy and structural dynamics in molecules are driven by the topology of the multidimensional potential energy surfaces that determines the coordinated electronic and nuclear motion. These processes are also strongly influenced by the interaction with the molecular environment, making very challenging a general understanding of these dynamics on a microscopic level. Here we use electrospray and mass spectrometry technologies to produce isolated molecular ions with a controlled micro-environment. We measure ultrafast photo-induced ππ*-πσ* dynamics in tryptophan species in the presence of a single, charged adduct. A striking increase of the timescale by more than one order of magnitude is observed when changing the added adduct atom. A model is proposed to rationalize the results, based on the localized and delocalized effects of the adduct on the electronic structure of the molecule. These results offer perspectives to control ultrafast molecular processes by designing the micro-environment on the Angström length scale.

Solvent Effects in the Ultraviolet and X-ray Absorption Spectra of Pyridazine in Aqueous Solution

Electrostatic interaction of the solvent with the solute and fluctuations of the solvent configurations may make excitation energies of the solute different from those in the gas phase. These effects may dominate photoinduced or chemical reaction dynamics in solution systems and can be observed as shifts or broadening of peaks in absorption spectra. In this work, the nitrogen K-edge X-ray absorption spectra were measured for pyridazine in the gas phase and in aqueous solution. The ultraviolet and X-ray absorption spectra of pyridazine in aqueous solution, as well as those in the gas phase, were then calculated with models based on the algebraic-diagrammatic construction through second order [ADC(2)] with the resolution-of-identity (RI) approximation and compared with the spectra obtained in experiments. For aqueous solution, explicit local solvation structures were extracted from an ab initio molecular dynamics (AIMD) trajectory of pyridazine in bulk water, and RI-ADC(2) was combined with the conductor-like screening model (COSMO). The experimental absorption spectra of pyridazine in aqueous solution were reproduced with good accuracy by theoretical treatment of an ensemble containing the explicit local solvation structures of pyridazine with relevant water molecules combined with the COSMO solvation model of water for long-range solvation.

X-ray transient absorption reveals the 1Au (nπ*) state of pyrazine in electronic relaxation

Electronic relaxation in organic chromophores often proceeds via states not directly accessible by photoexcitation. We report on the photoinduced dynamics of pyrazine that involves such states, excited by a 267 nm laser and probed with X-ray transient absorption spectroscopy in a table-top setup. In addition to the previously characterized ¹B_2u (ππ*) (S₂) and ¹B_3u (nπ*) (S₁) states, the participation of the optically dark ¹A_u (nπ*) state is assigned by a combination of experimental X-ray core-to-valence spectroscopy, electronic structure calculations, nonadiabatic dynamics simulations, and X-ray spectral computations. Despite ¹A_u (nπ*) and ¹B_3u (nπ*) states having similar energies at relaxed geometry, their X-ray absorption spectra differ largely in transition energy and oscillator strength. The ¹A_u (nπ*) state is populated in 200 ± 50 femtoseconds after electronic excitation and plays a key role in the relaxation of pyrazine to the ground state.

Mapping wave packet bifurcation at a conical intersection in CH3I by attosecond XUV transient absorption spectroscopy

Extreme ultraviolet (XUV) transient absorption spectroscopy has emerged as a sensitive tool for mapping the real-time structural and electronic evolution of molecules. Here, attosecond XUV transient absorption is used to track dynamics in the A-band of methyl iodide (CH₃I). Gaseous CH₃I molecules are excited to the A-band by a UV pump (277 nm, ∼20 fs) and probed by attosecond XUV pulses targeting iodine I(4d) core-to-valence transitions. Owing to the excellent temporal resolution of the technique, passage through a conical intersection is mapped through spectral signatures of nonadiabatic wave packet bifurcation observed to occur at 15 ± 4 fs following UV photoexcitation. The observed XUV signatures and time dynamics are in agreement with previous simulations [H. Wang, M. Odelius, and D. Prendergast, J. Chem. Phys. 151, 124106 (2019)]. Due to the short duration of the UV pump pulse, coherent vibrational motion in the CH₃I ground state along the C-I stretch mode (538 ± 7 cm^-1) launched by resonant impulsive stimulated Raman scattering and dynamics in multiphoton excited states of CH₃I are also detected.

