Ultrafast X-ray Transient Absorption Spectroscopy of Gas-Phase Photochemical Reactions: A New Universal Probe of Photoinduced Molecular Dynamics

Femtosecond Extreme Ultraviolet Absorption Spectroscopy of Transition Metal Complexes

In this review, we survey the use of extreme ultraviolet absorption spectroscopy to measure electronic and vibrational dynamics in transition metal complexes. Photons in this 30-100 eV energy range probe 3p → 3d transitions for 3d metals and 4f, 5p → 5d transitions in 5d metals, and the resulting spectra are sensitive to the spin state, oxidation state, and ligand field of the metal. Furthermore, the energy of the core level depends on the metal, providing elemental specificity. Use of tabletop high-harmonic sources allows these spectra to be measured with femtosecond to attosecond time resolution in a standard laser laboratory, revealing short-lived states in chromophores and photocatalysts that were unresolved using other techniques.

Ultrafast Spectroscopy and Dynamics of Photoredox Catalysis

Photoredox catalysis has emerged as a powerful platform for chemical synthesis, utilizing chromophore excited states as selective energy stores to surmount chemical activation barriers toward making desirable products. Developments in this field have pushed synthetic chemists to design and discover new photocatalysts with novel and impactful photoreactivity but also with uncharacterized excited states and only an approximate mechanistic understanding. This review highlights specific instances in which ultrafast spectroscopies dissected the photophysical and photochemical dynamics of new classes of photoredox catalysts and their photochemical reactions. After briefly introducing the photophysical processes and ultrafast spectroscopic methods central to this topic, the review describes selected recent examples that evoke distinct classes of photoredox catalysts with demonstrated synthetic utility and ultrafast spectroscopic characterization. This review cements the significant role of ultrafast spectroscopy in modern photocatalyzed organic transformations and institutionalizes the developing intersection of synthetic organic chemistry and physical chemistry.

Coupled Nuclear and Electron Dynamics in Chlorophyll Unraveled by XMS-CASPT2 X-ray Absorption Spectra

Attosecond spectroscopy, especially time-resolved X-ray absorption spectra (XAS), enables direct observation of ultrafast molecular dynamics. The complementary and even preceding development of theoretical simulations can offer the necessary guidance and stimulate new experiments. In this work, we simulated high-level XAS for the magnesium and nitrogen K-edge of chlorophyll a. In our previous work on the ultrafast relaxation process in the Q-band, our quantum dynamics simulations found the Qx and Qy states to be energetically close and therefore strongly coupled. Here, we analyze the strong coupling between Qx and Qy via XAS, indicating promising possibilities for experimental observation. The excited-state energies, potential energy surfaces, and XAS are computed at the XMS-CASPT2 level of theory to capture the complex multireference character of chlorophyll excitations. In our simulated spectra, we could follow the ultrafast population transfer between Qx and Qy and thus draw conclusions about the strong vibrational coupling between them.

Exploring the Influence of Approximations for Simulating Valence Excited X-ray Spectra

First-principles simulations of excited-state X-ray spectra are becoming increasingly important to interpret the wealth of electronic and geometric information contained within femtosecond X-ray absorption spectra recorded at X-ray Free Electron Lasers (X-FELs). However, because the transition dipole matrix elements must be calculated between two excited states (i.e., the valence excited state and the final core excited state arising from the initial valence excited state) of very different energies, this can be challenging and time-consuming to compute. Herein using two molecules, protonated formaldimine and cyclobutanone, we assess the ability of n-electron valence-state perturbation theory (NEVPT2), equation-of-motion coupled-cluster theory (EOM-CCSD), linear-response time-dependent density functional theory (LR-TDDFT) and the maximum overlap method (MOM) to describe excited state X-ray spectra. Our study focuses in particular on the behavior of these methods away from the Franck-Condon geometry and in the vicinity of important topological features of excited-state potential energy surfaces, namely, conical intersections. We demonstrate that the primary feature of excited-state X-ray spectra is associated with the core electron filling the hole created by the initial valence excitation, a process that all of the methods can capture. Higher energy states are generally weaker, but importantly much more sensitive to the nature of the reference electronic wave function. As molecular structures evolve away from the Franck-Condon geometry, changes in the spectral shape closely follow the underlying valence excitation, highlighting the importance of accurately describing the initial valence excitation to simulate the excited-state X-ray absorption spectra.

