Capturing Ultrafast Quantum Dynamics with Femtosecond and Attosecond X-ray Core-Level Absorption Spectroscopy

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.

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.

Exact Two-Component TDDFT with Simple Two-Electron Picture-Change Corrections: X-ray Absorption Spectra Near L- and M-Edges of Four-Component Quality at Two-Component Cost

X-ray absorption spectroscopy (XAS) has gained popularity in recent years as it probes matter with high spatial and elemental sensitivities. However, the theoretical modeling of XAS is a challenging task since XAS spectra feature a fine structure due to scalar (SC) and spin-orbit (SO) relativistic effects, in particular near L and M absorption edges. While full four-component (4c) calculations of XAS are nowadays feasible, there is still interest in developing approximate relativistic methods that enable XAS calculations at the two-component (2c) level while maintaining the accuracy of the parent 4c approach. In this article we present theoretical and numerical insights into two simple yet accurate 2c approaches based on an (extended) atomic mean-field exact two-component Hamiltonian framework, (e)amfX2C, for the calculation of XAS using linear eigenvalue and damped response time-dependent density functional theory (TDDFT). In contrast to the commonly used one-electron X2C (1eX2C) Hamiltonian, both amfX2C and eamfX2C account for the SC and SO two-electron and exchange-correlation picture-change (PC) effects that arise from the X2C transformation. As we demonstrate on L- and M-edge XAS spectra of transition metal and actinide compounds, the absence of PC corrections in the 1eX2C approximation results in a substantial overestimation of SO splittings, whereas (e)amfX2C Hamiltonians reproduce all essential spectral features such as shape, position, and SO splitting of the 4c references in excellent agreement, while offering significant computational savings. Therefore, the (e)amfX2C PC correction models presented here constitute reliable relativistic 2c quantum-chemical approaches for modeling XAS.

Ultrafast X-ray Spectroscopy of Intersystem Crossing in Hexafluoroacetylacetone: Chromophore Photophysics and Spectral Changes in the Face of Electron-Withdrawing Groups

Intersystem crossings between singlet and triplet states represent a crucial relaxation pathway in photochemical processes. Herein, we probe the intersystem crossing in hexafluoro-acetylacetone with ultrafast X-ray transient absorption spectroscopy at the carbon K-edge. We observe the excited state dynamics following excitation with 266 nm UV light to the ¹ππ* (S₂) state with element and site-specificity using a broadband soft X-ray pulse produced by high harmonic generation. These results are compared to X-ray spectra computed from orbital optimized density functional theory methods. It is found that the electron-withdrawing fluorine atoms decongest the X-ray absorption spectrum by enhancing separation between features originating from different carbon atoms. This facilitates the elucidation of structural and electronic dynamics at the chromophore. The evolution of the core-to-valence resonances at the carbon K-edge reveals an ultrafast population transfer between the ¹nπ* (S₁) and ³ππ* (T₁) states on a 1.6 ± 0.4 ps time scale, which is similar to the 1.5 ps time scale earlier observed for acetylacetone [ J. Am. Chem. Soc. 2017, 139, 16576-16583, DOI: 10.1021/jacs.7b07532]. It therefore appears that terminal fluorination has little influence on the intersystem crossing rate of the acetylacetone chromophore. In addition, the significant role of hydrogen-bond opened and twisted rotational isomers is elucidated in the excited state dynamics by comparison of the experimental transient X-ray spectra with theory.

Ultrafast disruptive probing: Simultaneously keeping track of tens of reaction pathways

Ultrafast science depends on different implementations of the well-known pump-probe method. Here, we provide a formal description of ultrafast disruptive probing, a method in which the probe pulse disrupts a transient species that may be a metastable ion or a transient state of matter. Disruptive probing has the advantage of allowing for simultaneous tracking of the yield of tens of different processes. Our presentation includes a numerical model and experimental data on multiple products resulting from the strong-field ionization of two different molecules, partially deuterated methanol and norbornene. The correlated enhancement and depletion signals between all the different fragmentation channels offer comprehensive information on photochemical reaction pathways. In combination with ion imaging and/or coincidence momentum imaging or as complementary to atom-specific probing or ultrafast diffraction methods, disruptive probing is a particularly powerful tool for the study of strong-field laser-matter interactions.