Time Resolved Photoelectron Spectroscopy as a Test of Electronic Structure and Nonadiabatic Dynamics

We compare different levels of theory for simulating excited state molecular dynamics and use time-resolved photoelectron spectroscopy measurements to benchmark the theory. We perform trajectory surface hopping simulations for uracil excited to the first bright state (ππ*) using three different levels of theory (CASSCF, MRCIS, and XMS-CASPT2) in order to understand the role of dynamical correlation in determining the excited state dynamics, with a focus on the coupling between different electronic states and internal conversion back to the ground state. These dynamics calculations are used to simulate the time-resolved photoelectron spectra. The comparison of the calculated and measured spectra allows us to draw conclusions regarding the relative insights and quantitative accuracy of the calculations at the three different levels of theory, demonstrating that detailed quantitative comparisons of time-resolved photoelectron spectra can be used to benchmark methodology.

Apparatus for generation of nanojoule-class water-window high-order harmonics

In our recent study [Fu et al., Commun. Phys. 3(1), 92 (2020)], we have developed an approach for energy-scaling of high-order harmonic generation in the water-window region under a neutral-medium condition. More specifically, we obtained a nanojoule-class water-window soft x-ray harmonic beam under a phase-matching condition. It has been achieved by combining a newly developed terawatt-class mid-infrared femtosecond laser and a loose-focusing geometry for high-order harmonic generation. The generated beam is more than 100 times intense compared to previously reported results. The experimental setup included two key parts: a terawatt mid-infrared femtosecond driving laser [Fu et al., Sci. Rep. 8(1), 7692 (2018)] and a specially designed gas cell. Despite the dramatic drop in the optimal gas pressure for phase-matching due to loose-focusing geometry, it still reached the 1 bar level for helium. Thus, we have designed a double-structured pulsed-gas cell with a differential pumping system, which enabled providing sufficiently high gas pressure. Moreover, it allowed reducing gas consumption significantly. A robust energy-scalable apparatus for high-order harmonic generation developed in this study will enable the generation of over ten-nanojoule water-window attosecond pulses in the near future.

Spiers Memorial Lecture: Introduction to ultrafast spectroscopy and imaging of photochemical reactions

A brief overview is presented on ultrafast spectroscopy and imaging of photochemical reactions by highlighting several experimental studies reported in the last five years. A particular focus is placed on new experiments performed using high-order harmonic generation, X-ray free electron lasers, and relativistic electron beams. Exploration of fundamental chemical reaction dynamics using these advanced experimental methodologies is in an early stage, and exciting new research opportunities await in this rapidly expanding and advancing research field. At the same time, there is no experimental methodology that provides all aspects of the electronic and structural dynamics in a single experiment, and investigations using different methodologies with various perspectives need to be considered in a comprehensive manner.

Transient resonant Auger-Meitner spectra of photoexcited thymine

We present the first investigation of excited state dynamics by resonant Auger-Meitner spectroscopy (also known as resonant Auger spectroscopy) using the nucleobase thymine as an example. Thymine is photoexcited in the UV and probed with X-ray photon energies at and below the oxygen K-edge. After initial photoexcitation to a ππ* excited state, thymine is known to undergo internal conversion to an nπ* excited state with a strong resonance at the oxygen K-edge, red-shifted from the ground state π* resonances of thymine (see our previous study Wolf, et al., Nat. Commun., 2017, 8, 29). We resolve and compare the Auger-Meitner electron spectra associated both with the excited state and ground state resonances, and distinguish participator and spectator decay contributions. Furthermore, we observe simultaneously with the decay of the nπ* state signatures the appearance of additional resonant Auger-Meitner contributions at photon energies between the nπ* state and the ground state resonances. We assign these contributions to population transfer from the nπ* state to a ππ* triplet state via intersystem crossing on the picosecond timescale based on simulations of the X-ray absorption spectra in the vibrationally hot triplet state. Moreover, we identify signatures from the initially excited ππ* singlet state which we have not observed in our previous study.