Elucidating Anomalous Intensity Ratios in Chlorine L-Edge X-ray Absorption Spectroscopy: Multiplet Effects and Core Rydberg Transitions

A relativistic core-valence-separated equation-of-motion coupled cluster (CVS-EOM-CC) study of chlorine L2,3-edge X-ray absorption near-edge structure (XANES) spectra using CH3Cl and CH2ICl as representative molecules is reported. The nearly identical intensity for the main features in the L2- and L3-edge XANES spectra is attributed to multiplet effects and the overlap between core-valence and core Rydberg transitions. The multiplet effects originating from the interaction between the core hole and the C-Cl σ* orbitals account for around half of the deviation of the L3 and L2 intensity ratio from the 2:1 ratio of the numbers of 2p3/2 and 2p1/2 electrons. The 2p3/2 → 4s core Rydberg transitions are shown to overlap with the 2p1/2 → σ* transitions and contribute to the other half of the intensity anomaly. We demonstrate that triple excitations in CVS-EOM-CC calculations play important roles in accurate simulation of the overlap between the 2p1/2 → σ* and 2p3/2 → 4s transitions.

Measurement of coherent vibrational dynamics with X-ray Transient Absorption Spectroscopy simultaneously at the Carbon K- and Chlorine L2,3- edges

X-ray Transient Absorption Spectroscopy (XTAS) is a powerful probe for ultrafast molecular dynamics. The evolution of XTAS signal is controlled by the shapes of potential energy surfaces of the associated core-excited states, which are difficult to directly measure. Here, we study the vibrational dynamics of Raman activated CCl4 with XTAS targeting the C 1s and Cl 2p electrons. The totally symmetric stretching mode leads to concerted elongation or contraction in bond lengths, which in turn induce an experimentally measurable red or blue shift in the X-ray absorption energies associated with inner-shell electron excitations to the valence antibonding levels. The ratios between slopes of different core-excited potential energy surfaces (CEPESs) thereby extracted agree very well with Restricted Open-Shell Kohn-Sham calculations. The other, asymmetric, modes do not measurably contribute to the XTAS signal. The results highlight the ability of XTAS to reveal coherent nuclear dynamics involving  < 0.01 Å atomic displacements and also provide direct measurement of forces on CEPESs.

Real-time observation of a metal complex-driven reaction intermediate using a porous protein crystal and serial femtosecond crystallography

Determining short-lived intermediate structures in chemical reactions is challenging. Although ultrafast spectroscopic methods can detect the formation of transient intermediates, real-space structures cannot be determined directly from such studies. Time-resolved serial femtosecond crystallography (TR-SFX) has recently proven to be a powerful method for capturing molecular changes in proteins on femtosecond timescales. However, the methodology has been mostly applied to natural proteins/enzymes and limited to reactions promoted by synthetic molecules due to structure determination challenges. This work demonstrates the applicability of TR-SFX for investigations of chemical reaction mechanisms of synthetic metal complexes. We fix a light-induced CO-releasing Mn(CO)3 reaction center in porous hen egg white lysozyme (HEWL) microcrystals. By controlling light exposure and time, we capture the real-time formation of Mn-carbonyl intermediates during the CO release reaction. The asymmetric protein environment is found to influence the order of CO release. The experimentally-observed reaction path agrees with quantum mechanical calculations. Therefore, our demonstration offers a new approach to visualize atomic-level reactions of small molecules using TR-SFX with real-space structure determination. This advance holds the potential to facilitate design of artificial metalloenzymes with precise mechanisms, empowering design, control and development of innovative reactions.