Accurate X-ray Absorption Spectra near L- and M-Edges from Relativistic Four-Component Damped Response Time-Dependent Density Functional Theory

The simulation of X-ray absorption spectra requires both scalar and spin-orbit (SO) relativistic effects to be taken into account, particularly near L- and M-edges where the SO splitting of core p and d orbitals dominates. Four-component Dirac-Coulomb Hamiltonian-based linear damped response time-dependent density functional theory (4c-DR-TDDFT) calculates spectra directly for a selected frequency region while including the relativistic effects variationally, making the method well suited for X-ray applications. In this work, we show that accurate X-ray absorption spectra near L2,3- and M4,5-edges of closed-shell transition metal and actinide compounds with different central atoms, ligands, and oxidation states can be obtained by means of 4c-DR-TDDFT. While the main absorption lines do not change noticeably with the basis set and geometry, the exchange-correlation functional has a strong influence with hybrid functionals performing the best. The energy shift compared to the experiment is shown to depend linearly on the amount of Hartee-Fock exchange with the optimal value being 60% for spectral regions above 1000 eV, providing relative errors below 0.2% and 2% for edge energies and SO splittings, respectively. Finally, the methodology calibrated in this work is used to reproduce the experimental L2,3-edge X-ray absorption spectra of [RuCl2(DMSO)2(Im)2] and [WCl4(PMePh2)2], and resolve the broad bands into separated lines, allowing an interpretation based on ligand field theory and double point groups. These results support 4c-DR-TDDFT as a reliable method for calculating and analyzing X-ray absorption spectra of chemically interesting systems, advance the accuracy of state-of-the art relativistic DFT approaches, and provide a reference for benchmarking more approximate techniques.

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.

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

Time-resolved spectroscopic investigations of light-induced chemical reactions with universal detection capitalize recently on single-photon molecular probing using laser pulses in the extreme ultraviolet or X-ray regimes. Direct and simultaneous mappings of the time-evolving populations of ground-state reactants, Franck-Condon (FC) and transition state regions, excited-state intermediates and conical intersections (CI), and photoproducts in photochemical reactions utilize probe pulses that are broadband and energy-tunable. The limits on temporal resolution are set by the transit- or dwell-time of the photoexcited molecules at specific locations on the potential energy surface, typically ranging from a few femtoseconds to several hundred picoseconds. Femtosecond high-harmonic generation (HHG) meets the stringent demands for a universal spectroscopic probe of large regions of the intramolecular phase-space in unimolecular photochemical reactions. Extreme-ultraviolet and soft X-ray pulses generated in this manner with few-femtosecond or sub-femtosecond durations have enormous bandwidths, allowing the probing of many elements simultaneously through excitation or ionization of core-electrons, creating molecular movies that shed light on entire photochemical pathways. At free electron lasers (FELs), powerful investigations are also possible, recognizing their higher flux and tunability but more limited bandwidths. Femtosecond time-resolved X-ray transient absorption spectroscopy, in particular, is a valuable universal probe of reaction pathways that maps changes via the fingerprint core-to-valence resonances. The particular power of this method over valence-ionization probes lies in its unmatched element and chemical-site specificities. The elements carbon, nitrogen, and oxygen constitute the fundamental building blocks of life; photochemical reactions involving these elements are ubiquitous, diverse, and manifold. However, table-top HHG sources in the "water-window" region (280-550 eV), which encompasses the 1s-absorption edges of carbon (284 eV), nitrogen (410 eV), and oxygen (543 eV), are far from abundant or trivial. Recent breakthroughs in the laboratory have embraced this region by using long driving-wavelength optical parametric amplifiers coupled with differentially pumped high-pressure gas source cells. This has opened avenues to study a host of photochemical reactions in organic molecules using femtosecond time-resolved transient absorption at the carbon K-edge. In this Account, we summarize recent efforts to deploy a table-top carbon K-edge source to obtain crucial chemical insights into ultrafast, ultraviolet-induced chemical reactions involving ring-opening, nonadiabatic excited-state relaxation, bond dissociation and radical formation. The X-ray probe provides a direct spectroscopic viewport into the electronic characters and configurations of the valence electronic states through spectroscopic core-level transitions into the frontier molecular orbitals of the photoexcited molecules, laying fertile ground for the real-time mapping of the evolving valence electronic structure. The profound detail and mechanistic insights emerging from the pioneering experiments at the carbon K-edge are outlined here. Comparisons of the experimental methodology with other techniques employed to study similar reactions are drawn, where applicable and relevant. We show that femtosecond time-resolved X-ray transient absorption spectroscopy blazes a new trail in the study of nonadiabatic molecular dynamics. Despite table-top implementations being largely in their infancy, future chemical applications of the technique will set the stage for widely applicable, universal probes of photoinduced molecular dynamics with unprecedented temporal resolution.