Ultrafast strong-field dissociation of vinyl bromide: An attosecond transient absorption spectroscopy and non-adiabatic molecular dynamics study

Attosecond extreme ultraviolet (XUV) and soft x-ray sources provide powerful new tools for studying ultrafast molecular dynamics with atomic, state, and charge specificity. In this report, we employ attosecond transient absorption spectroscopy (ATAS) to follow strong-field-initiated dynamics in vinyl bromide. Probing the Br M edge allows one to assess the competing processes in neutral and ionized molecular species. Using ab initio non-adiabatic molecular dynamics, we simulate the neutral and cationic dynamics resulting from the interaction of the molecule with the strong field. Based on the dynamics results, the corresponding time-dependent XUV transient absorption spectra are calculated by applying high-level multi-reference methods. The state-resolved analysis obtained through the simulated dynamics and related spectral contributions enables a detailed and quantitative comparison with the experimental data. The main outcome of the interaction with the strong field is unambiguously the population of the first three cationic states, D ₁, D ₂, and D ₃. The first two show exclusively vibrational dynamics while the D ₃ state is characterized by an ultrafast dissociation of the molecule via C-Br bond rupture within 100 fs in 50% of the analyzed trajectories. The combination of the three simulated ionic transient absorption spectra is in excellent agreement with the experimental results. This work establishes ATAS in combination with high-level multi-reference simulations as a spectroscopic technique capable of resolving coupled non-adiabatic electronic-nuclear dynamics in photoexcited molecules with sub-femtosecond resolution.

Ultrafast time-resolved x-ray absorption spectroscopy of ionized urea and its dimer through ab initio nonadiabatic dynamics

Investigating the early dynamics of chemical systems following ionization is essential for our understanding of radiation damage. However, experimental as well as theoretical investigations are very challenging due to the complex nature of these processes. Time-resolved x-ray absorption spectroscopy on a femtosecond timescale, in combination with appropriate simulations, is able to provide crucial insights into the ultrafast processes that occur upon ionization due to its element-specific probing nature. In this theoretical study, we investigate the ultrafast dynamics of valence-ionized states of urea and its dimer employing Tully's fewest switches surface hopping approach using Koopmans' theorem to describe the ionized system. We demonstrate that following valence ionization through a pump pulse, the time-resolved x-ray absorption spectra at the carbon, nitrogen, and oxygen K-edges reveal rich insights into the dynamics. Excited states of the ionized system give rise to time-delayed blueshifts in the x-ray absorption spectra as a result of electronic relaxation dynamics through nonadiabatic transitions. Moreover, our statistical analysis reveals specific structural dynamics in the molecule that induce time-dependent changes in the spectra. For the urea monomer, we elucidate the possibility to trace effects of specific molecular vibrations in the time-resolved x-ray absorption spectra. For the urea dimer, where ionization triggers a proton transfer reaction, we show how the x-ray absorption spectra can reveal specific details on the progress of proton transfer.

Highly efficient soft x-ray spectrometer for transient absorption spectroscopy with broadband table-top high harmonic sources

We present a novel soft x-ray spectrometer for ultrafast absorption spectroscopy utilizing table-top femtosecond high-order harmonic sources. Where most commercially available spectrometers rely on spherical variable line space gratings with a typical efficiency on the order of 3% in the first diffractive order, this spectrometer, based on a Hettrick-Underwood design, includes a reflective zone plate as a dispersive element. An improved efficiency of 12% at the N K-edge is achieved, accompanied by a resolving power of 890. The high performance of the soft x-ray spectrometer is further demonstrated by comparing nitrogen K-edge absorption spectra from calcium nitrate in aqueous solution obtained with our high-order harmonic source to previous measurements performed at the electron storage ring facility BESSY II.

Signatures of Conical Intersection Dynamics in the Time-Resolved Photoelectron Spectrum of Furan: Theoretical Modeling with an Ensemble Density Functional Theory Method

The non-adiabatic dynamics of furan excited in the ππ* state (S2 in the Franck-Condon geometry) was studied using non-adiabatic molecular dynamics simulations in connection with an ensemble density functional method. The time-resolved photoelectron spectra were theoretically simulated in a wide range of electron binding energies that covered the valence as well as the core electrons. The dynamics of the decay (rise) of the photoelectron signal were compared with the excited-state population dynamics. It was observed that the photoelectron signal decay parameters at certain electron binding energies displayed a good correlation with the events occurring during the excited-state dynamics. Thus, the time profile of the photoelectron intensity of the K-shell electrons of oxygen (decay constant of 34 ± 3 fs) showed a reasonable correlation with the time of passage through conical intersections with the ground state (47 ± 2 fs). The ground-state recovery constant of the photoelectron signal (121 ± 30 fs) was in good agreement with the theoretically obtained excited-state lifetime (93 ± 9 fs), as well as with the experimentally estimated recovery time constant (ca. 110 fs). Hence, it is proposed to complement the traditional TRPES observations with the trXPS (or trNEXAFS) measurements to obtain more reliable estimates of the most mechanistically important events during the excited-state dynamics.