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.

Reinvented: An Attosecond Chemist

Attosecond science requires a substantial rethinking of how to make measurements on very short timescales; how to acquire the necessary equipment, technology, and personnel; and how to build a set of laboratories for such experiments. This entails a rejuvenation of the author in many respects, in the laboratory itself, with regard to students and postdocs, and in generating funding for research. It also brings up questions of what it means to do attosecond science, and the discovery of the power of X-ray spectroscopy itself, which complements the short timescales addressed. The lessons learned, expressed in the meanderings of this autobiographical article, may be of benefit to others who try to reinvent themselves.

Spin Coupling Effect on Geometry-Dependent X-Ray Absorption of Diradicals

We theoretically investigate the influence of diradical electron spin coupling on the time-resolved X-ray absorption spectra of the photochemical ring opening of furanone. We predict geometry-dependent carbon K-edge signals involving transitions from core orbitals to both singly and unoccupied molecular orbitals. The most obvious features of the ring opening come from the carbon atom directly involved in the bond breaking through its transition to both the newly formed singly occupied and the available lowest unoccupied molecular orbitals (SOMO and LUMO, respectively). In addition to this primary feature, the singlet spin coupling of four unpaired electrons that arises in the core-to-LUMO states creates additional geometry dependence in some spectral features with both oscillator strengths and relative excitation energies varying observably as a function of the ring opening. We attribute this behavior to a spin-occupancy-induced selection rule, which occurs when singlet spin coupling is enforced in the diradical state. Notably, one of these geometry-sensitive core-to-LUMO transitions excites core electrons from a backbone carbon not involved in the bond breaking, providing a novel nonlocal X-ray probe of chemical dynamics arising from electron spin coupling.

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.

Following the Nonadiabatic Ultrafast Dynamics of Uracil via Simulated X-ray Absorption Spectra

The nucleobase uracil exhibits high photostability due to ultrafast relaxation processes mediated by conical intersections (CoIns), where the interplay between nuclear and electron dynamics becomes crucial. In our previous study, we observed seemingly long-lived traces of electronic coherence for the relaxation process through the S2/S1 CoIn by applying our ansatz for coupled nuclear and electron dynamics in molecules (NEMol). In this work, we theoretically investigate how time-dependent transient X-ray absorption spectroscopy can be used to observe this ultrafast dynamics. Therefore, we calculated X-ray absorption spectra (XAS) for the oxygen K-edge, using a multireference protocol in combination with NEMol dynamics. Thus, we have access to both the transient XAS based on the nuclear wavepacket dynamics and the modulation of the signals caused by the electronic coherence induced by the excitation process and the presence of a CoIn seam. In both cases, we were able to qualitatively predict its influence on the resulting XAS.

Tuning UV Pump X-ray Probe Spectroscopy on the Nitrogen K Edge Reveals the Radiationless Relaxation of Pyrazine: Ab Initio Simulations Using the Quasiclassical Doorway-Window Approximation

Transient absorption UV pump X-ray probe spectroscopy has been established as a versatile technique for the exploration of ultrafast photoinduced dynamics in valence-excited states. In this work, an ab initio theoretical framework for the simulation of time-resolved UV pump X-ray probe spectra is presented. The method is based on the description of the radiation-matter interaction in the classical doorway-window approximation and a surface-hopping algorithm for the nonadiabatic nuclear excited-state dynamics. Using the second-order algebraic-diagrammatic construction scheme for excited states, UV pump X-ray probe signals were simulated for the carbon and nitrogen K edges of pyrazine, assuming a duration of 5 fs of the UV pump and X-ray probe pulses. It is predicted that spectra measured at the nitrogen K edge carry much richer information about the ultrafast nonadiabatic dynamics in the valence-excited states of pyrazine than those measured at the carbon K edge.