Tracking Ultrafast Bond Dissociation Dynamics at 0.1 Å Resolution by Femtosecond Extreme Ultraviolet Absorption Spectroscopy

Visualizing the real-time dissociation of chemical bonds represents a challenge in the study of ultrafast molecular dynamics due to the simultaneous need for sub-angstrom spatial and femtosecond temporal resolution. Here, we follow the C-I dissociation dynamics of strong-field-ionized 2-iodopropane (2-C₃H₇I) with femtosecond extreme ultraviolet (XUV) absorption spectroscopy. By probing the iodine 4 d core-level absorption, we resolve a continuous XUV spectral shift on the sub-100 fs time scale that accompanies the dissociation of the 2-C₃H₇I⁺ spin-orbit-excited ² E_1/2 state to yield atomic I in the ² P_3/2 state. In combination with ab initio calculations of the C-I distance-dependent XUV transition energy, we reconstruct the temporal evolution of the C-I distance from the Franck-Condon region to the asymptotic region with 10 fs and 0.1 Å resolution. The C-I bond elongation appears to couple to coherent vibrational motion along the HC(CH₃)₂ umbrella mode of the 2-C₃H₇⁺ fragment, whose effect on the I 4 d XUV transition even at C-I distances of 3.5 Å points to the long-range nature of XUV absorption probing. Our results suggest that femtosecond XUV absorption spectroscopy, in combination with ab initio simulations of XUV transition energies, can be used to resolve the ultrafast structural dynamics of large polyatomic molecules.

Towards efficient time-resolved X-ray absorption studies of electron dynamics at photocatalytic interfaces

We present a picosecond time-resolved X-ray absorption spectroscopy (tr-XAS) setup designed for synchrotron-based studies of interfacial photochemical dynamics. The apparatus combines a high power, variable repetition rate picosecond laser system with a time-resolved X-ray fluorescence yield detection technique. Time-tagging of the detected fluorescence signals enables the parallel acquisition of X-ray absorption spectra at a variety of pump-probe delays employing the well-defined time structure of the X-ray pulse trains. The viability of the setup is demonstrated by resolving dynamic changes in the fine structure near the O1s X-ray absorption edge of cuprous oxide (Cu₂O) after photo-excitation with a 355 nm laser pulse. Two distinct responses are detected. A pronounced, quasi-static, reversible change of the Cu₂O O1s X-ray absorption spectrum by up to ∼30% compared to its static line shape corresponds to a redshift of the absorption edge by ∼1 eV. This value is small compared to the 2.2 eV band gap of Cu₂O but in agreement with previously published results. The lifetime of this effect exceeds the laser pulse-to-pulse period of 8 μs, resulting in a quasi-static spectral change that persists as long as the sample is exposed to the laser light, and completely vanishes once the laser is blocked. Additionally, a short-lived response corresponding to a laser-induced shift of the main absorption line by ∼2 eV to lower energies appears within <200 ps and decays with a characteristic timescale of 43 ± 5 ns. Both the picosecond rise and nanosecond decay of this X-ray response are simultaneously captured by making use of a time-tagging approach - highlighting the prospects of the experimental setup for efficient probing of the electronic and structural dynamics in photocatalytic systems on multiple timescales.

Sequential and direct ionic excitation in the strong-field ionization of 1-butene molecules

We study the Strong-Field Ionization (SFI) of the hydrocarbon 1-butene as a function of wavelength using photoion-photoelectron covariance and coincidence spectroscopy. We observe a striking transition in the fragment-associated photoelectron spectra: from a single Above Threshold Ionization (ATI) progression for photon energies less than the cation D0-D1 gap to two ATI progressions for a photon energy greater than this gap. For the first case, electronically excited cations are created by SFI populating the ground cationic state D0, followed by sequential post-ionization excitation. For the second case, direct sub-cycle SFI to the D1 excited cation state contributes significantly. Our experiments access ionization dynamics in a regime where strong-field and resonance-enhanced processes can interplay.