XABOOM: An X-ray Absorption Benchmark of Organic Molecules Based on Carbon, Nitrogen, and Oxygen 1s → π* Transitions

The performance of several standard and popular approaches for calculating X-ray absorption spectra at the carbon, nitrogen, and oxygen K-edges of 40 primarily organic molecules up to the size of guanine has been evaluated, focusing on the low-energy and intense 1s → π* transitions. Using results obtained with CVS-ADC(2)-x and fc-CVS-EOM-CCSD as benchmark references, we investigate the performance of CC2, ADC(2), ADC(3/2), and commonly adopted density functional theory (DFT)-based approaches. Here, focus is on precision rather than on accuracy of transition energies and intensities-in other words, we target relative energies and intensities and the spread thereof, rather than absolute values. The use of exchange-correlation functionals tailored for time-dependent DFT calculations of core excitations leads to error spreads similar to those seen for more standard functionals, despite yielding superior absolute energies. Long-range corrected functionals are shown to perform particularly well compared to our reference data, showing error spreads in energy and intensity of 0.2-0.3 eV and ∼10%, respectively, as compared to 0.3-0.6 eV and ∼20% for a typical pure hybrid. In comparing intensities, state mixing can complicate matters, and techniques to avoid this issue are discussed. Furthermore, the influence of basis sets in high-level ab initio calculations is investigated, showing that reasonably accurate results are obtained with the use of 6-311++G**. We name this benchmark suite as XABOOM (X-ray absorption benchmark of organic molecules) and provide molecular structures and ground-state self-consistent field energies and spectroscopic data. We believe that it provides a good assessment of electronic structure theory methods for calculating X-ray absorption spectra and will become useful for future developments in this field.

Ultrafast excited state dynamics of provitamin D3 and analogs in solution and in lipid bilayers

The photochemical ring-opening reaction of 7-dehydrocholesterol (DHC, provitamin D₃) is responsible for the light-initiated formation of vitamin D₃ in mammalian skin membranes. Visible transient absorption spectroscopy was used to explore the excited state dynamics of DHC and two analogs: ergosterol (provitamin D₂) and DHC acetate free in solution and confined to lipid bilayers chosen to model the biological cell membrane. In solution, the excited state dynamics of the three compounds are nearly identical. However, when confined to lipid bilayers, the heterogeneity of the lipid membrane and packing forces imposed on the molecule by the lipid alter the excited state dynamics of these compounds. When confined to lipid bilayers in liposomes formed using DPPC, two solvation environments are identified. The excited state dynamics for DHC and analogs in fluid-like regions of the liposome membrane undergo internal conversion and ring-opening on 1 ps-2 ps time scales, similar to those observed in isotropic solution. In contrast, the excited state lifetime of a subpopulation in regions of lower fluidity is 7 ps-12 ps. The long decay component is unique to these liposomes and results from the structural properties of the lipid bilayer. Additional measurements in liposomes prepared with lipids having slightly longer or shorter alkane tails support this conclusion. In the lipid environments studied, the longest lifetimes are observed for DHC. The unsaturated sterol tail of ergosterol and the acetate group of DHC acetate disrupt the packing around the molecule and permit faster internal conversion and relaxation back to the ground state.

An assessment of different electronic structure approaches for modeling time-resolved x-ray absorption spectroscopy

We assess the performance of different protocols for simulating excited-state x-ray absorption spectra. We consider three different protocols based on equation-of-motion coupled-cluster singles and doubles, two of them combined with the maximum overlap method. The three protocols differ in the choice of a reference configuration used to compute target states. Maximum-overlap-method time-dependent density functional theory is also considered. The performance of the different approaches is illustrated using uracil, thymine, and acetylacetone as benchmark systems. The results provide guidance for selecting an electronic structure method for modeling time-resolved x-ray absorption spectroscopy.