Theoretical Description of Attosecond X-ray Absorption Spectroscopy of Frenkel Exciton Dynamics

Frenkel excitons are responsible for the transport of light energy in many molecular systems. Coherent electron dynamics govern the initial stage of Frenkel-exciton transfer. Capability to follow coherent exciton dynamics in real time will help to reveal their actual contribution to the efficiency of light-harvesting. Attosecond X-ray pulses are the tool with the necessary temporal resolution to resolve pure electronic processes with atomic sensitivity. We describe how attosecond X-ray pulses can probe coherent electronic processes during Frenkel-exciton transport in molecular aggregates. We analyze time-resolved absorption cross section taking broad spectral bandwidth of an attosecond pulse into account. We demonstrate that attosecond X-ray absorption spectra can reveal delocalization degree of coherent exciton transfer dynamics.

A study of core-excited states of organic molecules computed with the generalized active space driven similarity renormalization group

This work examines the accuracy and precision of x-ray absorption spectra computed with a multireference approach that combines generalized active space (GAS) references with the driven similarity renormalization group (DSRG). We employ the x-ray absorption benchmark of organic molecule (XABOOM) set, consisting of 116 transitions from mostly organic molecules [Fransson et al., J. Chem. Theory Comput. 17, 1618 (2021)]. Several approximations to a full-valence active space are examined and benchmarked. Absolute excitation energies and intensities computed with the GAS-DSRG truncated to second-order in perturbation theory are found to systematically underestimate experimental and reference theoretical values. Third-order perturbative corrections significantly improve the accuracy of GAS-DSRG absolute excitation energies, bringing the mean absolute deviation from experimental values down to 0.32 eV. The ozone molecule and glyoxylic acid are particularly challenging for second-order perturbation theory and are examined in detail to assess the importance of active space truncation and intruder states.

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

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

Accurate Relativistic Real-Time Time-Dependent Density Functional Theory for Valence and Core Attosecond Transient Absorption Spectroscopy

First principles theoretical modeling of out-of-equilibrium processes observed in attosecond pump-probe transient absorption spectroscopy (TAS) triggering pure electron dynamics remains a challenging task, especially for heavy elements and/or core excitations containing fingerprints of scalar and spin-orbit relativistic effects. To address this, we formulate a methodology for simulating TAS within the relativistic real-time, time-dependent density functional theory (RT-TDDFT) framework, for both the valence and core energy regimes. Especially for TAS, full four-component (4c) RT simulations are feasible but computationally demanding. Therefore, in addition to the 4c approach, we also introduce the atomic mean-field exact two-component (amfX2C) Hamiltonian accounting for one- and two-electron picture-change corrections within RT-TDDFT. amfX2C preserves the accuracy of the parent 4c method at a fraction of its computational cost. Finally, we apply the methodology to study valence and near-L_2,3-edge TAS processes of experimentally relevant systems and provide additional physical insights using relativistic nonequilibrium response theory.

Signatures of the Bromine Atom and Open-Shell Spin Coupling in the X-ray Spectrum of the Bromobenzene Cation

Tabletop X-ray spectroscopy measurements at the carbon K-edge complemented by ab initio calculations are used to investigate the influence of the bromine atom on the carbon core-valence transitions in the bromobenzene cation (BrBz⁺). The electronic ground state of the cation is prepared by resonance-enhanced two-photon ionization of neutral bromobenzene (BrBz) and probed by X-rays produced by high-harmonic generation (HHG). Replacing one of the hydrogen atoms in benzene with a bromine atom shifts the transition from the 1s_C* orbital of the carbon atom (C*) bonded to bromine by ∼1 eV to higher energy in the X-ray spectrum compared to the other carbon atoms (C). Moreover, in BrBz⁺, the X-ray spectrum is dominated by two relatively intense transitions, 1s_C→π* and 1s_C*→σ*(C*-Br), where the second transition is enhanced relative to the neutral BrBz. In addition, a doublet peak shape for these two transitions is observed in the experiment. The 1s_C→π* doublet peak shape arises due to the spin coupling of the unpaired electron in the partially vacant π orbital (from ionization) with the two other unpaired electrons resulting from the transition from the 1s_C core orbital to the fully vacant π* orbitals. The 1s_C*→σ* doublet peak shape results from several transitions involving σ* and vibrational C*-Br mode activations following the UV ionization, which demonstrates the impact of the C*-Br bond length on the core-valence transition as well as on the relaxation geometry of BrBz⁺.