Spin-Orbit State-Selective C-I Dissociation Dynamics of the CH3I+ X̃ Electronic State Induced by Intense Few-Cycle Laser Fields

Studies of ultrafast molecular dynamics induced by intense laser fields can reveal new approaches to manipulating chemical reactions in the strong-field regime. Here, we show that intense few-cycle laser pulses can induce the spin-orbit state-selective C-I dissociation of the iodomethane cation (CH₃I⁺) in the X̃ electronic state. Irradiation of CH₃I by 6 fs laser pulses with peak intensities of 1.9 × 10¹⁴ W/cm² followed by femtosecond extreme ultraviolet probing of the iodine 4d core-level transitions reveals dissociation of the CH₃I⁺ X̃ ²E_1/2 state with a time constant of 0.76 ± 0.16 ps. By contrast, the X̃ ²E_3/2 spin-orbit ground state does not exhibit any appreciable dissociation on the picosecond time scale. The observed spin-orbit state-selective dissociation of the X̃ state is rationalized in terms of the laser-induced coupling to the à state. Our results suggest that the intense-laser control of photodissociation channels can be potentially extended to spin-orbit split states.

Disentangling Intracycle Interferences in Photoelectron Momentum Distributions Using Orthogonal Two-Color Laser Fields

We use orthogonally polarized two-color (OTC) laser pulses to separate quantum paths in the multiphoton ionization of Ar atoms. Our OTC pulses consist of 400 and 800 nm light at a relative intensity ratio of 10∶1. We find a hitherto unobserved interference in the photoelectron momentum distribution, which exhibits a strong dependence on the relative phase of the OTC pulse. Analysis of model calculations reveals that the interference is caused by quantum pathways from nonadjacent quarter cycles.

Elucidating the origins of multimode vibrational coherences of polyatomic molecules induced by intense laser fields

Strong-field laser–molecule interaction forms much of the basis for initiating and probing ultrafast quantum dynamics. Previous studies aimed at elucidating the origins of vibrational coherences induced by intense laser fields have been confined to diatomic molecules. Furthermore, in all cases examined to date, vibrational wave packet motion is found to be induced by R-selective depletion; wave packet motion launched by bond softening, though theoretically predicted, remains hitherto unobserved. Here we employ the exquisite sensitivity of femtosecond extreme ultraviolet absorption spectroscopy to sub-picometer structural changes to observe both bond softening-induced vibrational wave packets, launched by the interaction of intense laser pulses with iodomethane, as well as multimode vibrational motion of the parent ion produced by strong-field ionization. In addition, we show that signatures of coherent vibrational motion in the time-dependent extreme ultraviolet absorption spectra directly furnish vibronic coupling strengths involving core-level transitions, from which geometrical parameters of transient core-excited states are extracted.

Nuclear dynamics of polyatomic molecules involves multiple degrees of freedom and is challenging to explore. Here the authors study the internuclear distance-dependent depletion and bond-softening induced vibrational wavepacket dynamics of CH₃I molecules using femtosecond XUV transient absorption spectroscopy.

Direct observation of ring-opening dynamics in strong-field ionized selenophene using femtosecond inner-shell absorption spectroscopy

Femtosecond extreme ultraviolet transient absorption spectroscopy is used to explore strong-field ionization induced dynamics in selenophene (C₄H₄Se). The dynamics are monitored in real-time from the viewpoint of the Se atom by recording the temporal evolution of element-specific spectral features near the Se 3d inner-shell absorption edge (∼58 eV). The interpretation of the experimental results is supported by first-principles time-dependent density functional theory calculations. The experiments simultaneously capture the instantaneous population of stable molecular ions, the emergence and decay of excited cation states, and the appearance of atomic fragments. The experiments reveal, in particular, insight into the strong-field induced ring-opening dynamics in the selenophene cation, which are traced by the emergence of non-cyclic molecules as well as the liberation of Se⁺ ions within an overall time scale of approximately 170 fs. We propose that both products may be associated with dynamics on the same electronic surfaces but with different degrees of vibrational excitation. The time-dependent inner-shell absorption features provide direct evidence for a complex relaxation mechanism that may be approximated by a two-step model, whereby the initially prepared, excited cyclic cation decays within τ₁ = 80 ± 30 fs into a transient molecular species, which then gives rise to the emergence of bare Se⁺ and ring-open cations within an additional τ₂ = 80 ± 30 fs. The combined experimental and theoretical results suggest a close relationship between σ* excited cation states and the observed ring-opening reactions. The findings demonstrate that the combination of femtosecond time-resolved core-level spectroscopy with ab initio estimates of spectroscopic signatures provide new insights into complex, ultrafast photochemical reactions such as ring-opening dynamics in organic molecules in real-time and with simultaneous sensitivity for electronic and structural rearrangements.