Feshbach-Fano approach for calculation of Auger decay rates using equation-of-motion coupled-cluster wave functions. I. Theory and implementation

X-ray absorption creates electron vacancies in the core shell. These highly excited states often relax by Auger decay-an autoionization process in which one valence electron fills the core hole and another valence electron is ejected into the ionization continuum. Despite the important role of Auger processes in many experimental settings, their first-principles modeling is challenging, even for small systems. The difficulty stems from the need to describe many-electron continuum (unbound) states, which cannot be tackled with standard quantum-chemistry methods. We present a novel approach to calculate Auger decay rates by combining Feshbach-Fano resonance theory with the equation-of-motion coupled-cluster single double (EOM-CCSD) framework. We use the core-valence separation scheme to define projectors into the bound (square-integrable) and unbound (continuum) subspaces of the full function space. The continuum many-body decay states are represented by products of an appropriate EOM-CCSD state and a free-electron state, described by a continuum orbital. The Auger rates are expressed in terms of reduced quantities, two-body Dyson amplitudes (objects analogous to the two-particle transition density matrix), contracted with two-electron bound-continuum integrals. Here, we consider two approximate treatments of the free electron: a plane wave and a Coulomb wave with an effective charge, which allow us to evaluate all requisite integrals analytically; however, the theory can be extended to incorporate a more sophisticated description of the continuum orbital.

Dynamical transition orbitals: A particle-hole description in real-time TDDFT dynamics

We expand the concept of natural transition orbitals in the context of real-time time-dependent density functional theory (RT-TDDFT) and show its application in practical calculations. Kohn-Sham single-particle wavefunctions are propagated in RT-TDDFT simulation, and physical properties remain invariant under their unitary transformation. In this work, we exploit this gauge freedom and expand the concept of natural transition orbitals, which is widely used in linear-response TDDFT, for obtaining a particle-hole description in RT-TDDFT simulation. While linear-response TDDFT is widely used to study electronic excitation, RT-TDDFT can be employed more generally to simulate non-equilibrium electron dynamics. Studying electron dynamics in terms of dynamic transitions of particle-hole pairs is, however, not straightforward in the RT-TDDFT simulation. By constructing natural transition orbitals through projecting time-dependent Kohn-Sham wave functions onto occupied/unoccupied eigenstate subspaces, we show that linear combinations of a pair of the resulting hole/particle orbitals form a new gauge, which we refer to as dynamical transition orbitals. We demonstrate the utility of this framework to analyze RT-TDDFT simulations of optical excitation and electronic stopping dynamics in the particle-hole description.

Observing the Structural Evolution in the Photodissociation of Diiodomethane with Femtosecond Solution X-Ray Scattering

Resolving the structural dynamics of the initial steps of chemical reactions is challenging. We report the femtosecond time-resolved wide-angle x-ray scattering of the photodissociation of diiodomethane in cyclohexane. The data reveal with structural detail how the molecule dissociates into radicals, how the radicals collide with the solvent, and how they form the photoisomer. We extract how translational and rotational kinetic energy is dispersed into the solvent. We also find that 85% of the primary radical pairs are confined to their original solvent cage and discuss how this influences the downstream recombination reactions.

Transient Sub-nanosecond Soft X-ray NEXAFS Spectroscopy on Organic Thin Films

We demonstrate visible pump soft X-ray probe near-edge X-ray absorption fine structure (NEXAFS) spectroscopy measurements at the carbon K edge on thin molecular films in the laboratory. This opens new opportunities through the use of laboratory equipment for chemical speciation. We investigate the metal-free porphyrin derivative tetra(tert-butyl)porphyrazine as an ideal model system to elucidate electronic properties of tetrapyrroles like chlorophyll or heme. In contrast to measurements in gas or liquid state, the investigation of thin films is of high interest in the field of optoelectronic and photovoltaic devices though challenging due to the low damage thresholds of the samples upon excitation. With a careful pre-characterization using optical techniques, successful measurements were performed using a NEXAFS spectrometer based on a laser-produced plasma source and reflection zone plates with a resolving power of 1000 and a time resolution of 0.5 ns. In combination with density functional theory calculations, first insights into a long-lived excitonic state are gained and discussed.