HHG at the Carbon K-Edge Directly Driven by SRS Red-Shifted Pulses from an Ytterbium Amplifier

In this work, we introduce a simplified approach to efficiently extend the high harmonic generation (HHG) cutoff in gases without the need for laser frequency conversion via parametric processes. Instead, we employ postcompression and red-shifting of a Yb:CaF2 laser via stimulated Raman scattering (SRS) in a nitrogen-filled stretched hollow core fiber. This driving scheme circumvents the low-efficiency window of parametric amplifiers in the 1100-1300 nm range. We demonstrate this approach being suitable for upscaling the power of a driver with an optimal wavelength for HHG in the highly desirable XUV range between 200 and 300 eV, up to the carbon K-edge. Due to the combination of power scalability of a low quantum defect ytterbium-based laser system with the high conversion efficiency of the SRS technique, we expect a significant increase in the generated photon flux in comparison with established platforms for HHG in the water window. We also compare HHG driven by the SRS scheme with the conventional self-phase modulation (SPM) scheme.

From a one-mode to a multi-mode understanding of conical intersection mediated ultrafast organic photochemical reactions

This review discusses how ultrafast organic photochemical reactions are controlled by conical intersections, highlighting that decay to the ground-state at multiple points of the intersection space results in their multi-mode character.

Time-resolved X-ray and XUV based spectroscopic methods for nonadiabatic processes in photochemistry

The photochemistry of numerous molecular systems is influenced by conical intersections (CIs). These omnipresent nonadiabatic phenomena provide ultra-fast radiationless relaxation channels by creating degeneracies between electronic states and decide over the final photoproducts. In their presence, the Born-Oppenheimer approximation breaks down, and the timescales of the electron and nuclear dynamics become comparable. Due to the ultra-fast dynamics and the complex interplay between nuclear and electronic degrees of freedom, the direct experimental observation of nonadiabatic processes close to CIs remains challenging. In this article, we give a theoretical perspective on novel spectroscopic techniques capable of observing clear signatures of CIs. We discuss methods that are based on ultra-short laser pulses in the extreme ultraviolet and X-ray regime, as their spectral and temporal resolution allow for resolving the ultra-fast dynamics near CIs.

Generation of Sub-nanosecond H Atom Pulses for Scattering from Single-Crystal Epitaxial Graphene

Pulsed molecular beams allow high-density gas samples to be cooled to low internal temperatures and to produce narrow speed distributions. They are particularly useful in combination with pulsed-laser-based detection schemes and have also been used as pump pulses in pump–probe experiments with neutral matter. The mechanical response of pulsed valves and chopper wheels limits the duration of these pulses typically to about 10–100 μs. Bunch compression photolysis has been proposed as a means to produce atomic pulses shorter than 1 ns—an experimental capability that would allow new measurements to be made on chemical systems. This technique employs a spatially chirped femtosecond duration photolysis pulse that produced an ensemble of H atom photoproducts that rebunches into a short pulse downstream. To date, this technique could not produce strong enough beams to allow new experiments to be carried out. In this paper, we report production of pulsed H atom beams consistent with a 700 ps pulse duration and with sufficient intensity to carry out differentially resolved inelastic H scattering experiments from a graphene surface. We observe surprisingly narrow angular distributions for H atoms incident normal to the surface. At low incidence energies quasi-elastic scattering dominates, and at high incidence energy we observe a strongly inelastic scattering channel. These results provide the basis for future experiments where the H atoms synchronously collide with a pulsed-laser-excited surface.