Ultrafast modulation of electronic structure by coherent phonon excitations

Femtosecond x-ray absorption spectroscopy with a laser-driven high-harmonic source is used to map ultrafast changes of x-ray absorption by femtometer-scale coherent phonon displacements. In LiBH4, displacements along an A g phonon mode at 10 THz are induced by impulsive Raman excitation and give rise to oscillatory changes of x-ray absorption at the Li K-edge. Electron density maps from femtosecond x-ray diffraction data show that the electric field of the pump pulse induces a charge transfer from the BH 4 - to neighboring Li+ ions, resulting in a differential Coulomb force that drives lattice vibrations in this virtual transition state.

Shrinking the Synchrotron: Tabletop Extreme Ultraviolet Absorption of Transition-Metal Complexes

We show that the electronic structure of molecular first-row transition-metal complexes can be reliably measured using tabletop high-harmonic XANES at the metal M2,3 edge. Extreme ultraviolet photons in the 50-70 eV energy range probe 3p → 3d transitions, with the same selection rules as soft X-ray L2,3-edge absorption (2p → 3d excitation). Absorption spectra of model complexes are sensitive to the electronic structure of the metal center, and ligand field multiplet simulations match the shapes and peak-to-peak spacings of the experimental spectra. This work establishes high-harmonic spectroscopy as a powerful tool for studying the electronic structure of molecular inorganic, bioinorganic, and organometallic compounds.

Tracking dissociation dynamics of strong-field ionized 1,2-dibromoethane with femtosecond XUV transient absorption spectroscopy

Using femtosecond time-resolved extreme ultraviolet absorption spectroscopy, the dissociation dynamics of the haloalkane 1,2-dibromoethane (DBE) have been explored following strong field ionization by femtosecond near infrared pulses at intensities between 7.5 × 10¹³ and 2.2 × 10¹⁴ W cm⁻².

Two-dimensional attosecond electron wave-packet interferometry

We propose a two-dimensional interferometry based on the electron wave-packet interference by using a cycle-shaped orthogonally polarized two-color laser field. With such a method, the subcycle and intercycle interferences can be disentangled into different directions in the measured photoelectron momentum spectra. The Coulomb influence can be minimized and the overlapping of interference fringes with the complicated low-energy structures can be avoided as well. The contributions of the excitation effect and the long-range Coulomb potential can be traced in the Fourier domain of the photoelectron distribution. Because of these advantages, precise information on valence electron dynamics of atoms or molecules with attosecond temporal resolution and additional spatial information with angstrom resolution can be obtained with the two-dimensional electron wave-packet interferometry.

Broadband extreme ultraviolet probing of transient gratings in vanadium dioxide

Nonlinear spectroscopy in the extreme ultraviolet (EUV) and soft x-ray spectral range offers the opportunity for element selective probing of ultrafast dynamics using core-valence transitions (Mukamel et al., Acc. Chem. Res. 42, 553 (2009)). We demonstrate a step on this path showing core-valence sensitivity in transient grating spectroscopy with EUV probing. We study the optically induced insulator-to-metal transition (IMT) of a VO(2) film with EUV diffraction from the optically excited sample. The VO(2) exhibits a change in the 3p-3d resonance of V accompanied by an acoustic response. Due to the broadband probing we are able to separate the two features.

Subpicosecond and Sub-Angstrom Time and Space Studies by Means of Light, X-ray, and Electron Interaction with Matter

This Perspective article considers an experimental system that consists of ultrafast optical, electron, and X-ray time-resolved components. These techniques are used simultaneously on the same sample to study, in real time, the events that occur immediately upon disturbance with an ultrafast optical pulse. Excited states and metastable species are generated on the surface, and the electrical and mechanical waves propagating through the sample are recorded with subpicosecond and sub-Angstrom resolution. The characteristic of each technique is briefly described as a means of introducing the experimental system that intergrates these techniques. The processes evolved after femtosecond excitation of a Au single crystal have been monitored by these techniques. The data presented show changes with a resolution of 0.3 ± 0.1 ps in optical thermoreflectance, 1.0 ± 0.2 ps in electron Bragg diffraction, and 0.6 ± 0.1 ps in X-ray diffraction intensity accompanying shift and broadening.