Coulomb explosion imaging for gas-phase molecular structure determination: An ab initio trajectory simulation study

Coulomb explosion velocity-map imaging is a new and potentially universal probe for gas-phase chemical dynamics studies, capable of yielding direct information on (time-evolving) molecular structure. The approach relies on a detailed understanding of the mapping between the initial atomic positions within the molecular structure of interest and the final velocities of the fragments formed via Coulomb explosion. Comprehensive on-the-fly ab initio trajectory studies of the Coulomb explosion dynamics are presented for two prototypical small molecules, formyl chloride and cis-1,2-dichloroethene, in order to explore conditions under which reliable structural information can be extracted from fragment velocity-map images. It is shown that for low parent ion charge states, the mapping from initial atomic positions to final fragment velocities is complex and very sensitive to the parent ion charge state as well as many other experimental and simulation parameters. For high-charge states, however, the mapping is much more straightforward and dominated by Coulombic interactions (moderated, if appropriate, by the requirements of overall spin conservation). This study proposes minimum requirements for the high-charge regime, highlights the need to work in this regime in order to obtain robust structural information from fragment velocity-map images, and suggests how quantitative structural information may be extracted from experimental data.

Vibronic Dynamics of Photodissociating ICN from Simulations of Ultrafast X-Ray Absorption Spectroscopy

Ultrafast UV-pump/soft-X-ray-probe spectroscopy is a subject of great interest since it can provide detailed information about dynamical photochemical processes with ultrafast resolution and atomic specificity. Here, we focus on the photodissociation of ICN in the 1 Π1 excited state, with emphasis on the transient response in the soft-X-ray spectral region as described by the ab initio spectral lineshape averaged over the nuclear wavepacket probability density. We find that the carbon K-edge spectral region reveals a rich transient response that provides direct insights into the dynamics of frontier orbitals during the I-CN bond cleavage process. The simulated UV-pump/soft-X-ray-probe spectra exhibit detailed dynamical information, including a time-domain signature for coherent vibration associated with the photogenerated CN fragment.

Table-Top X-ray Spectroscopy of Benzene Radical Cation

Ultrafast table-top X-ray spectroscopy at the carbon K-edge is used to measure the X-ray spectral features of benzene radical cations (Bz⁺). The ground state of the cation is prepared selectively by two-photon ionization of neutral benzene, and the X-ray spectra are probed at early times after the ionization by transient absorption using X-rays produced by high harmonic generation (HHG). Bz⁺ is well-known to undergo Jahn-Teller distortion, leading to a lower symmetry and splitting of the π orbitals. Comparison of the X-ray absorption spectra of the neutral and the cation reveals a splitting of the two degenerate π* orbitals as well as an appearance of a new peak due to excitation to the partially occupied π-subshell. The π* orbital splitting of the cation, elucidated on the basis of high-level calculations in a companion theoretical paper [Vidal et al. J. Phys. Chem. A. http://dx.doi.org/10.1021/acs.jpca.0c08732], is discovered to be due to both the symmetry distortion and even more dominant spin coupling of the unpaired electron in the partially vacant π orbital (from ionization) with the unpaired electrons resulting from the transition from the 1s_C core orbital to the fully vacant π* orbitals.

Interplay of Open-Shell Spin-Coupling and Jahn-Teller Distortion in Benzene Radical Cation Probed by X-ray Spectroscopy

We report a theoretical investigation and elucidation of the X-ray absorption spectra of neutral benzene and of the benzene cation. The generation of the cation by multiphoton ultraviolet (UV) ionization and the measurement of the carbon K-edge spectra of both species using a table-top high-harmonic generation source are described in the companion experimental paper [Epshtein, M.; et al. J. Phys. Chem. A http://dx.doi.org/10.1021/acs.jpca.0c08736]. We show that the 1s_C → π transition serves as a sensitive signature of the transient cation formation, as it occurs outside of the spectral window of the parent neutral species. Moreover, the presence of the unpaired (spectator) electron in the π-subshell of the cation and the high symmetry of the system result in significant differences relative to neutral benzene in the spectral features associated with the 1s_C → π* transitions. High-level calculations using equation-of-motion coupled-cluster theory provide the interpretation of the experimental spectra and insight into the electronic structure of benzene and its cation. The prominent split structure of the 1s_C → π* band of the cation is attributed to the interplay between the coupling of the core → π* excitation with the unpaired electron in the π-subshell and the Jahn-Teller distortion. The calculations attribute most of the splitting (∼1-1.2 eV) to the spin coupling, which is visible already at the Franck-Condon structure, and we estimate the additional splitting due to structural relaxation to be around ∼0.1-0.2 eV. These results suggest that X-ray absorption with increased resolution might be able to disentangle electronic and structural aspects of the Jahn-Teller effect in the benzene cation.