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 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.

Substituent Effect in the Cation Radicals of Monosubstituted Benzenes

In 30 monosubstituted benzene cation radicals, studied at the ωB97XD/aug-cc-pVTZ level, the phenyl rings usually adopt a compressed form, but a differently compressed form-equivalent to an elongated one-may coexist. The computational and literature ionization potentials are well correlated. The geometrical and magnetic aromaticity, estimated using HOMA and NICS indices, show the systems to be structurally aromatic but magnetically antiaromatic or only weakly aromatic. The partial charge is split between the substituent and ring and varies the most at C(ipso). In the ring, the spin is 70%, concentrated equally at the C(ipso) and C(p) atoms. The sEDA(D) and pEDA(D) descriptors of the substituent effect in cation radicals, respectively, were determined. In cation radicals, the substituent effect on the σ-electron system is like that in the ground state. The effect on the π-electron systems is long-range, and its propagation in the radical quinone-like ring is unlike that in the neutral molecules. The pEDA(D) descriptor correlates well with the partial spin at C(ipso) and C(p) and weakly with the HOMA(D) index. The correlation of the spin at the ring π-electron system and the pEDA(D) descriptor shows that the electron charge supplied to the ring π-electron system and the spin flow oppositely.

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.

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.

Improved insights in time-resolved photoelectron imaging

We review new light source developments and data analysis considerations relevant to the time-resolved photoelectron imaging technique. Case studies illustrate how these themes may enhance understanding in studies of excited state molecular dynamics.

Surface chemistry of quantum-sized metal nanoparticles under light illumination

Size reduction of metal nanoparticles increases the exposure of metal surfaces significantly, favoring heterogeneous chemistry at the surface of the nanoparticles. The optical properties of metal nanoparticles, such as light absorption, also exhibit a strong dependence on their size. It is expected that there will be strong coupling of light absorption and surface chemistry when the metal nanoparticles are small enough. For instance, metal nanoparticles with sizes in the range of 2–10 nm exhibit both surface plasmon resonances, which can efficiently produce high-energy hot electrons near the surface of the nanoparticles under light illumination, and the Coulomb blockade effect, which favors electron transfer from the metal nanoparticles to the surface adsorbates. The synergy of efficient hot electron generation and electron transfer on the surface of small metal nanoparticles leads to double-faced effects: (i) surface (adsorption) chemistry influences optical absorption in the metal nanoparticles, and (ii) optical absorption in the metal nanoparticles promotes (or inhibits) surface adsorption and heterogeneous chemistry. This review article focuses on the discussion of typical quantum phenomena in metal nanoparticles of 2–10 nm in size, which are referred to as “quantum-sized metal nanoparticles”. Both theoretical and experimental examples and results are summarized to highlight the strong correlations between the optical absorption and surface chemistry for quantum-sized metal nanoparticles of various compositions. A comprehensive understanding of these correlations may shed light on achieving high-efficiency photocatalysis and photonics.

Size reduction of metal nanoparticles increases the exposure of metal surfaces significantly, favoring heterogeneous photochemistry at the surface of the nanoparticles.

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.

Compact Ho:YLF-pumped ZnGeP2-based optical parametric amplifiers tunable in the molecular fingerprint regime

We report on a compact mid-infrared laser architecture, comprising a chain of $ {\rm ZnGeP}_2 $ZnGeP₂-based optical parametric amplifiers (OPAs), which afford a higher energy yield ($ \mathbin{\lower.3ex\hbox{$\buildrel \lt \over{\smash{\scriptstyle\sim}\vphantom{_x}}$}} 60\;\unicode{x00B5} {\rm J} $∼_x<60µJ at 1 kHz) compared to most conventional OPA gain media transparent in the 2-8-µm wavelength range. Specifically, our OPA scheme allows ready tunability in the molecular fingerprint regime and is tailored for strong-field excitation and coherent control of both stretch and bend (or torsional) vibrational modes in molecules. The OPAs are pumped and directly seeded (via supercontinuum generation) by a 2-µm, 3-ps Ho:YLF regenerative amplifier. The compressibility of the OPA output is demonstrated by a representative measurement of the near-Gaussian temporal profile of a dispersion-compensated 105-fs idler pulse at a central wavelength of 5.1 µm, corresponding to ${\sim}6 $∼6 optical cycles. Detailed numerical simulations closely corroborate the experimental measurements, providing a benchmark and a platform to further explore the parameter space for future design, optimization, and implementation of high-energy, ultrafast, mid-infrared laser schemes.

Probing competing relaxation pathways in malonaldehyde with transient X-ray absorption spectroscopy

Excited-state intramolecular hydrogen transfer (ESIHT) is a fundamental reaction relevant to chemistry and biology. Malonaldehyde is the simplest example of ESIHT, yet only little is known experimentally about its excited-state dynamics. Several competing relaxation pathways have been proposed, including internal conversion mediated by ESIHT and C[double bond, length as m-dash]C torsional motion as well as intersystem crossing. We perform an in silico transient X-ray absorption spectroscopy (TRXAS) experiment at the oxygen K-edge to investigate its potential to monitor the proposed ultrafast decay pathways in malonaldehyde upon photoexcitation to its bright S₂(ππ*) state. We employ both restricted active space perturbation theory and algebraic-diagrammatic construction for the polarization propagator along interpolated reaction coordinates as well as representative trajectories from ab initio multiple spawning simulations to compute the TRXAS signals from the lowest valence states. Our study suggests that oxygen K-edge TRXAS can distinctly fingerprint the passage through the H-transfer intersection and the concomitant population transfer to the S₁(nπ*) state. Potential intersystem crossing to T₁(ππ*) is detectable from reappearance of the double pre-edge signature and reversed intensities. Moreover, the torsional deactivation pathway induces transient charge redistribution from the enol side towards the central C-atom and manifests itself as substantial shifts of the pre-edge features. Given the continuous advances in X-ray light sources, our study proposes an experimental route to disentangle ultrafast excited-state decay channels in this prototypical ESIHT system and provides a pathway-specific mapping of the TRXAS signal to facilitate the interpretation of future experiments.

Highly Accurate Prediction of Core Spectra of Molecules at Density Functional Theory Cost: Attaining Sub-electronvolt Error from a Restricted Open-Shell Kohn-Sham Approach

We present the use of the recently developed square gradient minimization (SGM) algorithm for excited-state orbital optimization to obtain spin-pure restricted open-shell Kohn-Sham (ROKS) energies for core excited states of molecules. The SGM algorithm is robust against variational collapse and offers a reliable route to converging orbitals for target excited states at only 2-3 times the cost of ground-state orbital optimization (per iteration). ROKS/SGM with the modern SCAN/ωB97X-V functionals is found to predict the K-edge of C, N, O, and F to a root mean squared error of ∼0.3 eV. ROKS/SGM is equally effective at predicting L-edge spectra of third period elements, provided a perturbative spin-orbit correction is employed. This high accuracy can be contrasted with traditional time-dependent density functional theory (TDDFT), which typically has greater than 10 eV error and requires translation of computed spectra to align with experiment. ROKS is computationally affordable (having the same scaling as ground-state DFT and a slightly larger prefactor) and can be applied to geometry optimizations/ab initio molecular dynamics of core excited states, as well as condensed phase simulations. ROKS can also model doubly excited/ionized states with one broken electron pair, which are beyond the ability of linear response based methods.

Short-wavelength probes in time-resolved photoelectron spectroscopy: an extended view of the excited state dynamics in acetylacetone

Time-resolved photoelectron spectroscopy using a vacuum ultraviolet probe brings new insight to the excited state dynamics operating in acetylacetone.

Ultrafast dissociative ionization and large-amplitude vibrational wave packet dynamics of strong-field-ionized di-iodomethane

We employ few-cycle pulses to strong-field-ionize di-iodomethane (CH₂I₂) and femtosecond extreme ultraviolet (XUV) transient absorption spectroscopy to investigate the subsequent ultrafast dissociative ionization and vibrational wave packet dynamics. Probing in the spectral region of the I 4d core-level transitions, the time-resolved XUV differential absorption spectra reveal the population of several electronic states of CH₂I₂ ⁺ by strong-field ionization. Global analysis reveals three distinct time scales for the observed dynamics: 20 ± 2 fs, 49 ± 6 fs, and 157 ± 9 fs, ascribed to relaxation of the CH₂I₂ ⁺ parent ion from the Franck-Condon region, dissociation of high-lying excited states of CH₂I₂ ⁺ to I⁺ (³P₂), CH₂I, and I₂ ⁺ (²Π_3/2,g), and dissociation of CH₂I₂ ⁺ to I (²P_3/2) and CH₂I⁺, respectively. Oscillatory features in the time-resolved XUV differential absorption spectra point to the generation of vibrational wave packets in both the residual CH₂I₂ and the CH₂I₂ ⁺ parent ion. Analysis of the oscillation frequencies and phases reveals, in the case of neutral CH₂I₂, C-I symmetric stretching induced by bond softening and I-C-I bending driven by a combination of bond softening and R-selective depletion. In the case of CH₂I₂ ⁺, both the fundamental and first overtone frequencies of the I-C-I bending mode are observed, indicating large-amplitude I-C-I bending motion, in good agreement with results obtained from ab initio simulations of the XUV transition energy along the I-C-I bend coordinate. These results show that femtosecond XUV absorption spectroscopy is well-suited for studying ultrafast photodissociation and vibrational wave packet dynamics.

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

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

A combined multi-reference pump-probe simulation method with application to XUV signatures of ultrafast methyl iodide photodissociation

UV pump-XUV/X-ray probe measurements have been successfully applied in the study of photo-induced chemical reactions. Although rich element-specific electronic structure information is accessible within XUV/X-ray (inner-shell) absorption spectra, it can be difficult to interpret the chemistry directly from the spectrum without supporting theoretical simulations. A multireference method to completely simulate UV pump-XUV/X-ray probe measurement has been developed and applied to study the methyl iodide photodissociation process. Multireference, fewest-switches surface hopping (FSSH) trajectories were used to explore the coupled electronic and ionic dynamics upon photoexcitation of methyl iodide. Interpretation of previous measurements is provided by associated multireference, restricted active space, inner-shell spectral simulations. This combination of multireference FSSH trajectories and XUV spectra provides an interpretation of transient features appearing in previous measurements within the first 100 fs after photoexcitation and validates the significant branching ratio in the final excited-state population. This methodology should prove useful for interpretation of the increasing number of inner-shell probe studies of molecular excited states or for directing new experiments toward interesting regions of the potential energy landscape.

Recent Advances in Ultrafast Structural Techniques

A review that summarizes the most recent technological developments in the field of ultrafast structural dynamics with focus on the use of ultrashort X-ray and electron pulses follows. Atomistic views of chemical processes and phase transformations have long been the exclusive domain of computer simulators. The advent of femtosecond (fs) hard X-ray and fs-electron diffraction techniques made it possible to bring such a level of scrutiny to the experimental area. The following review article provides a summary of the main ultrafast techniques that enabled the generation of atomically resolved movies utilizing ultrashort X-ray and electron pulses. Recent advances are discussed with emphasis on synchrotron-based methods, tabletop fs-X-ray plasma sources, ultrabright fs-electron diffractometers, and timing techniques developed to further improve the temporal resolution and fully exploit the use of intense and ultrashort X-ray free electron laser (XFEL) pulses.